Chapter 6.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 6 - Linear Model Selection and Regularization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- [Model Selection Methods](https://xavierbourretsicotte.github.io/subset_selection.html#Comparing-models:-AIC,-BIC,-Mallows'CP)\n",
    "    - [Best Subset Selection](#subset) \n",
    "    - [Forward Stepwise Selection](#forward) \n",
    "    - [Comparing models: AIC, BIC, Mallows'CP](#compare)\n",
    "- [Lab 2: Ridge Regression](#6.6.1-Ridge-Regression)\n",
    "- [Lab 2: The Lasso](#6.6.2-The-Lasso)\n",
    "- [Lab 3: Principal Components Regression](#6.7.1-Principal-Components-Regression)\n",
    "- [Lab 3: Partial Least Squares](#6.7.2-Partial-Least-Squares)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# %load ../standard_import.txt\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "from sklearn.preprocessing import scale \n",
    "from sklearn import model_selection\n",
    "from sklearn.linear_model import LinearRegression, Ridge, RidgeCV, Lasso, LassoCV\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.cross_decomposition import PLSRegression\n",
    "from sklearn.model_selection import KFold, cross_val_score\n",
    "from sklearn.metrics import mean_squared_error\n",
    "\n",
    "import itertools\n",
    "import time\n",
    "import statsmodels.api as sm\n",
    "#Importing tqdm for the progress bar\n",
    "from tqdm import tnrange, tqdm_notebook\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "%matplotlib inline\n",
    "plt.style.use('seaborn-white')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Model Selection Methods"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dataset\n",
    "The credit dataset is a use case for linear regression where some predictors are qualitative."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Income</th>\n",
       "      <th>Limit</th>\n",
       "      <th>Rating</th>\n",
       "      <th>Cards</th>\n",
       "      <th>Age</th>\n",
       "      <th>Education</th>\n",
       "      <th>Gender</th>\n",
       "      <th>Student</th>\n",
       "      <th>Married</th>\n",
       "      <th>Ethnicity</th>\n",
       "      <th>Balance</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>14.891</td>\n",
       "      <td>3606</td>\n",
       "      <td>283</td>\n",
       "      <td>2</td>\n",
       "      <td>34</td>\n",
       "      <td>11</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Caucasian</td>\n",
       "      <td>333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>106.025</td>\n",
       "      <td>6645</td>\n",
       "      <td>483</td>\n",
       "      <td>3</td>\n",
       "      <td>82</td>\n",
       "      <td>15</td>\n",
       "      <td>Female</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Asian</td>\n",
       "      <td>903</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>104.593</td>\n",
       "      <td>7075</td>\n",
       "      <td>514</td>\n",
       "      <td>4</td>\n",
       "      <td>71</td>\n",
       "      <td>11</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>Asian</td>\n",
       "      <td>580</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      "text/plain": [
       "    Income  Limit  Rating  Cards  Age  Education  Gender Student Married  \\\n",
       "0   14.891   3606     283      2   34         11    Male      No     Yes   \n",
       "1  106.025   6645     483      3   82         15  Female     Yes     Yes   \n",
       "2  104.593   7075     514      4   71         11    Male      No      No   \n",
       "\n",
       "   Ethnicity  Balance  \n",
       "0  Caucasian      333  \n",
       "1      Asian      903  \n",
       "2      Asian      580  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "credit = pd.read_csv('Data/Credit.csv', usecols=list(range(1,12)))\n",
    "credit.head(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Encoding qualitative data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Income</th>\n",
       "      <th>Limit</th>\n",
       "      <th>Rating</th>\n",
       "      <th>Cards</th>\n",
       "      <th>Age</th>\n",
       "      <th>Education</th>\n",
       "      <th>Balance</th>\n",
       "      <th>Gender_Female</th>\n",
       "      <th>Student_Yes</th>\n",
       "      <th>Married_Yes</th>\n",
       "      <th>Ethnicity_Asian</th>\n",
       "      <th>Ethnicity_Caucasian</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>14.891</td>\n",
       "      <td>3606</td>\n",
       "      <td>283</td>\n",
       "      <td>2</td>\n",
       "      <td>34</td>\n",
       "      <td>11</td>\n",
       "      <td>333</td>\n",
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       "      <td>0</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>106.025</td>\n",
       "      <td>6645</td>\n",
       "      <td>483</td>\n",
       "      <td>3</td>\n",
       "      <td>82</td>\n",
       "      <td>15</td>\n",
       "      <td>903</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>104.593</td>\n",
       "      <td>7075</td>\n",
       "      <td>514</td>\n",
       "      <td>4</td>\n",
       "      <td>71</td>\n",
       "      <td>11</td>\n",
       "      <td>580</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
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       "    Income  Limit  Rating  Cards  Age  Education  Balance  Gender_Female  \\\n",
       "0   14.891   3606     283      2   34         11      333              0   \n",
       "1  106.025   6645     483      3   82         15      903              1   \n",
       "2  104.593   7075     514      4   71         11      580              0   \n",
       "\n",
       "   Student_Yes  Married_Yes  Ethnicity_Asian  Ethnicity_Caucasian  \n",
       "0            0            1                0                    1  \n",
       "1            1            1                1                    0  \n",
       "2            0            0                1                    0  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "credit = pd.get_dummies(credit, columns = ['Gender', 'Student','Married','Ethnicity'],drop_first = True)\n",
    "credit.head(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='subset'></a>\n",
    "## Best Subset Selection\n",
    "To perform best selection, we fit separate models for each possible combination of the n predictors and then select the best subset. That is we fit:\n",
    "\n",
    "- All models that contains exactly one predictor\n",
    "- All models that contain 2 predictors at the second step\n",
    "- All models that contain 3 predictors at the thrid step\n",
    "- ...\n",
    "- Until reaching the end point where all n predictors are included in the model\n",
    "\n",
    "This results in 2n possibilities as this is a power set problem. In our case there are 2^11=2048 possible combinations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Helper function for fitting linear regression (Sklearn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fit_linear_reg(X,Y):\n",
    "    #Fit linear regression model and return RSS and R squared values\n",
    "    model_k = LinearRegression(fit_intercept = True)\n",
    "    model_k.fit(X,Y)\n",
    "    RSS = mean_squared_error(Y,model_k.predict(X)) * len(Y)\n",
    "    R_squared = model_k.score(X,Y)\n",
    "    return RSS, R_squared"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementing Best subset selection (using itertools.combinations)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Initialization variables\n",
    "Y = credit.Balance\n",
    "X = credit.drop(columns = 'Balance', axis = 1)\n",
    "k = 11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
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       "      <th></th>\n",
       "      <th>Income</th>\n",
       "      <th>Limit</th>\n",
       "      <th>Rating</th>\n",
       "      <th>Cards</th>\n",
       "      <th>Age</th>\n",
       "      <th>Education</th>\n",
       "      <th>Gender_Female</th>\n",
       "      <th>Student_Yes</th>\n",
       "      <th>Married_Yes</th>\n",
       "      <th>Ethnicity_Asian</th>\n",
       "      <th>Ethnicity_Caucasian</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
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       "      <th>0</th>\n",
       "      <td>14.891</td>\n",
       "      <td>3606</td>\n",
       "      <td>283</td>\n",
       "      <td>2</td>\n",
       "      <td>34</td>\n",
       "      <td>11</td>\n",
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       "      <td>0</td>\n",
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       "      <th>1</th>\n",
       "      <td>106.025</td>\n",
       "      <td>6645</td>\n",
       "      <td>483</td>\n",
       "      <td>3</td>\n",
       "      <td>82</td>\n",
       "      <td>15</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>104.593</td>\n",
       "      <td>7075</td>\n",
       "      <td>514</td>\n",
       "      <td>4</td>\n",
       "      <td>71</td>\n",
       "      <td>11</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>148.924</td>\n",
       "      <td>9504</td>\n",
       "      <td>681</td>\n",
       "      <td>3</td>\n",
       "      <td>36</td>\n",
       "      <td>11</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>55.882</td>\n",
       "      <td>4897</td>\n",
       "      <td>357</td>\n",
       "      <td>2</td>\n",
       "      <td>68</td>\n",
       "      <td>16</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>80.180</td>\n",
       "      <td>8047</td>\n",
       "      <td>569</td>\n",
       "      <td>4</td>\n",
       "      <td>77</td>\n",
       "      <td>10</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>20.996</td>\n",
       "      <td>3388</td>\n",
       "      <td>259</td>\n",
       "      <td>2</td>\n",
       "      <td>37</td>\n",
       "      <td>12</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>71.408</td>\n",
       "      <td>7114</td>\n",
       "      <td>512</td>\n",
       "      <td>2</td>\n",
       "      <td>87</td>\n",
       "      <td>9</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>15.125</td>\n",
       "      <td>3300</td>\n",
       "      <td>266</td>\n",
       "      <td>5</td>\n",
       "      <td>66</td>\n",
       "      <td>13</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>71.061</td>\n",
       "      <td>6819</td>\n",
       "      <td>491</td>\n",
       "      <td>3</td>\n",
       "      <td>41</td>\n",
       "      <td>19</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>63.095</td>\n",
       "      <td>8117</td>\n",
       "      <td>589</td>\n",
       "      <td>4</td>\n",
       "      <td>30</td>\n",
       "      <td>14</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>15.045</td>\n",
       "      <td>1311</td>\n",
       "      <td>138</td>\n",
       "      <td>3</td>\n",
       "      <td>64</td>\n",
       "      <td>16</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>80.616</td>\n",
       "      <td>5308</td>\n",
       "      <td>394</td>\n",
       "      <td>1</td>\n",
       "      <td>57</td>\n",
       "      <td>7</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>43.682</td>\n",
       "      <td>6922</td>\n",
       "      <td>511</td>\n",
       "      <td>1</td>\n",
       "      <td>49</td>\n",
       "      <td>9</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>19.144</td>\n",
       "      <td>3291</td>\n",
       "      <td>269</td>\n",
       "      <td>2</td>\n",
       "      <td>75</td>\n",
       "      <td>13</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>20.089</td>\n",
       "      <td>2525</td>\n",
       "      <td>200</td>\n",
       "      <td>3</td>\n",
       "      <td>57</td>\n",
       "      <td>15</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>53.598</td>\n",
       "      <td>3714</td>\n",
       "      <td>286</td>\n",
       "      <td>3</td>\n",
       "      <td>73</td>\n",
       "      <td>17</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>36.496</td>\n",
       "      <td>4378</td>\n",
       "      <td>339</td>\n",
       "      <td>3</td>\n",
       "      <td>69</td>\n",
       "      <td>15</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>49.570</td>\n",
       "      <td>6384</td>\n",
       "      <td>448</td>\n",
       "      <td>1</td>\n",
       "      <td>28</td>\n",
       "      <td>9</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>42.079</td>\n",
       "      <td>6626</td>\n",
       "      <td>479</td>\n",
       "      <td>2</td>\n",
       "      <td>44</td>\n",
       "      <td>9</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>17.700</td>\n",
       "      <td>2860</td>\n",
       "      <td>235</td>\n",
       "      <td>4</td>\n",
       "      <td>63</td>\n",
       "      <td>16</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>37.348</td>\n",
       "      <td>6378</td>\n",
       "      <td>458</td>\n",
       "      <td>1</td>\n",
       "      <td>72</td>\n",
       "      <td>17</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>20.103</td>\n",
       "      <td>2631</td>\n",
       "      <td>213</td>\n",
       "      <td>3</td>\n",
       "      <td>61</td>\n",
       "      <td>10</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>64.027</td>\n",
       "      <td>5179</td>\n",
       "      <td>398</td>\n",
       "      <td>5</td>\n",
       "      <td>48</td>\n",
       "      <td>8</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>10.742</td>\n",
       "      <td>1757</td>\n",
       "      <td>156</td>\n",
       "      <td>3</td>\n",
       "      <td>57</td>\n",
       "      <td>15</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>14.090</td>\n",
       "      <td>4323</td>\n",
       "      <td>326</td>\n",
       "      <td>5</td>\n",
       "      <td>25</td>\n",
       "      <td>16</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>42.471</td>\n",
       "      <td>3625</td>\n",
       "      <td>289</td>\n",
       "      <td>6</td>\n",
       "      <td>44</td>\n",
       "      <td>12</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>32.793</td>\n",
       "      <td>4534</td>\n",
       "      <td>333</td>\n",
       "      <td>2</td>\n",
       "      <td>44</td>\n",
       "      <td>16</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>186.634</td>\n",
       "      <td>13414</td>\n",
       "      <td>949</td>\n",
       "      <td>2</td>\n",
       "      <td>41</td>\n",
       "      <td>14</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>26.813</td>\n",
       "      <td>5611</td>\n",
       "      <td>411</td>\n",
       "      <td>4</td>\n",
       "      <td>55</td>\n",
       "      <td>16</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>370</th>\n",
       "      <td>35.610</td>\n",
       "      <td>6135</td>\n",
       "      <td>466</td>\n",
       "      <td>4</td>\n",
       "      <td>40</td>\n",
       "      <td>12</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>371</th>\n",
       "      <td>39.116</td>\n",
       "      <td>2150</td>\n",
       "      <td>173</td>\n",
       "      <td>4</td>\n",
       "      <td>75</td>\n",
       "      <td>15</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>372</th>\n",
       "      <td>19.782</td>\n",
       "      <td>3782</td>\n",
       "      <td>293</td>\n",
       "      <td>2</td>\n",
       "      <td>46</td>\n",
       "      <td>16</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>373</th>\n",
       "      <td>55.412</td>\n",
       "      <td>5354</td>\n",
       "      <td>383</td>\n",
       "      <td>2</td>\n",
       "      <td>37</td>\n",
       "      <td>16</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>374</th>\n",
       "      <td>29.400</td>\n",
       "      <td>4840</td>\n",
       "      <td>368</td>\n",
       "      <td>3</td>\n",
       "      <td>76</td>\n",
       "      <td>18</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>375</th>\n",
       "      <td>20.974</td>\n",
       "      <td>5673</td>\n",
       "      <td>413</td>\n",
       "      <td>5</td>\n",
       "      <td>44</td>\n",
       "      <td>16</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>376</th>\n",
       "      <td>87.625</td>\n",
       "      <td>7167</td>\n",
       "      <td>515</td>\n",
       "      <td>2</td>\n",
       "      <td>46</td>\n",
       "      <td>10</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>377</th>\n",
       "      <td>28.144</td>\n",
       "      <td>1567</td>\n",
       "      <td>142</td>\n",
       "      <td>3</td>\n",
       "      <td>51</td>\n",
       "      <td>10</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>378</th>\n",
       "      <td>19.349</td>\n",
       "      <td>4941</td>\n",
       "      <td>366</td>\n",
       "      <td>1</td>\n",
       "      <td>33</td>\n",
       "      <td>19</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>379</th>\n",
       "      <td>53.308</td>\n",
       "      <td>2860</td>\n",
       "      <td>214</td>\n",
       "      <td>1</td>\n",
       "      <td>84</td>\n",
       "      <td>10</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>380</th>\n",
       "      <td>115.123</td>\n",
       "      <td>7760</td>\n",
       "      <td>538</td>\n",
       "      <td>3</td>\n",
       "      <td>83</td>\n",
       "      <td>14</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>381</th>\n",
       "      <td>101.788</td>\n",
       "      <td>8029</td>\n",
       "      <td>574</td>\n",
       "      <td>2</td>\n",
       "      <td>84</td>\n",
       "      <td>11</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>382</th>\n",
       "      <td>24.824</td>\n",
       "      <td>5495</td>\n",
       "      <td>409</td>\n",
       "      <td>1</td>\n",
       "      <td>33</td>\n",
       "      <td>9</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>383</th>\n",
       "      <td>14.292</td>\n",
       "      <td>3274</td>\n",
       "      <td>282</td>\n",
       "      <td>9</td>\n",
       "      <td>64</td>\n",
       "      <td>9</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>384</th>\n",
       "      <td>20.088</td>\n",
       "      <td>1870</td>\n",
       "      <td>180</td>\n",
       "      <td>3</td>\n",
       "      <td>76</td>\n",
       "      <td>16</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>385</th>\n",
       "      <td>26.400</td>\n",
       "      <td>5640</td>\n",
       "      <td>398</td>\n",
       "      <td>3</td>\n",
       "      <td>58</td>\n",
       "      <td>15</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>386</th>\n",
       "      <td>19.253</td>\n",
       "      <td>3683</td>\n",
       "      <td>287</td>\n",
       "      <td>4</td>\n",
       "      <td>57</td>\n",
       "      <td>10</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>387</th>\n",
       "      <td>16.529</td>\n",
       "      <td>1357</td>\n",
       "      <td>126</td>\n",
       "      <td>3</td>\n",
       "      <td>62</td>\n",
       "      <td>9</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>388</th>\n",
       "      <td>37.878</td>\n",
       "      <td>6827</td>\n",
       "      <td>482</td>\n",
       "      <td>2</td>\n",
       "      <td>80</td>\n",
       "      <td>13</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>389</th>\n",
       "      <td>83.948</td>\n",
       "      <td>7100</td>\n",
       "      <td>503</td>\n",
       "      <td>2</td>\n",
       "      <td>44</td>\n",
       "      <td>18</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>390</th>\n",
       "      <td>135.118</td>\n",
       "      <td>10578</td>\n",
       "      <td>747</td>\n",
       "      <td>3</td>\n",
       "      <td>81</td>\n",
       "      <td>15</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>391</th>\n",
       "      <td>73.327</td>\n",
       "      <td>6555</td>\n",
       "      <td>472</td>\n",
       "      <td>2</td>\n",
       "      <td>43</td>\n",
       "      <td>15</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>392</th>\n",
       "      <td>25.974</td>\n",
       "      <td>2308</td>\n",
       "      <td>196</td>\n",
       "      <td>2</td>\n",
       "      <td>24</td>\n",
       "      <td>10</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>393</th>\n",
       "      <td>17.316</td>\n",
       "      <td>1335</td>\n",
       "      <td>138</td>\n",
       "      <td>2</td>\n",
       "      <td>65</td>\n",
       "      <td>13</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>394</th>\n",
       "      <td>49.794</td>\n",
       "      <td>5758</td>\n",
       "      <td>410</td>\n",
       "      <td>4</td>\n",
       "      <td>40</td>\n",
       "      <td>8</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>395</th>\n",
       "      <td>12.096</td>\n",
       "      <td>4100</td>\n",
       "      <td>307</td>\n",
       "      <td>3</td>\n",
       "      <td>32</td>\n",
       "      <td>13</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>396</th>\n",
       "      <td>13.364</td>\n",
       "      <td>3838</td>\n",
       "      <td>296</td>\n",
       "      <td>5</td>\n",
       "      <td>65</td>\n",
       "      <td>17</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>397</th>\n",
       "      <td>57.872</td>\n",
       "      <td>4171</td>\n",
       "      <td>321</td>\n",
       "      <td>5</td>\n",
       "      <td>67</td>\n",
       "      <td>12</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>398</th>\n",
       "      <td>37.728</td>\n",
       "      <td>2525</td>\n",
       "      <td>192</td>\n",
       "      <td>1</td>\n",
       "      <td>44</td>\n",
       "      <td>13</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>399</th>\n",
       "      <td>18.701</td>\n",
       "      <td>5524</td>\n",
       "      <td>415</td>\n",
       "      <td>5</td>\n",
       "      <td>64</td>\n",
       "      <td>7</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>400 rows × 11 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      Income  Limit  Rating  Cards  Age  Education  Gender_Female  \\\n",
       "0     14.891   3606     283      2   34         11              0   \n",
       "1    106.025   6645     483      3   82         15              1   \n",
       "2    104.593   7075     514      4   71         11              0   \n",
       "3    148.924   9504     681      3   36         11              1   \n",
       "4     55.882   4897     357      2   68         16              0   \n",
       "5     80.180   8047     569      4   77         10              0   \n",
       "6     20.996   3388     259      2   37         12              1   \n",
       "7     71.408   7114     512      2   87          9              0   \n",
       "8     15.125   3300     266      5   66         13              1   \n",
       "9     71.061   6819     491      3   41         19              1   \n",
       "10    63.095   8117     589      4   30         14              0   \n",
       "11    15.045   1311     138      3   64         16              0   \n",
       "12    80.616   5308     394      1   57          7              1   \n",
       "13    43.682   6922     511      1   49          9              0   \n",
       "14    19.144   3291     269      2   75         13              1   \n",
       "15    20.089   2525     200      3   57         15              1   \n",
       "16    53.598   3714     286      3   73         17              1   \n",
       "17    36.496   4378     339      3   69         15              1   \n",
       "18    49.570   6384     448      1   28          9              1   \n",
       "19    42.079   6626     479      2   44          9              0   \n",
       "20    17.700   2860     235      4   63         16              1   \n",
       "21    37.348   6378     458      1   72         17              1   \n",
       "22    20.103   2631     213      3   61         10              0   \n",
       "23    64.027   5179     398      5   48          8              0   \n",
       "24    10.742   1757     156      3   57         15              1   \n",
       "25    14.090   4323     326      5   25         16              1   \n",
       "26    42.471   3625     289      6   44         12              1   \n",
       "27    32.793   4534     333      2   44         16              0   \n",
       "28   186.634  13414     949      2   41         14              1   \n",
       "29    26.813   5611     411      4   55         16              1   \n",
       "..       ...    ...     ...    ...  ...        ...            ...   \n",
       "370   35.610   6135     466      4   40         12              0   \n",
       "371   39.116   2150     173      4   75         15              0   \n",
       "372   19.782   3782     293      2   46         16              1   \n",
       "373   55.412   5354     383      2   37         16              1   \n",
       "374   29.400   4840     368      3   76         18              1   \n",
       "375   20.974   5673     413      5   44         16              1   \n",
       "376   87.625   7167     515      2   46         10              1   \n",
       "377   28.144   1567     142      3   51         10              0   \n",
       "378   19.349   4941     366      1   33         19              0   \n",
       "379   53.308   2860     214      1   84         10              0   \n",
       "380  115.123   7760     538      3   83         14              1   \n",
       "381  101.788   8029     574      2   84         11              0   \n",
       "382   24.824   5495     409      1   33          9              0   \n",
       "383   14.292   3274     282      9   64          9              0   \n",
       "384   20.088   1870     180      3   76         16              0   \n",
       "385   26.400   5640     398      3   58         15              1   \n",
       "386   19.253   3683     287      4   57         10              0   \n",
       "387   16.529   1357     126      3   62          9              0   \n",
       "388   37.878   6827     482      2   80         13              1   \n",
       "389   83.948   7100     503      2   44         18              0   \n",
       "390  135.118  10578     747      3   81         15              1   \n",
       "391   73.327   6555     472      2   43         15              1   \n",
       "392   25.974   2308     196      2   24         10              0   \n",
       "393   17.316   1335     138      2   65         13              0   \n",
       "394   49.794   5758     410      4   40          8              0   \n",
       "395   12.096   4100     307      3   32         13              0   \n",
       "396   13.364   3838     296      5   65         17              0   \n",
       "397   57.872   4171     321      5   67         12              1   \n",
       "398   37.728   2525     192      1   44         13              0   \n",
       "399   18.701   5524     415      5   64          7              1   \n",
       "\n",
       "     Student_Yes  Married_Yes  Ethnicity_Asian  Ethnicity_Caucasian  \n",
       "0              0            1                0                    1  \n",
       "1              1            1                1                    0  \n",
       "2              0            0                1                    0  \n",
       "3              0            0                1                    0  \n",
       "4              0            1                0                    1  \n",
       "5              0            0                0                    1  \n",
       "6              0            0                0                    0  \n",
       "7              0            0                1                    0  \n",
       "8              0            0                0                    1  \n",
       "9              1            1                0                    0  \n",
       "10             0            1                0                    1  \n",
       "11             0            0                0                    1  \n",
       "12             0            1                1                    0  \n",
       "13             0            1                0                    1  \n",
       "14             0            0                0                    0  \n",
       "15             0            1                0                    0  \n",
       "16             0            1                0                    0  \n",
       "17             0            1                1                    0  \n",
       "18             0            1                1                    0  \n",
       "19             0            0                1                    0  \n",
       "20             0            0                1                    0  \n",
       "21             0            0                0                    1  \n",
       "22             0            1                0                    0  \n",
       "23             0            1                0                    0  \n",
       "24             0            0                0                    1  \n",
       "25             0            1                0                    0  \n",
       "26             1            0                0                    1  \n",
       "27             0            0                0                    0  \n",
       "28             0            1                0                    0  \n",
       "29             0            0                0                    1  \n",
       "..           ...          ...              ...                  ...  \n",
       "370            0            0                0                    1  \n",
       "371            0            0                0                    1  \n",
       "372            1            0                0                    1  \n",
       "373            1            1                0                    1  \n",
       "374            0            1                0                    1  \n",
       "375            0            1                0                    1  \n",
       "376            0            0                0                    0  \n",
       "377            0            1                0                    1  \n",
       "378            0            1                0                    1  \n",
       "379            0            1                0                    1  \n",
       "380            0            0                0                    0  \n",
       "381            0            1                0                    1  \n",
       "382            1            0                0                    1  \n",
       "383            0            1                0                    1  \n",
       "384            0            0                0                    0  \n",
       "385            0            0                1                    0  \n",
       "386            0            0                0                    0  \n",
       "387            0            0                1                    0  \n",
       "388            0            0                0                    1  \n",
       "389            0            0                0                    1  \n",
       "390            0            1                1                    0  \n",
       "391            0            0                0                    1  \n",
       "392            0            0                1                    0  \n",
       "393            0            0                0                    0  \n",
       "394            0            0                0                    1  \n",
       "395            0            1                0                    1  \n",
       "396            0            0                0                    0  \n",
       "397            0            1                0                    1  \n",
       "398            0            1                0                    1  \n",
       "399            0            0                1                    0  \n",
       "\n",
       "[400 rows x 11 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(X.columns) + 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "9e05c6e202e848fdabc3756e541f48e8",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, description='Loop...', max=11.0, style=ProgressStyle(description_width…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Loop...:   0%|<bar/>| 0/11 [00:00<?, ?it/s]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tnrange(1,len(X.columns) + 1, desc = 'Loop...')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "c9d64872097142d7891538f8d93c77d6",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, description='Loop...', max=11.0, style=ProgressStyle(description_width…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "for k in tnrange(1,len(X.columns) + 1, desc = 'Loop...'):\n",
    "    for combo in itertools.combinations(X.columns, k):\n",
    "        ; #print(combo)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "2107b6c77f1b4b369d6e950ae8ce1ed5",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, description='Loop...', max=11.0, style=ProgressStyle(description_width…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>numb_features</th>\n",
       "      <th>RSS</th>\n",
       "      <th>R_squared</th>\n",
       "      <th>features</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>6.620874e+07</td>\n",
       "      <td>0.214977</td>\n",
       "      <td>(Income,)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>2.171566e+07</td>\n",
       "      <td>0.742522</td>\n",
       "      <td>(Limit,)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>2.143512e+07</td>\n",
       "      <td>0.745848</td>\n",
       "      <td>(Rating,)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>8.370950e+07</td>\n",
       "      <td>0.007475</td>\n",
       "      <td>(Cards,)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>8.433963e+07</td>\n",
       "      <td>0.000003</td>\n",
       "      <td>(Age,)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1</td>\n",
       "      <td>8.433443e+07</td>\n",
       "      <td>0.000065</td>\n",
       "      <td>(Education,)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1</td>\n",
       "      <td>8.430102e+07</td>\n",
       "      <td>0.000461</td>\n",
       "      <td>(Gender_Female,)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1</td>\n",
       "      <td>7.868154e+07</td>\n",
       "      <td>0.067090</td>\n",
       "      <td>(Student_Yes,)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1</td>\n",
       "      <td>8.433720e+07</td>\n",
       "      <td>0.000032</td>\n",
       "      <td>(Married_Yes,)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1</td>\n",
       "      <td>8.433179e+07</td>\n",
       "      <td>0.000096</td>\n",
       "      <td>(Ethnicity_Asian,)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1</td>\n",
       "      <td>8.433900e+07</td>\n",
       "      <td>0.000011</td>\n",
       "      <td>(Ethnicity_Caucasian,)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>2</td>\n",
       "      <td>1.087083e+07</td>\n",
       "      <td>0.871107</td>\n",
       "      <td>(Income, Limit)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>2</td>\n",
       "      <td>1.053254e+07</td>\n",
       "      <td>0.875118</td>\n",
       "      <td>(Income, Rating)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>2</td>\n",
       "      <td>6.544847e+07</td>\n",
       "      <td>0.223992</td>\n",
       "      <td>(Income, Cards)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>2</td>\n",
       "      <td>6.565932e+07</td>\n",
       "      <td>0.221492</td>\n",
       "      <td>(Income, Age)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>2</td>\n",
       "      <td>6.620682e+07</td>\n",
       "      <td>0.215000</td>\n",
       "      <td>(Income, Education)</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    numb_features           RSS  R_squared                features\n",
       "0               1  6.620874e+07   0.214977               (Income,)\n",
       "1               1  2.171566e+07   0.742522                (Limit,)\n",
       "2               1  2.143512e+07   0.745848               (Rating,)\n",
       "3               1  8.370950e+07   0.007475                (Cards,)\n",
       "4               1  8.433963e+07   0.000003                  (Age,)\n",
       "5               1  8.433443e+07   0.000065            (Education,)\n",
       "6               1  8.430102e+07   0.000461        (Gender_Female,)\n",
       "7               1  7.868154e+07   0.067090          (Student_Yes,)\n",
       "8               1  8.433720e+07   0.000032          (Married_Yes,)\n",
       "9               1  8.433179e+07   0.000096      (Ethnicity_Asian,)\n",
       "10              1  8.433900e+07   0.000011  (Ethnicity_Caucasian,)\n",
       "11              2  1.087083e+07   0.871107         (Income, Limit)\n",
       "12              2  1.053254e+07   0.875118        (Income, Rating)\n",
       "13              2  6.544847e+07   0.223992         (Income, Cards)\n",
       "14              2  6.565932e+07   0.221492           (Income, Age)\n",
       "15              2  6.620682e+07   0.215000     (Income, Education)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RSS_list, R_squared_list, feature_list = [],[], []\n",
    "numb_features = []\n",
    "\n",
    "#Looping over k = 1 to k = 11 features in X\n",
    "# tqdm.tnrange : progress bar\n",
    "for k in tnrange(1,len(X.columns) + 1, desc = 'Loop...'):\n",
    "\n",
    "    #Looping over all possible combinations: from 11 choose k\n",
    "    for combo in itertools.combinations(X.columns,k):\n",
    "        tmp_result = fit_linear_reg(X[list(combo)],Y)   #Store temp result \n",
    "        RSS_list.append(tmp_result[0])                  #Append lists\n",
    "        R_squared_list.append(tmp_result[1])\n",
    "        feature_list.append(combo)\n",
    "        numb_features.append(len(combo))   \n",
    "\n",
    "#Store in DataFrame\n",
    "df = pd.DataFrame({'numb_features': numb_features,'RSS': RSS_list, 'R_squared':R_squared_list,'features':feature_list})\n",
    "df.head(16)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Finding the best subsets for each number of features\n",
    "Using the smallest RSS value, or the largest R_squared value\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.groupby.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      height\n",
      "name        \n",
      "a        200\n",
      "b        300\n"
     ]
    }
   ],
   "source": [
    "print(pd.DataFrame({'name':['a','b','a','b'], 'height':[100,200,300,400]}).groupby('name').mean())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   height\n",
      "0     400\n",
      "1     600\n",
      "2     400\n",
      "3     600\n"
     ]
    }
   ],
   "source": [
    "print(pd.DataFrame({'name':['a','b','a','b'], 'height':[100,200,300,400]}).groupby('name').transform('sum'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((2047, 4),       numb_features           RSS  R_squared  \\\n",
       " 0                 1  6.620874e+07   0.214977   \n",
       " 1                 1  2.171566e+07   0.742522   \n",
       " 2                 1  2.143512e+07   0.745848   \n",
       " 3                 1  8.370950e+07   0.007475   \n",
       " 4                 1  8.433963e+07   0.000003   \n",
       " 5                 1  8.433443e+07   0.000065   \n",
       " 6                 1  8.430102e+07   0.000461   \n",
       " 7                 1  7.868154e+07   0.067090   \n",
       " 8                 1  8.433720e+07   0.000032   \n",
       " 9                 1  8.433179e+07   0.000096   \n",
       " 10                1  8.433900e+07   0.000011   \n",
       " 11                2  1.087083e+07   0.871107   \n",
       " 12                2  1.053254e+07   0.875118   \n",
       " 13                2  6.544847e+07   0.223992   \n",
       " 14                2  6.565932e+07   0.221492   \n",
       " 15                2  6.620682e+07   0.215000   \n",
       " 16                2  6.614972e+07   0.215677   \n",
       " 17                2  6.093905e+07   0.277459   \n",
       " 18                2  6.616711e+07   0.215471   \n",
       " 19                2  6.620845e+07   0.214981   \n",
       " 20                2  6.620586e+07   0.215011   \n",
       " 21                2  2.142716e+07   0.745943   \n",
       " 22                2  2.120720e+07   0.748551   \n",
       " 23                2  2.109859e+07   0.749839   \n",
       " 24                2  2.170303e+07   0.742672   \n",
       " 25                2  2.170056e+07   0.742701   \n",
       " 26                2  1.582835e+07   0.812327   \n",
       " 27                2  2.162638e+07   0.743581   \n",
       " 28                2  2.168790e+07   0.742851   \n",
       " 29                2  2.171562e+07   0.742523   \n",
       " ...             ...           ...        ...   \n",
       " 2017              9  4.141050e+06   0.950900   \n",
       " 2018              9  4.138778e+06   0.950927   \n",
       " 2019              9  1.022597e+07   0.878753   \n",
       " 2020              9  4.129171e+06   0.951041   \n",
       " 2021              9  4.118335e+06   0.951170   \n",
       " 2022              9  4.164275e+06   0.950625   \n",
       " 2023              9  4.129351e+06   0.951039   \n",
       " 2024              9  5.950071e+07   0.294513   \n",
       " 2025              9  1.463967e+07   0.826421   \n",
       " 2026              9  1.462615e+07   0.826581   \n",
       " 2027              9  1.464801e+07   0.826322   \n",
       " 2028              9  2.027102e+07   0.759651   \n",
       " 2029              9  1.461802e+07   0.826677   \n",
       " 2030              9  1.461790e+07   0.826679   \n",
       " 2031              9  1.518187e+07   0.819992   \n",
       " 2032              9  1.505752e+07   0.821466   \n",
       " 2033              9  1.461817e+07   0.826675   \n",
       " 2034              9  1.487465e+07   0.823635   \n",
       " 2035             10  3.793418e+06   0.955022   \n",
       " 2036             10  3.800555e+06   0.954938   \n",
       " 2037             10  3.793349e+06   0.955023   \n",
       " 2038             10  1.011274e+07   0.880095   \n",
       " 2039             10  3.798000e+06   0.954968   \n",
       " 2040             10  3.791345e+06   0.955047   \n",
       " 2041             10  3.829288e+06   0.954597   \n",
       " 2042             10  3.949432e+06   0.953172   \n",
       " 2043             10  3.839044e+06   0.954481   \n",
       " 2044             10  4.117780e+06   0.951176   \n",
       " 2045             10  1.461789e+07   0.826679   \n",
       " 2046             11  3.786730e+06   0.955102   \n",
       " \n",
       "                                                features  \n",
       " 0                                             (Income,)  \n",
       " 1                                              (Limit,)  \n",
       " 2                                             (Rating,)  \n",
       " 3                                              (Cards,)  \n",
       " 4                                                (Age,)  \n",
       " 5                                          (Education,)  \n",
       " 6                                      (Gender_Female,)  \n",
       " 7                                        (Student_Yes,)  \n",
       " 8                                        (Married_Yes,)  \n",
       " 9                                    (Ethnicity_Asian,)  \n",
       " 10                               (Ethnicity_Caucasian,)  \n",
       " 11                                      (Income, Limit)  \n",
       " 12                                     (Income, Rating)  \n",
       " 13                                      (Income, Cards)  \n",
       " 14                                        (Income, Age)  \n",
       " 15                                  (Income, Education)  \n",
       " 16                              (Income, Gender_Female)  \n",
       " 17                                (Income, Student_Yes)  \n",
       " 18                                (Income, Married_Yes)  \n",
       " 19                            (Income, Ethnicity_Asian)  \n",
       " 20                        (Income, Ethnicity_Caucasian)  \n",
       " 21                                      (Limit, Rating)  \n",
       " 22                                       (Limit, Cards)  \n",
       " 23                                         (Limit, Age)  \n",
       " 24                                   (Limit, Education)  \n",
       " 25                               (Limit, Gender_Female)  \n",
       " 26                                 (Limit, Student_Yes)  \n",
       " 27                                 (Limit, Married_Yes)  \n",
       " 28                             (Limit, Ethnicity_Asian)  \n",
       " 29                         (Limit, Ethnicity_Caucasian)  \n",
       " ...                                                 ...  \n",
       " 2017  (Income, Rating, Cards, Age, Education, Gender...  \n",
       " 2018  (Income, Rating, Cards, Age, Education, Gender...  \n",
       " 2019  (Income, Rating, Cards, Age, Education, Gender...  \n",
       " 2020  (Income, Rating, Cards, Age, Education, Studen...  \n",
       " 2021  (Income, Rating, Cards, Age, Gender_Female, St...  \n",
       " 2022  (Income, Rating, Cards, Education, Gender_Fema...  \n",
       " 2023  (Income, Rating, Age, Education, Gender_Female...  \n",
       " 2024  (Income, Cards, Age, Education, Gender_Female,...  \n",
       " 2025  (Limit, Rating, Cards, Age, Education, Gender_...  \n",
       " 2026  (Limit, Rating, Cards, Age, Education, Gender_...  \n",
       " 2027  (Limit, Rating, Cards, Age, Education, Gender_...  \n",
       " 2028  (Limit, Rating, Cards, Age, Education, Gender_...  \n",
       " 2029  (Limit, Rating, Cards, Age, Education, Student...  \n",
       " 2030  (Limit, Rating, Cards, Age, Gender_Female, Stu...  \n",
       " 2031  (Limit, Rating, Cards, Education, Gender_Femal...  \n",
       " 2032  (Limit, Rating, Age, Education, Gender_Female,...  \n",
       " 2033  (Limit, Cards, Age, Education, Gender_Female, ...  \n",
       " 2034  (Rating, Cards, Age, Education, Gender_Female,...  \n",
       " 2035  (Income, Limit, Rating, Cards, Age, Education,...  \n",
       " 2036  (Income, Limit, Rating, Cards, Age, Education,...  \n",
       " 2037  (Income, Limit, Rating, Cards, Age, Education,...  \n",
       " 2038  (Income, Limit, Rating, Cards, Age, Education,...  \n",
       " 2039  (Income, Limit, Rating, Cards, Age, Education,...  \n",
       " 2040  (Income, Limit, Rating, Cards, Age, Gender_Fem...  \n",
       " 2041  (Income, Limit, Rating, Cards, Education, Gend...  \n",
       " 2042  (Income, Limit, Rating, Age, Education, Gender...  \n",
       " 2043  (Income, Limit, Cards, Age, Education, Gender_...  \n",
       " 2044  (Income, Rating, Cards, Age, Education, Gender...  \n",
       " 2045  (Limit, Rating, Cards, Age, Education, Gender_...  \n",
       " 2046  (Income, Limit, Rating, Cards, Age, Education,...  \n",
       " \n",
       " [2047 rows x 4 columns])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.shape, df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pandas.core.groupby.groupby.SeriesGroupBy object at 0x000001DC382BDEB8>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.groupby('numb_features')['RSS']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0       2.143512e+07\n",
       "1       2.143512e+07\n",
       "2       2.143512e+07\n",
       "3       2.143512e+07\n",
       "4       2.143512e+07\n",
       "5       2.143512e+07\n",
       "6       2.143512e+07\n",
       "7       2.143512e+07\n",
       "8       2.143512e+07\n",
       "9       2.143512e+07\n",
       "10      2.143512e+07\n",
       "11      1.053254e+07\n",
       "12      1.053254e+07\n",
       "13      1.053254e+07\n",
       "14      1.053254e+07\n",
       "15      1.053254e+07\n",
       "16      1.053254e+07\n",
       "17      1.053254e+07\n",
       "18      1.053254e+07\n",
       "19      1.053254e+07\n",
       "20      1.053254e+07\n",
       "21      1.053254e+07\n",
       "22      1.053254e+07\n",
       "23      1.053254e+07\n",
       "24      1.053254e+07\n",
       "25      1.053254e+07\n",
       "26      1.053254e+07\n",
       "27      1.053254e+07\n",
       "28      1.053254e+07\n",
       "29      1.053254e+07\n",
       "            ...     \n",
       "2017    3.798367e+06\n",
       "2018    3.798367e+06\n",
       "2019    3.798367e+06\n",
       "2020    3.798367e+06\n",
       "2021    3.798367e+06\n",
       "2022    3.798367e+06\n",
       "2023    3.798367e+06\n",
       "2024    3.798367e+06\n",
       "2025    3.798367e+06\n",
       "2026    3.798367e+06\n",
       "2027    3.798367e+06\n",
       "2028    3.798367e+06\n",
       "2029    3.798367e+06\n",
       "2030    3.798367e+06\n",
       "2031    3.798367e+06\n",
       "2032    3.798367e+06\n",
       "2033    3.798367e+06\n",
       "2034    3.798367e+06\n",
       "2035    3.791345e+06\n",
       "2036    3.791345e+06\n",
       "2037    3.791345e+06\n",
       "2038    3.791345e+06\n",
       "2039    3.791345e+06\n",
       "2040    3.791345e+06\n",
       "2041    3.791345e+06\n",
       "2042    3.791345e+06\n",
       "2043    3.791345e+06\n",
       "2044    3.791345e+06\n",
       "2045    3.791345e+06\n",
       "2046    3.786730e+06\n",
       "Name: RSS, Length: 2047, dtype: float64"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.groupby('numb_features')['RSS'].transform(min)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>numb_features</th>\n",
       "      <th>RSS</th>\n",
       "      <th>R_squared</th>\n",
       "      <th>features</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>2.143512e+07</td>\n",
       "      <td>0.745848</td>\n",
       "      <td>(Rating,)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>2</td>\n",
       "      <td>1.053254e+07</td>\n",
       "      <td>0.875118</td>\n",
       "      <td>(Income, Rating)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>79</th>\n",
       "      <td>3</td>\n",
       "      <td>4.227219e+06</td>\n",
       "      <td>0.949879</td>\n",
       "      <td>(Income, Rating, Student_Yes)</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    numb_features           RSS  R_squared                       features\n",
       "2               1  2.143512e+07   0.745848                      (Rating,)\n",
       "12              2  1.053254e+07   0.875118               (Income, Rating)\n",
       "79              3  4.227219e+06   0.949879  (Income, Rating, Student_Yes)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>numb_features</th>\n",
       "      <th>RSS</th>\n",
       "      <th>R_squared</th>\n",
       "      <th>features</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>2.143512e+07</td>\n",
       "      <td>0.745848</td>\n",
       "      <td>(Rating,)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>2</td>\n",
       "      <td>1.053254e+07</td>\n",
       "      <td>0.875118</td>\n",
       "      <td>(Income, Rating)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>79</th>\n",
       "      <td>3</td>\n",
       "      <td>4.227219e+06</td>\n",
       "      <td>0.949879</td>\n",
       "      <td>(Income, Rating, Student_Yes)</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    numb_features           RSS  R_squared                       features\n",
       "2               1  2.143512e+07   0.745848                      (Rating,)\n",
       "12              2  1.053254e+07   0.875118               (Income, Rating)\n",
       "79              3  4.227219e+06   0.949879  (Income, Rating, Student_Yes)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_min = df[df.groupby('numb_features')['RSS'].transform(min) == df['RSS']]\n",
    "df_max = df[df.groupby('numb_features')['R_squared'].transform(max) == df['R_squared']]\n",
    "display(df_min.head(3))\n",
    "display(df_max.head(3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Adding columns to the dataframe with RSS and R squared values of the best subset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>numb_features</th>\n",
       "      <th>RSS</th>\n",
       "      <th>R_squared</th>\n",
       "      <th>features</th>\n",
       "      <th>min_RSS</th>\n",
       "      <th>max_R_squared</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>6.620874e+07</td>\n",
       "      <td>0.214977</td>\n",
       "      <td>(Income,)</td>\n",
       "      <td>2.143512e+07</td>\n",
       "      <td>0.745848</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>2.171566e+07</td>\n",
       "      <td>0.742522</td>\n",
       "      <td>(Limit,)</td>\n",
       "      <td>2.143512e+07</td>\n",
       "      <td>0.745848</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>2.143512e+07</td>\n",
       "      <td>0.745848</td>\n",
       "      <td>(Rating,)</td>\n",
       "      <td>2.143512e+07</td>\n",
       "      <td>0.745848</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>8.370950e+07</td>\n",
       "      <td>0.007475</td>\n",
       "      <td>(Cards,)</td>\n",
       "      <td>2.143512e+07</td>\n",
       "      <td>0.745848</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>8.433963e+07</td>\n",
       "      <td>0.000003</td>\n",
       "      <td>(Age,)</td>\n",
       "      <td>2.143512e+07</td>\n",
       "      <td>0.745848</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   numb_features           RSS  R_squared   features       min_RSS  \\\n",
       "0              1  6.620874e+07   0.214977  (Income,)  2.143512e+07   \n",
       "1              1  2.171566e+07   0.742522   (Limit,)  2.143512e+07   \n",
       "2              1  2.143512e+07   0.745848  (Rating,)  2.143512e+07   \n",
       "3              1  8.370950e+07   0.007475   (Cards,)  2.143512e+07   \n",
       "4              1  8.433963e+07   0.000003     (Age,)  2.143512e+07   \n",
       "\n",
       "   max_R_squared  \n",
       "0       0.745848  \n",
       "1       0.745848  \n",
       "2       0.745848  \n",
       "3       0.745848  \n",
       "4       0.745848  "
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['min_RSS'] = df.groupby('numb_features')['RSS'].transform(min)\n",
    "df['max_R_squared'] = df.groupby('numb_features')['R_squared'].transform(max)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting the best subset selection process"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ybt06rrjiCi6//HL8fj+rVq3a/wdFREREUkKzbAkdP34+OTnppKf7KC8PkZ7uIycnnfHj57vWgjV9+rK66/WHUNUvT7YdE9CmypMh1Y7T+PHzqaioYe3abYTDkJYGrVpluvpeKinxU14e4JNP1rF5czWFhdn84AcFlJT46d9fraHNzmWXNdlqmWiFhYV11w8//HAefPBBOnTowNy5c9m0aRPFxcW0bduWp59+mnnz5vHII48wZcoUPB7PTmNCp0+fzuDBg7ntttuYMGEC//rXvzj88MPZtGkTAF991fAEzqJFi2jXrh2ff/45RUVFje7r97//Pd26deOpp57C4/EwefJkjjrqKD799FNXx6SKiIhIYjTLJHTdugpatEgjGoX0dG+8VS3GunUVrsUUiexd+cEq1Y7TV19tZuvW7bN/hsOwZUuQr77a7E5AwOLFm3n55W9YsWIbVVU15ORkMHduHj/96dH079/etbjURbh5qe2O6/V6qaysZMyYMWRlZXH33Xdz2223EYl/6O6//37y8/O56aabeOaZZ/B6vdxwww2A04p57bXX8uyzz+LxeADo2bMnY8aMIScnh/T0dO69915atWrFCy+8wNChQznmmGPIzc2ti2PWrFk888wz5Obm8uCDDxKNRnfa19FHH81JJ53E0KFDqamp4dhjj6Vdu3YcddRRjB8/nmOOOYYLL7ww+QdR5CCSat/x48fP44kn5rN5cxWFhTlcf31vRo06zrV4ALp1m8DSpdvqbh95ZB5Llox0MSJISxvX4DeUzwfh8C3uBURqxnTYYeNZvbqy7nbnzrmsWjXKxYhg3LhPGT9+PqWlAQoKshg1qje33NLPtXiS/R3g2bHrVKIZY7oCy9999106deq0T9vo2fMfVFWFKCjIqisrLQ2Qk5POokVX7p9A95LHM26X98Vi7nzwFFPTUi0egGHD/sPs2ato1SqT7Gwf1dURysuDnHHGYUyd+iNXYqrtIpybm05OThpVVWEqK0P0799eiai4bs2aNbXjRg+Pr5Mpe2l/1M2y51It4SstreaWW2YzY8Zytm2rIS8vg/POO5xx485wJa7x4+dx/fXv7lT+xBNnuZaI7piA1nIzEd0x2avlZtKXijHtmIDWcjMRHTfuU+6992MyMnxkZnoJBqPU1ES4666TXUlEE/E7r6m6uVm2hJ53XlemTl1MebmH3Nw0KivDVFeHuOSSItdiysqCQKDxcpG9sXDhRnJy0sjK8uHxeMjK8hEKpbFwoXvdqEtK/OTmppObmw5Qd6kuwiIie6e0tJp33llJWVmAUChCerqPFSvKGTiwy/dL+GIxCAadHyOBQMPr9f8aKf/vi4voMmcVo6NhPMTwVoDvmRhfzH+aswd0cbZd/y8a3blsP5a3e8XyKjE8gKfepff6STD98KTHQzTKG0tLG8RSZynQ7WHncbt6XfakbG/LYzGWRXZOij3EIAJ0/vN+39+ePHZNpBJPY4+LAG0bWSosCbEt8Afrihq8dquB/Nv3+/725LE3VIe4Pgae+gcrBp5bgTt9+31/TT22NXBe/HqosB1fvvIh5KYn9Hdes0xCf/rTo8nI8DJ9+jI2bqymTZtsLr30KC6++CjXYjruuPYsXPgdlZXbX9DcXA/HHnuoazH5fI13c/X5di6T1BEOR2nVKjN+PUZamodWrTKprAw18czE8fsDtGnT8IxKTk4aW7Y0cuZFRER2ae7c71i5vIzeq+bQqnIzsaoANdsq8b+eTkHH7D1OHHe6Lxhseue7MCj+F8ZLNP4zPRr1EJvnAZvu/FKu/fN6G95OQHkRW4gBsXgsMTzxuDywadOeb9/n229xzrO2QTz1f9J3O/EHzpUGGUU9jZXvzWN3UT5rcuOTKMaAq8/pud/3tyePnTZhQV0MOxr1k94JOxa7e+yzjzdcb7p+bDdecfx+39+elD3557lkZPrwerffF43GCASj3PR/fff7/pp67LKlfrJz0vAAoUMOJZaeQU6mN6G/85plElpUlM+pp3bm3HOPaNBkXFSU71pMo0b15s47P+TIIzPIz8/A76+hvLyGUaN6uxbTRRcdwbRpzoQ/Xu/2iYAuuugI12Lq2bOARYtKGy13Q9eueaxYsa2uropEnOPUtWueK/EAdO/ehq+/LqVNmyzS032EQhG2bAnQvXsb12LKz8+iqipc1wIKUFUVJj9fTf0iIntj4ztzuPzlP9Ju+aIG5TGPx+k+teNfZub26wUFjZfv6vF7Up6VRW6bvxPER1rm9u/4YND50RCrTH4XymN3N1TmM3e6dA79165j+uVz7sR09eRdx3T1JHdiGjVh1zGNGu9OTDc+vuuYbnzMnZjGPvc3QqEoeXkZdWXbttWQ3sLLTQ/ekPR4NsdXZWjwO68ylNDfec0yCS0oyKZ///aUlPjZssUZT9GjR6Gr4ylqZ1IdP34+a9Y4603ecks/V9ebfO21S1JuTc7Zs4dyyilT+eYbf13Z0UfnM3v2UFfiefTRAVxzzQzKyoKEQk6y3qZNJo8+OsCVeABGj+7D7bf/l6qqMB5PiFjMQ8uWGYwe3ce1mIqK8ikuXg/Q4MRPjx6FTTxTREQAqKiAu+9m6KOPEcxtyUcj72fdsT8kkp7JtrCHqqCHX9/YSAtIElR7MojFdv5RuKsGFRH5fn76U8PTTy/C4/HUzf9RXR1m6NCeTT85Adz4ndcsk1CoTURTayza8OHHuJp0NsbNhLMxBQXZfPTRsJSZkGHQIGcc8cSJC1i3roIOHVowYkSvunI3DBjQhT/+8TSeffYr1q7dRseOeVx22TEMGNDFtZhS8cSPiEizMW0a/OpXsGYNay8YymsnXEl2x7ZkZfkIBCKUbQvSu/chroXXqVMuq1dXEgpFdyoX2RstW6axdWu40XK3PPzwafz2t/9ttNwt99xzClVVId56azmlpQFatsxkyJCjueeeU1yJx43fec02CZXmK9VOIAwaVORq0tmYAQO6uJp0NibVXjcRkZS3ciX83//B669Dz57w4ovkHn0ch85aSWlpNX5/mPR0L127tqRv33auhXn//acxevQ7VFaGicUnS2nZMo3773fnR/qgQduHE+1Y7pazz+7ErFlrGi13SyomV8uXj6Rr1/Fs27b9hEZenpfly91byqZ2ttlUWg6loCCbhx8+g2uv7Z0SjTK1MSXzd56SUBGRA0xxcTE33ngj3bp1A6CyspJOnToxbtw43njjDV577TV8Ph+xWIxrrrmGU089lUAgwN13383GjRvxeDy0aNGCu+++m9atW7v834g0Q6EQPPYY3H23c/vhh+HXv4b0dAqAs8/ukjI9gqDhkKING5whRaNG9Xatd1cqDid6550hDBz4zwaJ6Nlnd+Kdd4a4FlOqJlcrVoxKqfc3OMfKzePSmIP95L6SUBGRA9CJJ57Io48+Wnf7N7/5DW+88QZPPPEEb7zxBhkZGWzYsIFLL72U2bNn88orr1BYWMjYsWMBmDx5Mn/729+444473PoXRJqnjz6C666DL7+Eiy+Gv/wFDjuswUNS8cdnqg0pSrXhRICrCeeuKLmS5kpJqIiIyxK9cH1NTQ0bN27k0EMPJRKJ8MILL3DmmWdy2GGHMWvWLLxeLx07duTll1+mT58+9OvXj+HDhxPb1XpjIrKz0lK47TZ46ino3NkZB/rjH7sdlYhISvK6HYCIyMGstLSa4vjU6G3aZBEMhikuXk9pafX32u6cOXMYPnw4F1xwAZdccgkDBw7kpJNO4h//+AcrV67kmmuu4cwzz+Tll18G4IwzzmDUqFG8/PLLnHXWWVxxxRUsXbp0f/yLIge2WAyefRaMgX/8A265BRYvVgIqIrIbagkVEXFRSYmf3Nz0urW5ai9LSvzfqztTbXfcsrIyrrrqKjp16sSGDRsIBALcddddACxfvpxrrrmG448/nqqqKk466STOOeccIpEI//73v7n99tt59dVXv/8/KXKg+uYbGDUKZs+Gk06Cv/8djj3W7ahERFJeQlpCjTHpxpjnjTEfG2P+Z4w5OhH7ERFp7vz+ADk5Dc8H5uSk4fcH9sv2W7duzcMPP8wdd9zBmjVruOWWWygvLwegY8eOtG7dmvT0dN544w2eeuopAHw+H8YYMjIydrdpkYNXdTXceaeTcM6fDxMmwIcfKgEVEdlDiWoJvQBIs9aebIwZCNwP/CRB+xIRabby87OoqgrXtYACVFWFyc/P2m/76NatG8OHD+eZZ57hsssu4/LLLycrK4tIJMKll17KEUccwY033sh9993Hj3/8Y7Kzs8nJyeH+++/fbzGIHDBmzoTrr4dly2D4cBg3Dtq2dTsqEZFmJVFJ6LdAmjHGC7QEQgnaj4hIs1ZUlE9x8XrAaQGtqgpTWRmiR4/Cfd5m//796d+/f4OyUaNG1V2/9NJLd3pOixYtePDBB/d5nyIHvPXr4aab4MUX4aij4N13YcAAt6MSEWmWEpWEVgBdgW+AQuBHCdqPiEiz5kxl356SEj9btjiz4/boUej6mmoiEheJwPjx8PvfQzAI994Lt94KmZluRyYi0mwlKgm9CZhprb3dGNMZeM8Y09Nau38GOYmIHEC0pppIipo7F0aOdC4HDoQnnoBu3dyOSkSk2UtUElrG9i64pUA64NufO0j0unr7YsqUrxg/fj4bNlTSrl0uo0b1dn3h58GDX2X69GVEIuDzwUUXHeH6AtD9+j3LZ59trLt9wglt+fTTy1yLJxWPUSq+l1LxMycikhBbtzoTD/31r3DIIfDCC/Dzn4PH43ZkIiIHhEStE/oo0McY8z/gPeB31trK/bXxRK2r931MmfIVd975IZWVNXTqlEtlZQ133vkhU6Z85VpMgwe/yrRpTnLl9To9iqZNW8bgwe4tubBjAgrw2Wcb6dfvWVfiScVjlIrvpVT8zImI7HexGLz0Ehx9NPzlL3Dddc4yLEOGKAEVEdmPEtISaq2tAH6WiG1D4tbV+z7Gj59PTk466ek+ystDpKf7yMlJZ/z4+a61YE2fvgyAzMzt5xqCwWhduRtqE9D6dXksxk6JabKk4jEaP34+rVplUFjovJdrL918L6XiZ05EZL9atgxGj4a33oLjjoNp06BfP7ejEhE5ICWqO25C+f0B2rRpuHxBTk4aW7a4N+R03boKWrRIIxqF9HRvvGUtxrp1Fa7FFIk4l8FgtNFyN8VibkfgSMVjtGFDJaWlVSxcuKWuLD8/jYKCHNdi8vsDzJmzjldeKaG0tJqCgmx+8pMiTjyxg2sxgboIi8h+UFPjLLNy332QlgaPPQY33OBcFxGRhEhUd9yEql1Xr779va7e3srLy6C6OoIvPvLV54Pq6gh5eVrsXfbOli3V+P0N399+f5gtW9zr+vrxx2t54on5VFeHaNs2m+rqEE88MZ+PP17rWkzqIiwi39t//wu9ezsz3154odP19te/VgIqIpJgzfJbNhHr6n1f553XlalTF1Ne7iE3N43KyjDV1SEuuaTItZhatkxj69Zwo+WSusrLG19Wd1flyfDmm8vJyUkjLy8dr9dDXl464XCUN99czj33nOpKTOoiLCL7bPNm+O1vYfJk6NoV/vMfJwk9iL333kqeffYr1q7dRseOeVx22TEMGNDFtXj69JnMvHmb624fd1whX3xxhWvxAPh844jW6zjlzCVxi3sBAR7PuJ3KYjF3Y2rX7q9s3Li9d2Lbtlls2DDaxYjg3ns/YsKEBZSX19CqVQYjR/birrtOcTWmg703V7NsCa1dVy8z0+mCm5mZRv/+7V194X7606O58soeZGWlsXFjNVlZaVx5ZQ9++tOjXYupsDCH/PyGCWd+fhqFhe5165TmqbS0mvbtc/B6PYTDMbxeD+3b57ja6uj3B8jJafj+zslJw+/XSlAisl1tr4mZM5dT/MlaKh4fD8bAc8/B7bfDV18lPQG9996P6NjxCVq0eIyOHZ/g3ns/Sur+d/TeeysZOPAlnnlmMbNmreaZZxYzcOBLvPfeSlfi2TEBBZg3bzN9+kx2JR7YOQEFiEadcrc0loDurjwZdkxAATZuDNCu3V9disj5vI0d+ymBQITWrTMIBCKMHfupq5879eZqpi2hkHrr6hUV5XPqqZ0599wjGrTOFhVwqGHKAAAgAElEQVTluxZTu3a5tGiRTp8+24/T5s3V5Oa610XY53PGW+44EZBvvy7gs/d2nCjJTal4jNq1c2bprZ0kCZz3Urt2ua7FVNstv7YFFNzvli8iqaW0tJp33llJWVmAvJWWY196kBZL5xE68WTSn3oSjkn+ZG/33vsRf/jDJ4TinVsqK8P84Q+fALjWMnP++S81mmCdf/5LBIPJb1XbMQFtqjwZdjw+TZUfrHZMQJsqT4YJExaQnZ1Gy5bO79+WLX115W595tSbq5m2hKaiVGydHTWqN+XlNWzeXE04HGHz5mrKy2sYNaq3azFddNERgJNUhULRugmBasuT7YQT2gJO4ln7V7/cDal2jCA130tFRflUVoaorAwRi8Xqrrt54kdEUsvcud+xcoWfE96cwNCHf0nr75bz5k/vYPbdz7qSgAI88sjnhELOsNPMTA9paRAKOeVuqanZu3KR5qS8vIacnIZn8nNyfJSXu/cGV28uJaH7VW0ieu65h7uegAIMH34M9913Krm5GaxZU0lubgb33Xeqa8t8ALz22iUMGnQEPl9tNxYYNOgIXnvtElfi+fTTy3ZKOE84oS2ffnqZK/FA6h0jSM33Uiqe+BGR1LJ4cSln/3cSx0//Oyv7ncv0h6ezZuBPWPyN37WYasf3+3xewBO/dHfcv8iBrFWrDKqqGi57UFUVoVUr93oGpuIkq8nWbLvjyp4ZPvwYVxOFxriZTDXGzYRzV1LtGEFqvpdSrVu+iKSW495/jj5vPkXJGT+h+Kq7nbEXVe4ne/WHgNTednsoiMj+4PU23kXZ62Kz18iRvRg79lPAaQGtqopQXR3m17/u41pMqTjJarKpJVREREQOPE89xWn/foxvep7FB0N+Rwyorg7j99fQvXsb18Lq0CGHWAxqaqKEw1FqaqLEYk65yN7I3sU52F2VJ8Pjj5+5V+XJcNddpzBmTD+ysnyUldWQleVjzJh+rs6Oq95cagkVERGRA81LL8G111Jz1kC+vGoc4a0Rqv1B0tO9dO3akr5927kW2tixp3PDDTOpqIgSiTitoHl5XsaOPd21mAYNOoJp05Y1Wu6GE05oy2efbWy03C2pdowAJkw4nyuueGunZWMmTDjftZiGDv0BW7eG+OCD1ZSWVlNQkM3pp3dm6NAfuBYTOImo20uy7Ohg782lJFREREQOHDNmwLBhcMopZLw+jQEBT0qtxVc7rGH8+Pls2FBJu3a5jBrV2/X5GgYPfpXp05cRiThzEVx0kbvzNfTr92yDRDQV5mtIpWMEqfleKijIZuTIXgwY0CVlPnOSmjyxJA9CMMZ0BZa/++67dOrUKan7FhGRA8+aNWs466yzAA631q5wOZxm6YCpmz/8EM45x1kH9P33IV+zZYuIuKGpulljQkVERKT5mzcPLrwQOneGmTOVgIqIpDAloSIiItK8WQvnngutWsE770Bb98YOiohI05SEioiISPO1ahUMHOhcnzULDjvM3XhERKRJmphIREREmqcNG5wEdOtWmD0bjjrK7YhERGQPKAkVERGR5sfvd7rgrl7tdMHt3dvtiEREZA8pCRUREZHmpbISfvQjWLwYpk+HU1Jr/T8REdk9JaEiIiLSfNTUwE9+Ap98Av/8p9MaKt9baWl1Sq2nOmXKVym1/iWQcuuEAim3niqk5nFKxfdTqn3mkk0TE4mIiEjzEInAsGHOEixPPgmXXup2RAeE0tJqZs1aybx53/Htt6XMm/cds2atpLS02pV4pkz5iptvfp+FCzeyfn0lCxdu5Oab32fKlK9ciQecxGraNCexAuetOG3aMgYPftW1mHZMQAE++2wj/fo961JEqXmcpkz5ijFjPmDVqq2Ew1FWrdrKmDEfuPp+Ki2tprh4PcFgmDZtsggGwxQXr3ftM+cGtYSKiIhI6ovFYORIePll+NOf4Oqr3Y5on82d+x2vvlrC2rXb6Ngxj0suKeL44w91LZ7PP9/A73//AUuWbKsr69Ytj/z8cznnnK5Jj+e++z5m8+ZAg7LKygj33fexa61X06Yt26vyZNgxAW2qPBlS8Tg9+uhn1NREyc72EYnE8HqhujrKo49+5tr7qaTET25uOrm56QB1lyUlfvr3PzhaQ9USKiIiIqktFoNbboFJk+COO+Dmm92OaJ/NnfsdY8fOYcmSUsLhCEuWlDJ27Bzmzv3OtZhGj57ZIAEFWLJkG6NHz3QlnpKS8r0qF9mdlSvL8XrB6/WQnu7B6/Xg9TrlbvH7A+TkNGwLzMlJw+8P7OIZBx61hIqIiEhqu/9+eOQRGD0a7r13r566dGkZH3ywhvXrK2jfvgWnn96JI49snaBAmzZ16mI+/3w9q1dX1o2Z69w5l6lTF7vWGlpSsm2vykWaE5/PaQH1eDwAeDwQicTw+XyuxZSfn0VVVbiuBRSgqipMfn6WazElm1pCRUREJHX99a9w550wfDj8+c/OL8g9tHRpGVOnLqaysobOnVtQWVnD1KmLWbq0LIEB794rr1hWrKgkGnUS0GgUVqyo5JVXrGsxiRzIjjuuLTU1YaqrQ8RiMaqrQ9TUhDnuuLauxVRUlE9lZYjKSiem2utFRfmuxZRsSkJFREQkNU2ZAr/6Ffz4x/D00+Ddu58tH3ywhtats2jdOguv11t3/YMP1iQo4KatXVsJQEaGl7Q0LxkZ3gblIs3Zrj6ie/nR3a9GjOhN797t8Ho9+P0BvF4PvXu3Y8QI99YWLijIpn//9mRmprFlS4DMzDT6929/UM2Oq+64IiIiknr+/W+48koYMMBZiiVt73+yrF9fQefOLRqUtWqVwerVFfsryr0WjdZexvB6PUSjsQblIs3Z6ad35P331zZa7pYBAzqzdWsAa0vZurWGli0zMKaAAQM6uxYT1CaiB0/SuSMloSIiIs2cMcYLPAH0AoLANdbaJfXuvwUYCkSBB6y1r7kS6J5691342c/g+ONh2jTI2rdxUu3bt6C8vIbWrbc/v7y8hvbtW+zmWYnVokU6VVUhPB4PkUgUr9eLzxcjJye96SeL1NO9e2u+/nrnruXdu7s35nnixPP4xS/+w4IFGwkGY2RmeujVqy0TJ57nWkwFBdkMGlR0UK/JmYqUhIqIiDR/g4Asa+1JxpgTgT8BPwYwxuQD/wd0A3KB+UDqJqHFxU7326OOgrfegry8fd7U6ad3YurUxYDTAlpeXkNZWYALLjhif0W716688hj+9rf5QJSMDA/hcLSu3C1HHpnH0qU7T0J05JH7fuy/j7Zts9i4cedZQtu2dW/SlpNPPpSPP955BuOTT3ZvaZ0HHjiN669/m7KyQHyiHQ+tW2fxwAOnuRbTkUe25vnnf5RSk4GBWh1TUUKSUGPMFcAV8ZtZQG/gUGutPxH7ExEROcidCswAsNbOMcb0rXdfJbASJwHNxWkNTU1ffgnnnw/t2sHbb0NBwffa3JFHtmbYsB/wwQdrWL3a+UF8wQVHuPqD+M9/PhuAZ575isrKELm56Vx++TF15W5YsmQk3bpNaJCIHnlkHkuWjHQlng0bRtOu3V8bJKJt22axYcNoV+IB+OijX3LKKc81SERPPvlQPvrol67FNGhQEQATJy5g3boKOnRowYgRverK3XLkka1dTzol9SUkCbXWTgYmAxhj/gY8rQRUREQkYVoC9Re9ixhj0qy14fjt1cBiwAf8MdnB7ZGlS2HgQMjOhlmzoH37/bLZVPxB/Oc/n+1q0tkYtxLOXXEz4dwVNxPOXRk0qMj1pFNkXyR0rqr4mdhjrLVPJnI/IiIiB7mtQP2+k956Cej5QHvgcOAwYJAxpl+S49u9tWudBLSmxmkBPfxwtyMSEZEESvSEyb8D7knwPkRERA52HwEXAMTHhC6qd18ZUA0ErbUBwA+kzmJ0W7bAOefApk0wYwYc497YSBERSY6ETUwUnwjhaGvt+4nah4iIiADOREMDjTEfAx7gSmPMzcASa+3rxpizgTnGmCjwIfCOi7Fut3UrnHee0xV3xgw44QS3IxIRkSRI5Oy4pwGzErh9ERERAay1UeC6HYq/qXf//wP+X1KDakp1tTML7rx58NprcMYZbkckIiJJksgk1ADLErh9ERERaY5CIfj5z+GDD2DKFLjoIrcjEhGRJEpYEmqtfThR2xYREZFmKhqFK66A6dPhb3+DYcPcjkhERJIs0RMTiYiIiDhiMfjVr+D55+H+++H6692OSEREXKAkVERERJLjjjvgiSfgt7+F2293OxoREXFJIseEioiIiDgefhgeeABGjIAHHwSPx+2IRJq9uXO/49VXS1i7dhsdO+ZxySVFHH/8oa7G9N57K3n22a/qYrrssmMYMKCLqzGVllZTUuLH7w+Qn59FUVE+BQXZrsZ0sFMSKiIiIok1cSLceiv87GcwfvxBn4Cm4g/ikSNnMHXq11RXR8jO9jFsWHcmTDjPtXhat/4zfn+o7nZ+fjplZb92LR6A7OxxBALbb2dlQXX1La7FM3fud5x55gts2xapK/vLXz7n/feHupaIvvfeSm666T38/gChUJRvvy1l3rwNPProANcS0dLSaoqL15Obm06bNllUVYUpLl5P//7tXf/cHczUHVdEREQS58UXYeRIOP98ZyZcny+pu6/9ATpz5nKKi9dTWlqd1P03Fs8dd3zIkCGvM3Tofxgy5HXuuONDV+MaOXIGTz75JZWVEaJRqKyM8OSTXzJy5AxX4tkxAQXw+0O0bv1nV+KBnRNQgEDAKXfLuee+1CABBdi2LcK5577kUkQwdmwxa9dW4PV6adkyA6/Xy9q1FYwdW+xaTCUlfnJz08nNTcfj8dRdLynxuxaTKAkVERGRRHnzTfjlL+GUU+DllyEjI6m7Ly2t5p13VjJv3oa6Fpl33lnpasI3duwcJk9exOrV2ygrC7J69TYmT17E2LFzXIvpySe/3KvyRNsxAW2qPBl2TECbKk+GLVuCe1WeDAsXbiI7Ow2IUVUVAWJkZ6excOEm12Ly+wPk5DTs/JmTk4bf7+KLJ+qOKyIiIgnwv//BT34CPXvCf/4DOTlJD2Hu3O944YWv+fTT9VRWhsjNTadfv/YUFGQycODhSY8HYNKkL6mujtbdjkSgujrKpElf8tBDZ7oSk8j+Eo3GCATC5Oam4/M5E2IHAmE8LnbBz893uuDm5qbXlVVVhcnPz3ItJmnGSWgqjqeYNq2EiRMXsG5dBR06tGDEiF4MGlTkakxjxsxm0qRFbNsWIi8vnauv7snYsWcopnpS8XVLxfe3iEhTar+7Ip99Tr8xw/B0OgzfjBnQqpUr8UyYsICZM5cSDjvLk1ZVhZg5cylpaR7XktDS0sZbqXZVLtKcHH54K77+egvp6T4yM73U1EQJBiN0797GtZiKivIpLl4POC2gVVVhKitD9OhR6FpM0ky749aO7wgGw7Rpk0UwGHZ9nMe0aSXcddeHVFSE6NIlj4qKEHfd9SHTppW4FtOYMbN55JG5BIMRWrZMJxiM8MgjcxkzZrZiikvF1y0V398iIk2p7fq6/K05HDfmMqozc3njxr9TmpbnWkyzZq2o6y5ZOxQ1EHDKRWT/Gzy4iHbtcolEYpSXB4lEYrRrl8vgwe6d3C8oyKZ///ZkZqaxZUuAzMw0TUqUApplS2j9AcZA3WVJiZ/+/d15Q02cuIDc3Ay8Xg+bNwdIT/eRm5vBxIkLXGtVmzRpEV4vBINRqqvDeL1evF6n3K2Wx0mTFhGLxdi2Lcy2bWEA0tLci2nixAWUlgb45ptSwuEYaWke2rbNcfV1Kynx88UXG3jrrWVs2lTNIYdkc/75R8S/RN37wlTrrIjszty537FyZTkXvf88+Ly8ddMEVlTmkD33O9daHWvrGa/Xg8fjdA2EWF25SHN2yCFZbNq087jGQw5xr5vpmWd2ISvLx7vvrmTDhmratcvmrLO6cNJJnVyLCXD9N5TsrFkmoX5/gDZtGn7AcnKcsxtuWbVqG5mZHgKBMNFoDK83jM8XY9WqGtdi8vuDhMMAsXiJMwYlEnGvy09paZBotGFZOOxeN6TPPvuuwRd4KBRj7dpKamoiu3lWYr3xxlKefHIBlZUhwuEI69ZVsGSJn2AwQv/+7V2JqbaFo6wsQCgUIT3dx4oV5Qwc2EWJqIgAsHhxKfn5mSz8xc0sHPYbQjl55FeFWLy41LUk1OOp/fMQi8XweDx4PLGDfYUYOUAMGXI0Tz21kIwML2lpXsLhKDU1UYYMOdq1mIqK8iktraZPn0MbdH0tKsp3LSZJTc2yO27tAOP63B5gnJ2dxubNQTweDxkZXjweD5s3B+MzhLkjUi+Pql/hRtzLr3ZKQJsqT7TGziDurjwZ/vWvrykrq8bn89CiRQY+n4eysmr+9a+vXYuptoXD5/OQn5+Jz+dh5cpy5s79zrWYRCQ1hXJbEspxrwtufR06OJMhRSJRYrEYkUi0Qbmkptzcxs8S7Ko8GW69te9elSfD3XefwtChPyAnJ4NgMEpOTgZDh/6Au+8+xbWY1PVV9lSzbAlNxQHGPXoUMnPmMqqqasjJ8VFVFSEUCrsa0/auR9sva8slda1ZU0E4DOXl26ei93qdcrcsXlzK8uXlPP/815SVBWjdOouTTupAZmaaay0coC7CIqmke/c2zJ+/EY/HQ1aWj0Aggt9fQ+/ebV2L6YYbjuehh4qprKwhHHaGf7RsmcENNxzvWky33daXBx/8vNFyt6RaTM89dzE///m/qanXmSwjwyl3y2239aeiIsybby5l69YaWrbM4IILjuS22/q7FlNBQTYPP3w6117bK6XqQXV9lT3RLJPQ2rMsJSV+tmxxPnQ9ehS6+qHr1astmZlePv54HVu2BMnPz+TMM7tx9NHuJaHZ2U4yvGMCmp2d3IXCZe8EApGdWoajUafcLQsWbGTmzOXk5WVQWJhFZWWY119fQjDoXky1Ezjl5qbTpo3TO6K4eL3OuIq4pG/fdvj9AUpLq/H7w6Sne+natSV9+7ZzLaYRI46loqKmbm3QgoJsBg7swogRx7oWU+38B6k0S3yqxTRoUBEvvvjjlJq5vqAgm/vuO4XLLjtGCZ/IftAsk1BIvQ9d9+5tCAYj9OlzaN0Z4LKyoKtTUnfo0IIVK7aSne3D56tdiyxChw4tXItJmrar7tJudqNetGgzGRk+cnLS8Hg85OSkEQxGWLRos2sxpeIEZSIHs4KCbM4+u0tK9U4oKMjmppv68qMfdUuZmMBJ+txeLm1HqRbToEFFri+XtqNU++0p0pw12yQ01aTiGeAhQ47myScXUllZQyjkTE9fUJDl6oD1wsJMNm/eeRKiwsJMF6JJTV5v42NkvS6O4A4EQhQWZhEOxwiFoni9HgoLswgEQk0/OUFScYIykYNdKv5IT8WYREQOdkpC95NUPAN84YXdyMz08dZby9m4sYq2bXM4//zDOfts98bw9evXnvnzN7JpUxWhEKSnwyGH5Lg2ZqiwMJOysmCDVkafD1q3di8pLijIpKLCiSkadZJPnw9atHAvpsMOa0lZWZC8PGfh6YwML4FAlLZtc12LqXaCstoWUHB/gjIRERERaZqS0P0o1c62OtNkH8oPf9g5ZabJHjGiF3fd9SHdurWmdesMyspqKCsLMGJEL1fiufrqnjzyyFxycnx13agDgQhXX93TlXjqx5SVlTox1b5u6elZFBZmUVZWQ0VFDbfe2s+1mFJxgjIRERERaZqS0ANYKk7gVDu+Y+LEBaxcuY0OHVpw0019XRv3UX8yhq1bnckYrr++d8pMEJEqMaXa6wap+f4WERERkaZ5YvWnTk0CY0xXYPm7775Lp06dkrpvERE58KxZs4azzjoL4HBr7QqXw2mWVDeLiMj+1FTd7OJUJyIiIiIiInKwURIqIiIiIiIiSaMkVERERERERJJGSaiIiIiIiIgkjZJQERERERERSRoloSIiIiIiIpI0Wid0PyotraakxI/f76xZWFSU7/qahdOmlTBx4gLWraugQ4cWjBjRy9W1HQHGjJnNpEmL2LbNWQPz6qt7uroGZqrFA6n5uqXi+1tEREREmh+1hO4npaXVFBevJxgM06ZNFsFgmOLi9ZSWVrsW07RpJdx114dUVITo0iWPiooQd931IdOmlbgW05gxs3nkkbkEgxFatkwnGIzwyCNzGTNmtuKJS8XXLRXf3yIiIiLSPCkJ3U9KSvzk5qaTm5uOx+Opu15S4nctpokTF5Cbm4HX62Hz5gBer4fc3AwmTlzgWkyTJi3C64VgMEpZWZBgMIrX65S7FU8sFmPbtjCbNgXZti1MLBZzLR5wXrfS0gCffLKO119fziefrKO0NODq61ZS4ueLLzbwu9/9l2HD3uB3v/svX3yxwdX3N2xPjmfOXK6kWERERKSZSFh3XGPM7cDFQAbwhLV2UqL2lQr8/gBt2mQ1KMvJSWPLloBLEcGqVdvIzPQQCISJRmN4vWF8vhirVtW4FpPfHyQcBojFS6IARCJBV+IpLQ0SjTYsC4edcrd89tl3bNq0/X0TCsVYu7aSmpqIazG98cZSnnpqIYFAiHA4yqZNlSxbVk4wGKF///auxFSbgObmptOmTRZVVU7rbP/+7dVNWERERCSFJaQl1BhzBnAycApwOtA5EftJJfn5zo/g+qqqwuTnZ+3iGYmXnZ3G5s1BPB4PGRlePB4PmzcHyc52byhwpF4e5fE0Xp5MOyagTZUnQ/0EdE/Kk+Hlly1+fzWxGKSlpRGLgd9fzcsvW9diKinxE4lEWb68nDlz1rN8eTmRSNT11lkRERER2b1EZSPnAouA14CWwG8TtJ+UUVSUT3HxesBpAa2qClNZGaJHj0LXYurRo5CZM5dRVVVDTo6PqqoIoVDY1Zg8HojFG0FrL2vLJXWtWVNBMBijujpUV+b1OuVuWbWqnBkzlvPpp+spL6+hVasM+vVrz3nnHe5a6yxoAicRERGRpiRqTGgh0Be4FLgOmGqMOaDTjIKCbPr3b09mptMFNzMzzfVugb16teXii7uRmeljy5YgmZk+Lr64G716tXUtpuxs304Jp8fjlEvqqq4O7dQ6HI3SIClNttmzV/PWW8sJhaIcckgWoVCUt95azuzZq12LSRM4iYiIiDQtUS2hW4BvrLU1gDXGBIBDgI0J2l9KcBLR1Gnx6N69DcFghD59DiUry0cgEKGsLEj37m1ci6lDhxasWLGV7GwfPp/TDbe6OkKHDi1ci0maFg7vXXkyfPzxWrKy0sjJScPj8ZCTk0ZNTZSPP17rWkz1JygD6i5LSvwp9d0gIiIi4qZEtYR+CJxnjPEYYzoAuTiJqSRR377t6Nq1JZFIFL8/SCQSpWvXlvTt2861mIYMOZqCgiyi0RiBQIxoNEZBQRZDhhztSjyFhZl7VX6w2lV3aTe7UVdWhjjkkCy8Xg/hcAyv18Mhh2RRWele66zfHyAnp+G5vZycNPx+98bzioiIiKSahLSEWmv/Y4w5DfgUJ9G9wVrr3tSeB6mCgmzOPrtLSo1Pu/BCp3vwW28tZ+PGKtq2zeH88w/n7LMPdyWefv3aM3/+RjZtqiIUgvR0OOSQHHr3dq/LcmFhJmVlwQaTNfl80Lq1e4lx69YZbNvmzKocjTrjQQHy8jJci6lLl5asX19FmzaZ+HweIpEYW7YE6dKlpWsx1U5QVtsCCu5PUCYiIiKSahI2Taq19tZEbVv2XKp1ES4qyqe09FB++MPODSZwKirKdyWeESN6cdddH9KtW2tat86grKyGsrIAI0b0ciUegKuv7skjj8wlJ8dX1406EIhw9dU9XYtpxIhj+dOfPicjw0tampdwOEpNTZQRI451LaYbbujD7373X7Zurak7TtFolBtu6ONaTKk4QZmIiIhIqnFvrQ45KNVO4FRS4mfLFqd1tkePQtdaZwcNKgJg4sQFrFy5jQ4dWnDTTX3ryt0wduwZAEyatIitW0Pk5aVz/fW968rdjmnbNiemX/2qp6sx1X/t1q2roEOHFowY0cvV1y7V3t8iIiIiqcgTq79ORhIYY7oCy9999106deqU1H2LiMiBZ82aNZx11lkAh1trV7gcTrOkullERPanpurmRE1MJCIiIiIiIrITJaEiIiIiIiKSNEpCRUREREREJGmUhIqIiIiIiEjSKAkVERERERGRpFESKiIiIiIiIkmjJFRERERERESSRkmoiIiIiIiIJI2SUBEREREREUkaJaEiIiIiIiKSNEpCRUREREREJGmUhIqIiIiIiEjSpLkdgIiIiHw/xhgv8ATQCwgC11hrl9S7/3zg/8VvfgHcYK2NJT1QERER1BIqIiJyIBgEZFlrTwLGAH+qvcMYkwc8DPzIWnsisAIodCNIERERUBIqIiJyIDgVmAFgrZ0D9K1338nAIuBPxpj/ARustZuSH6KIiIhDSaiIiEjz1xIor3c7YoypHXJTCJwJ3AacD9xojDkqyfGJiIjUURIqIiLS/G0F8urd9lprw/HrW4DPrLXfWWsrgP8CvZMdoIiISC0loSIiIs3fR8AFAMaYE3G639aaC/QwxhTGW0dPBBYnP0QRERGHZscVERFp/l4DBhpjPgY8wJXGmJuBJdba140xtwMz44/9l7X2S7cCFRERURIqIiLSzFlro8B1OxR/U+/+fwL/TGpQIiIiu6DuuCIiIiIiIpI0SkJFREREREQkaZSEioiIiIiISNIoCRUREREREZGkURIqIiIiIiIiSaMkVERERERERJJGSaiIiIiIiIgkTcLWCTXGzAPK4zeXW2uvTNS+REREREREpHlISBJqjMkCsNaekYjti4iIiIiISPOUqJbQXkCOMebt+D5+Z62dk6B9iYiIiIiISDORqDGhVcA44FzgOmCqMSZhXX9FRERERESkeUhUYvgtsMRaGwO+NcZsAdoDqxO0PxERkWbPGPMPINbYfdbaq5IcjoiISEIkqiX0KuBPAMaYDkBLYH2C9iUiIlfx334AACAASURBVHKg+CfwIlAAfANMAhYCWW4GJSIisj8lqiV0EjDZGPMhzhndq6y14QTtS0RE5IBgrZ0JYIz5jbX2oXjxR8aYd1wMS0REZL9KSBJqra0BfpGIbYuIiBwEWhhjBgCfAScDGS7HIyIist8kqjuuiIiI7LurgFHAHOBa4OfuhiMiIrL/aMZaERGRFGOt/cYY83ugG86Y0A0uhyQiIrLfKAkVERFJMcaY0cBgnAmKJgP/n707j4+quvs4/pktmWwkJCyCKEKM1wVFQQ2IdcUFqFa08lgV3K3YumtFrGip9dGWYmtbKYI+VUTUWkXRigutWBWiQEFcuIZNRCJLhiH77M8fk4SAgbDMzJnA9/168crcM8v9MnOTO797zj23BPi5yUwiIiKJouG4IiIi6ecSYDDgt237j0Cp4TwiIiIJoyJUREQk/TTtn5uuGRowFURERCTRNBxXREQk/TwHvA/0tCzrn8BMw3lEREQSRkWoiIhI+nkHmAP0AWzbtj81nEdERCRhVISKiIiknydt2z4Z+NJ0EBERkURTESoiIpJ+ai3LehSwgSiAbdtPmI0kIiKSGCpCRURE0s9HjT+7Nv6M7eiBIiIi7c1Oi1DLsgqB+4A7gCOJX6usAbjGtm076elERET2Q7Zt/8qyrG6AB3AA3Q1HEhERSZi2ekIfZ+vR2MeAPwFLgT8C5yYxl4iIyH7LsqwngYFADpAFrAQGGA0lIiKSIG1dJ7TAtu3HiO8EjwGesW17UeOyiIiIJMcRwFHAW8RHIjWYjSMiIpI4bRWhTU4F/mPbdtM5KSpCRUREkqe6cZ+bY9v2JiDDdCAREZFEaWs4boVlWQ8BZwMPWpbVAbgL0PXKREREkmehZVl3Aussy3oeTSQoIiL7kLZ6QkcD3wDjbNueSXxIUAfg58kOJiIisr+ybXssMBm4B5gO/NBsIhERkcTZ6ZFV27YbgEktmqqBP9u2XZPUVCIiIvsxy7LGbdd0HDDeRBYREZFEa+sSLWcBTwLFwDXEh+JutCxrqm3bU1OQT0REZH+0vvGnA+jHrs/hICIikvbaOsfkLqDUtu2QZVl3A2cRH577HqAiVEREJAls257cctmyrDdNZREREUm0torQmG3bFZZl9QZCtm0vB7AsK5z8aCIiIvsny7IOa7HYDTjYVBYREZFEa6sIdVuW5SY+IcJbAJZlFaBLtIiIiCRTy57QBuBOU0FEREQSra0i9BngS8AFDLYsqw/xWfr+mOxgIiIi+yvbtk83nUFERCRZ2ipCnwNiwDe2ba+0LKsb8cu23AI8lexwIiIi+yPLspYAecR7Qb2NzQ7ip8n0NhZMREQkAdqabe9Z4Bzgl5Zl/Zz4DH0vA4uTHUxERGQ/9hFwmW3bRwI/Aj4ADgeOMJpKREQkAdrqCS22bft4y7IygIVAADjdtu0vkx9NRERkv3WkbdvzAGzbXmpZ1sG2bQdMhxIREUmEtorQKgDbtoOWZTmBs23b9iU/loiIyH7Nb1nWr4GPgZOBrw3nERERSZjdufj1ehWgIiIiKXEp8QPBQ4CVwDVm44iIiCROWz2hR1mW9RzxyRCabgNg2/alSU0mIiKyf5sBhIHrgANRb6iIiOwj2ipCR7S4/ddkBhEREZFm04nPQv9j4AvgCeITBYqIiLR7Oy1Cbdueu6cvbFlWF+KTGZ1l2/ayPX0dERGR/VBHYBZwq23boyzLOtd0IBERkUTZnXNCd5llWR5gMlCfjNcXERHZx2UAdwALLcs6Esg1nEdERCRhklKEAhOID99dl6TXFxER2ZfdAXQBfgOcDtxoNo6IiEjitHVO6G6zLOtKYKNt229ZlnVPol9fRERkX2fb9kfAR42LfzGZRUREJNGS0RN6NXCWZVnvAccCz1iWdUAS1iMiIiIiIiLtTMJ7Qm3bPqXpdmMheoNt298lej0iIiIiIiLS/iTrnFARERHZTZZluS3LutCyrNNbtHW1LOsFk7lEREQSKeE9oS3Ztn1aMl9fRERkHzMdCAPdLMs6ClgFPAn80WgqERGRBEpqESoiIiK7pdi27eMty8ogfq3tAHC6bdtf7uxJlmU5gceBvo3Puda27eWtPOYN4FXbtv+alPQiIiK7QMNxRURE0kcVgG3bQeL76LPbKkAbXQB4bdseCIwBft/KYx4EChMVVEREZE+pCBUREUlP623b9u3iY08GZgPYtj0fOL7lnZZl/RiIAm8mNKGIiMge0HBcERGR9HGUZVnPAY4WtwGwbfvSnTyvA7ClxXLEsiy3bdthy7L6AJcCPwbGJSO0iIjI7lARKiIikj5GtLi9O+dtVgF5LZadtm2HG2+PAg4E/gUcAgQty1pt2/bsvQkqIiKyp1SEioiIpAnbtufu4VM/BM4DXrQsawCwtMVr/qLptmVZDwDfqQAVERGTVISKiIi0f68AZ1mW9RHxobxXWZZ1O7Dctu3XzEYTERHZlopQERGRds627Shww3bNy1p53AMpCSQiIrITmh1XREREREREUkZFqIiIiIiIiKSMilARERERERFJGRWhIiIiIiIikjIqQkVERERERCRlVISKiIiIiIhIyqgIFRERERERkZRRESoiIiIiIiIpoyJUREREREREUkZFqIiIiIiIiKSMilARERERERFJGRWhIiIiIiIikjIqQkVERERERCRlVISKiIiIiIhIyqgIFRERERERkZRRESoiIiIiIiIpoyJUREREREREUkZFqIiIiIiIiKSMilARERERERFJGRWhIiIiIiIikjIqQkVERERERCRl3Ml4UcuyXMAUwAIiwFW2ba9IxrpERERERESk/UhWT+h5ALZtDwLGAROTtB4RERERERFpR5JShNq2PRO4vnGxJ7A+GesRERERERGR9iUpw3EBbNsOW5b1NDAc+HGy1iMiIiIiIiLtR1InJrJt+wrgMGCKZVk5yVyXiIiIiOwZn6+esrIK3nprFWVlFfh89UbzzJxZzrBhL3HccX9j2LCXmDmz3GgegDFj3qNz5z/h9U6kc+c/MWbMe6YjpWWmdPzs0m37liQVoZZljbQs657GxTogSnyCIhERERFJI01f0AOBMEVFXgKBsNEv6jNnljNu3AfU1ITo2TOPmpoQ48Z9YLSYGTPmPSZOXEggEKFDBw+BQISJExcaLfrSMVM6fnbptn1LXLJ6Ql8GjrMs633gLeBW27YbkrQuERERkXYj3Xplysv9LFr0HWPHvs+ll77O2LHvs2jRd5SX+43kmTJlCZWV9cyb9y2vvrqKefO+pbKynilTlhjJA/Dkk0uJRmNUV4fZuDFAdXWYaDTGk08uNZrJ5YrR0BDG5wvQ0BDG5TKbacqUJeTmZuBywaZNDbhckJubYfSzKy/3k5PjISfHg8PhaL5tavuWuKScE2rbdi0wIhmvLSIiItJeNRWgOTkeioq81NXFe2VKS7tRWJhlJNMbbyzn6ac/JxaL4XQ6WLOmiiee+JRAIEJpabeU5/n44wo2bQo0L4dCsG5dHcFgRcqzNGmZp0kk0np7qvh8AaLRbfOEQhAMmsu0Zk0VXq+L+voY0Wh8e3K7HaxZYy6T399AUZF3m7bsbDeVleofMymp54SKiIiIyFbl5X4ikSirVvmZP38dq1bFl032ysyatZLq6gDV1QEqK+ubb8+atdJInh0VdiYLvnTUsgDdlfZU8Ho9bNrUgMMBHo8ThyPeI+r1eoxlKiiIH+xpqa4uTEGBdwfPkFRI2uy4IiIiIqb5fPWUl/vx+xsoKPBSUlJgrMcR4JtvqvjnP1dQVlZBdXWIvDwPpaXdGDq02EivI8DatVVs3hz6XrvLVWUgjewqlyve+9lauylHH92Jt95aRV1dmJwcN3V1YYLBCEcf3clYppKSAsrK4r3o2dnxTLW1Ifr0MZdJ1BMqIiIi+6h0nJDk3/9ew+zZq4hEYnTqlEkkEmP27FX8+99rjGXasqX1HsYdtUt68HpdOLf7Ju90xttN6du3C+effyher7uxB9TN+ecfSt++XYxlKizMorS0G5mZ8SG4mZluo8PfJU49oSIiIrJPajkhCdD8s7zcT2mpmS+g8+Z9S1aWm+zs+OQt2dkuQqEI8+Z9ayQPxM8jbOJwQCz2/XZJPz165LJq1Raysjx4PE5CoSj19SF69Mg1lunIIwsJBML069cVr9dFQ0OEzZsbOPLIQmOZoKkQVdGZTtQTKiIiIvskv7+B7Oxtj7dnZ7vx+81NSFJdHaJTpyycTgiFojid0KlTFtXV5io+h2Pr7aYCdPv2VNrRek3lAejcufXzB3fUngojRhxBx45ZRCIxamqCRCIxOnbMYsSII4xl6t//AHr2zCcSieH3B4hEYvTsmU///gcYyyTpST2hIiIisk9qmpCkqQcUzE9I0qtXPt9+W0OnTtnN5/Rt2lRHr175xjJ16OChqiqE2721yguHY3ToYGYymYKCTLZs2XbmV6cT8vMzjeQBOOGEA1iyZCMbNtQRDsdwux106ZJN376djWUaNqyYzEwXb765ko0b6+ncOYshQ3ozePAhxjIVFmZx1lk90+o8bElPKkJFRERkn5SOE5LceONxjB37PlVV9WRmugkEwsRiMW688ThjmW64oS+///0CYi26QV2ueLsJ119/NBMnLiAz04nH4yAUihEOR7n++qON5AG47rq+jBv3AcXFBXTsmMHmzUE2b27guuvMvEcQ3759vq784Ac9ttm+S0oKjGUCDX2VXaMiVERERPZJTROSlJf7qayM98r06dPJaK/MBReUADBlyhLWrauhe/c8rruub3O7CQ8/fBoATz65tHnG3muuObq5fX/PA9t+bl9/XU337rncdtvxRj+3dNy+RXaVo+VRr1SwLOsQYNWcOXPo0aNHStctIiL7nrVr13LmmWcC9LJte7XhOO2S9s0iIpJIbe2bNTGRiIiIiIiIpIyKUBEREREREUkZFaEiIiIiIiKSMipCRUREREREJGVUhIqIiIiIiEjKqAgVERERERGRlNF1QkVERERSyOerp7zcj98fv7ZjSUmB8Ws7zpxZ3uLapbnGr106Zsx7aXWd0HTNlG6fG6Tn9i3pRz2hIiIiIini89VTVlZBIBCmqMhLIBCmrKwCn6/eWKaZM8sZN+4DampC9OyZR01NiHHjPmDmzHIjecaMeY+JExcSCETo0MFDIBBh4sSFjBnznpE86Zop3T43SM/tW9KTilARERHZZzV9KX7rrVVp8WW4vNzPokXfMXbs+1x66euMHfs+ixZ9R3m531imKVOWUFlZz7x53/Lqq6uYN+9bKivrmTJliZE8Tz65lGg0RnV1mI0bA1RXh4lGYzz55FIjeZoyuVwxGhrC+HwBGhrCuFxmM02ZsoTc3AxcLti0qQGXC3JzM4x9bhDfvnNyPOTkeHA4HM23TW7fkp40HFdERET2ST5fPe+++zU+Xz2hUBSPx8nXX29h8OCexoYHvvHGcp544lNqa4NEIlBRUcPy5X4CgQilpd2MZPr44wo2bQo0L4dCsG5dHcFghZE8LbM0iURab08Vny9ANLptnlAIgkFzmdasqcLrdVFfHyMajeF0OnC7HaxZYy6T399AUZF3m7bsbDeVlQ2GEkm6Uk+oiIiI7JMWLFjP6tVVuFxOCgoycbmcrF5dxYIF641lev75Zfh8DTidDrxeB06nA5+vgeefX2Ys046KO5NFX7ppWYDuSnsqeL0eNm1qwOEAj8eJwxHvEfV6PcYyFRR4qasLb9NWVxemoMC7g2fI/ko9oSIiIpIQ6TYhyZdfVrJq1WamT1+H3x+goCCTk07qTmami7PPPsRIpnXragiHY1RVbf2i7nDE2yV9uVzx3s/W2k05+uhOvPXWKurqwuTkuKmrCxMMRjj66E7GMpWUFFBWFu9Bz86OZ6qtDdGnj7lMkp7UEyoiIiJ7LR0nJFmyZAOvvbacQCBCUVEmgUCE115bzpIlG4xlqq+PEItt2xaLxdslfXm9LpzbfWt2OuPtpvTt24Xzzz8Ur9fd2APq5vzzD6Vv3y7GMhUWZlFa2o3MzPgQ3MxMN6Wl3TQ7rnxPu+0JTbejremaSUREJBVaTkgCNP8sL/dTWmpmX/jZZ5vweNxkZ8cnb8nOdtHQEOGzzzYZyQNsU4A6HFuXty9MJb306JHLqlVbyMry4PE4CYWi1NeH6NEj11imI48sJBAI069fV7ze+La9eXMDRx5ZaCwTNBWi+v4rO9cui9Cmo605OR6KiuJjz8vKKoweafH56pk8eQnvv/8NlZX1FBVlccopB/HTn/Y1Woim4zWt0i2TrrElIrL30nFCkvr6MJ06ZRKJxAgG4xO3dOqUSX19uO0nJ4nLBeHG1bcsPE0O63Q6Wz+3cfuev1Tp3NnLxo3f3246dzZ3XuGIEUfwxBNLqK0NEQgEcbtddOyYxYgRRxjL1L//Afh8ATZvbsDvD+DxuOjZM5/+/Q8wlklkV7XLIrS83E8kEmXVKj/V1UHy8jIoKsoyerT1uee+5LHHFrJ5cz2RSHxnsnjxBvLyMvj5z/sZyTRmzHs88siC5uVAINC8bKroS7dMM2eWc8klrxJonHth8eJNzJmzmuef/5GxQtTnq+e++z7kn/9cQVVVkA4dMhg6tJhf/3qQ0UJUhbFI+rIsywk8DvQFAsC1tm0vb3H/bcAljYv/tG37V4nO0DQhSVMPKJifkOTgg/Pw+QLk5bkIhSJ4PPHeoq5dM41lKijIpLo6SCzmIBqN4nQ6cThi5OVlGMtUWJiJ3x9oLo4B3O54VhNOOOEAlizZyIYNdYTDMdxuB126ZNO3b2cjeQCGDSsmM9PFm2+uZOPGejp3zmLIkN4MHnyIsUyFhVmcdVZP7ZulXWqX54R+800VK1b4iVVV0ykjRDAYZcUKP998U2Us0x/+8Anr19c3/wEPh2H9+nr+8IdPjGVqWeztSnsqpFumUaPeaC5AmwQC8XZTHnmkjMcfX8zq1dX4fAFWr67m8ccX88gjZcYy+Xz13HXXXIYPf4Uf//hVhg9/hbvummv8envpdv0/EYMuALy2bQ8ExgC/b7rDsqzewGXAScBA4GzLso5JdICSkgJqa0PU1oaIxWLNt0tKChK9ql123XV9qa0NEo3G6NTJSzQao7Y2yHXX9TWW6ZprjiYahcxMJx07ZpKZ6SQajbebzORwOMjLc9O5cyZ5eW4cDoexTNdd15fCQi8DB3bn/PN7MXBgdwoLvUY/t5KSAvr168pDD53C9OnDeOihU+jXr6vR7Ru2noN5zjm9dO6ltCvtsgitqgridDoYMOsvXHDnMLps+Ran00FVVdBYptWrqwFwu52N12lybtMu6am6uvUhWTtqT4Xf/rb1gnxH7anwwAMfMmPGF9TVBcnMdFJXF2TGjC944IEPjWVKx0lQRAw6GZgNYNv2fOD4Fvd9A5xr23bEtu0o4AESPkY2HSckueCCEsaPP5ncXA9ff11Nbq6H8eNPNnrKxcMPn8btt/cnM9NFVVWIzEwXt9/e3+hpKemWKR0/t3TcvkXas3Y5HDcvz0N1dYBPfzCCQ+a/yRkPX8cLN08l74BexjLFYk3/Yo0TDcSa20Tau+efX0Z9fZT6+uj32h97bLCRTE3Dj+bN+5ZNmxro1MnLEUcUGR2WL2JQB2BLi+WIZVlu27bDtm2HgE2WZTmA3wH/tW37q2SESMcJSS64oMT4ef7be/jh04zPz7C9dMuUjp9bOm7fIu1VwotQy7I8wFPAIUAm8KBt268lch0HH5xPVpabykovr93wGMP/9FNGPHUrX02ZmcjV7JacHBfV1ZHvzXKXk2NwpgGRBGltgoidtafCF19s5OmnP8e2N1NXFyI724NldeSKK46itLSbsVw6d1YMqQLyWiw7bdtuHtJhWZaX+L65GrgxxdlERES2kYzhuJcDlbZt/wAYAvw50SsoKSnA5XLSq1c+vUecyZcPTSX329X0/eXVUFeX6NXtktNOOxiPB6LRGOFwjGg0hscTbxeRxHvllXIWLlxPNBqloCCDaDTKwoXreeWVcmOZNERYDPoQGApgWdYAYGnTHY09oK8CS2zb/qlt27ogpYiIGJWM4bh/B15qsZzwk+uaxuWXl/uprGyg4KTTqJ3yf+RdfTlcfDHMnAkeT9svlEA33dSPcDjGxx9XUFcXJjvbzYknduOmm8zMjAuQn5/Bli3fP082P9/cDHwiibJw4XoyMlxkZblxOCAry004HGPhwvXGMqXjdRJlv/EKcJZlWR8BDuAqy7JuB5YDLuBUINOyrCGNj7/Htu15ZqKKiMj+LuFFqG3bNQCWZeURL0Z/meh1QCvj8ksvhWAN/PSncPXV8PTTKb3AVf/+B3DFFX04//xDm6eB79jRa/RaTRdddCgzZiwjGIwSjcbfjowMJxdddKixTCKJEgxGGmdwpPmySHl5bmprzU0qlY7XSZT9Q+OEQzds17ysxW1z10kRERHZTlImJrIs6yDiR2Uft237uWSso1XXXw8bN8IvfwmdOsHEieBwpGTV6XitprFjB+LzBVm06Lvmc+b69TuAsWMHGss0dGhP/vnPr1ttNyEvL34ub2vtpsQntmq93ZSMDAi2Mvl0hsFO9YMOyuPbb2vo0MGL1xu/LFJVVQMHHZTX9pOTJB2vkygiIiKSbpIxMVFX4G3g57Ztz0n067dp7Nh4IfqHP0DnzvHlFEm3WdOKizsyYcKpzJ27loqKGrp1y+XUU3tQXNzRWKY33riYYcP+zptvfk0sFi+shgzpyRtvXGwkT1XVbXTo8Og2hWhenouqqtuM5AH45JPLOf74Z1ttN+U3vzmFu+56v9V2U2677QTGjHmP+voQLle8N9TtdnDbbScYy1RSUkBZWQUQ7wGtqwtTWxuiT59OxjKJiIiIpJtk9ISOBToC91mWdV9j2xDbtlMzM4fDEe8BrayEe++N94hef31KVp2Oios7Gi06W2Oq4NwRkwVna/r3P4AFCy7n5ZfL+fbbag48MI8LLywxOrT7zjtPBGDSpMX4fA0UFnoZPfrY5nYTRo48qjnT+vW1HHhgDqNHH9vcbsL3zlcv8NKnTyfNjisiIiLSQjLOCb0FuCXRr7tbnE546inw+WD0aCgqgosuMhpJZHf073+A0aKzNXfeeaLRorM1I0ceZbTobE26jYgQERERSTepm7kn1Twe+PvfYcAAuPRS+Ne/TCcSERERERHZ7+27RShAdja8/jocdhj86EewYIHpRCIiIiIiIvu1fbsIBejYEd56K35u6JAhYNumE4mIiIiIiOy39v0iFKB7d3j77fi5omefDWvXmk4kIiIiIiKyX9o/ilCAkhJ4803YvBnOOSc+e66IiIiIiIik1P5ThAL06wevvgrLl8MPfwi1taYTiYiIiIiI7Ff2ryIU4PTT4fnn4eOP45dtCQZNJxIREREREdlv7H9FKMDw4TB5cnzCoiuvhGjUdCIREREREZH9gtt0AGOuvRY2bYJ77oGiInjsMXA49uolfb56ysv9+P0NFBR4KSkpoLDQ7EXrZ84sZ8qUJaxbV0P37rlcd11fLrigxGimMWPe48knl1JdHSIvz8M11xzNww+fpjwtpOPnlo7bt4iIiIi0P/tvEQpw992wcSNMnAidO8O4cXv8Uj5fPe+++zU+Xz2hUBSPx8nXX29h8OCexr6oz5xZzujRb+P3NxCNxli2rJJFi9YDGCtoxox5j0ce2Xq91kAg0LxsovBLtzwQ/9wuuujV5g76xYs3MXv2av7xjx8Z+9x8vnpuvnkOs2evorY2RE6Oh3PP7cVjj51ptBBVYSwiIiLS/uyfw3GbOBzwu9/BqFFw//0wadIev9SCBetZvboKl8tJQUEmLpeT1aurWLBgfQID7557732fDRvqCYdjRCIQDsfYsKGee+9931imlgXfrrQnW7rlAfjJT1793gjxaDTebsqYMXOZPn0ZlZUBGhqiVFYGmD59GWPGzDWWyeer59FHF3DLLXO46aZ3ueWWOTz66AJ8vnpjmURERESkbft3TyjErx06dSr4fPCzn8WH5o4Ysdsv8+WXlRQUZJCVFX9Ls7LcxGIxvvyykrPPPiTBoXdNeflmYjFwOJw4nTFiMQexWJTy8s1G8siuaWjYvfZUmDLlsx22P/HEuSlOEzd16hL++McF1NREGrfzLXzxxUby8jz84hcDjGQCWLFiM3PnrqWiooZu3XI59dQeFBd3NJZHREREJN3s3z2hTTweePFFGDQILr8c3n7bdKKECIdp/HIODocDhyO+HA6bTiay9yZOXEh1dbwAhfi2XV0dYeLEhcYyrVixmcceW8Q773zNokXreeedr3nssUWsWKEDPyIiIiJN1BPaJCsLZs2CU0+FCy+EOXOgtHSXn37kkYX8978bcDgceL0uGhoi+P0BjjuuSxJD71xWlou6ugixWAyHw0Gs8dt6VpbLWCaRRFm/vvVhtztqT4W//93m/ffXsn59LfX1IbKyPHTtmkO3bjmMGWOud1bnzoqIiEg6UU9oSwUFMHs2dO0KQ4fCl1/u8lP79z+Anj3ziURi+P0BIpEYPXvm07//AUkMvHOlpQfgdkMkEiMQiBKJxHC74+0ikngvv/wVK1duJhaLkZ+fSSwWY+XKzbz88lfGMvl89ZSVVRAIhCkq8hIIhCkrq9C5syIiImKMekK3161bfDjuoEFw9tnw4Ydw8MFtPq2wMIuzzuqZVr0NP/tZP+rqIpSXb6ahIYLX66KkpCM/+1k/Y5lyclzU1kZabRdp71avriIjw4XXG//T6vW6CYejrF5dZSxTebmfnBwPOTkegOaf5eV+SkvVGyoiIiKppyK0NcXF8R7RU0+NF6IffACdOrX5tMLCrLT6Unf66Qfj9wf46qvNVFUF6NAhk8MO68jpp7ddVCfLjTceyx/+sJBQaGubxxNvNyEjA4LB1ttFdpfL5SAUihEOR3G7HYTDMWIxcLv37hrEXYBhXwAAIABJREFUe8Pvb6CoyLtNW3a2m8pKgzNdiYiIyH5NReiOHHts/BzRc86JD82dMwfy8kyn2i2FhVkMH16SVr2zY8YMoKYmzJtvrmTLliD5+RkMGdLb2Ply99xTyq9+VdZquyldumSxYcP3h0p26WLuc2ua1Kq1dlMyMyEQaL3dFMsq5KuvfESj0NAQwel0kpHh5LDDCo1lKijwUlcXbu4BBairC1NQ4N3Js0RERESSR0XozpxyCrzwQnyiogsvhNdfN/sNdw+kW+9sYWEWDz54Mldc0SctCuObbz6+sShe1ZxnyJBe3Hzz8UbyAEyefDYjR75OTc3WYcu5uS4mTz7bWKZf/OL4Vq+d+otfmHufbr219Uy33mo20913v0csFsPp9BCNRnE43EYzlZQUUFZWAcR7QOvqwtTWhujTp+3RHSIiIiLJoCK0LeefH7+O6FVXwciRMGMGuHT+4t5Ip8K4sDCLsWMHcPHFh6dFUQxwwQUlTJv2Q6ZMWcK6dTV0757Lddf15YILSoxlevjh0wB48smlVFeHyMvzcM01Rze3K1Nc02eUTp9d/PetG+Xlfior49t4nz6dNDuuiIiIGOOItTbGLoksyzoEWDVnzhx69OiR0nXvlQkT4K674IYb4PHHzY5DFBGRZmvXruXMM88E6GXb9mrDcdqldrtvFhGRtNTWvlk9obvqzjth40b47W+hc2cYP950IhERERERkXZHRejuePhh2LQJfv3r+Gy5N99sOpGIiIiIiEi7oiJ0dzgcMHky+Hxwyy3xQvTSS02nEhERERERaTecpgO0O253fHKiU0+FK66AN980nUhERERERKTdUBG6J7xeePVV6NMHLroI5s0znUhERERERKRd0HDcPZWfD7Nnw8knw7Bh8J//4OvWm/Jyf9pc6gNg4cLvePnlcr79tpoDD8zjwgtL6N//AGVqweerT7vPTURE9l0rVmxm7ty1VFTU0K1bLqee2oPi4o5GM91yy7s8/fTn1NaGyMnxcMUVR/HHPw42lmfQoGf56KPvmpdPOukAPvzwcmN5AIYPf5lZs1YSicSv1nfeeb155ZULjWaaNu1zJk1azPr1tXTtmsPo0ccycuRRRjPpe5XsChWhe6NrV3j7bRg0iOjgs/j0f5/H2bsXRUVe6urClJVVUFrazdgv3sKF3/HLX/6HjRvrCQYjfPbZJhYt+o4HH/yBsaJv4cLv+J//eZVVq6qJRsHphBde+IIXXviRkUw+Xz2DBj3LsmVbmtsOPzyfDz+83OgfTO3odo12dCLSlnT7O7FixWbGj5/Hl19WUlMTIDc3k7lzv2HcuIHGCtFbbnmXP/95MbEYxGJQVRXiz39eDGCkEN2+AAX46KPvGDToWWOF6PDhLzNz5kog/t0lEoGZM1cyfPjLxvbP06Z9zn33fUB+fgY9euTg9we5774PAIztn32+esrKKsjJ8aTN92FJTxqOu7d69YK33iJaW8fx915BxZIVzJ+/jlWr/EQiUcrL/cai/eUvi5g//zsWL97A0qWVLF68gfnzv+Mvf1lkLNO1185mxYp4AQoQjcKKFdVce+1sI3lOO23GNgUowLJlWzjttBlG8sDWHV0kEl9uuaMzZdq0zxk16k3mzatg5coq5s2rYNSoN5k27XNjmXy+em6++V2GDXuJCy54hWHDXuLmm9/F56s3lqkpV1lZBW+9tYqysgrjeUT2Z02/j4FAmKIiL4FA2Pjv5aRJi/noo7XEYjG6dMkmFovx0UdrmTRpsbFMU6d+SjQKbreDzEwHbreDaDTebkJTAepwbP3Xst2EWbPiBWhmphOPx0lmpnObdhMmTVpMfn4GnTpl4Xa76NQpi/z8DKPbUnm5n5wcDzk5HhwOR/Ntk9+HJT0lrSfUsqxS4BHbtk9L1jrSxtFH859fTOLk8VdxxoQbmXPvU1QH3axY4aehIUJpaTcjsWbNWonfH8DhiPemRaPg9weM/sFcvHjTbrUn29Klvt1qT4WmI6272p4Ko0a1PgHXqFFvGjvaevfdc5k+3W5ebmgIMH26TVaWhylTzjWSyeer56673uPNN1dRXR0kLy+DIUN68bvfnWb0CHC69QTJvivdtrXycj8ffPANs2atpLKynqKiLM47rzeFhVmUlprJNWfOGr77robly6ua23JzncyZs8ZIHoC6uviR4VAo1mq7KbFY249JlaYDw4FAtNV2E+Ijk7LYsiVAOBzD7XaQk+Nm/fpaY5n8/gaKirzbtGVnu6msbDCUSNJVUnpCLcv6BTAV8Lb12H3Fqu59mH31IxSt/Ypzf3UZB3/zKU6ng6qqoLFMTb/wGRlO3G4nGRnObdpF2rOpUz/brfZUuP/+D5kxwyYYjNCxYybBYIQZM2zuv/9DY5nSsSdI9k3puK299NIy/u//PqOhIUyXLlk0NIT5v//7jJdeWmYs01dfbaSmZttCpqYmyldfbTSUSNqrwsIsKirqiEZjjb3XMSoq6owe+CkoiA/BbamuLkxBwX5TEsguStZw3BWA2RPYUiwvz8PKIwYx+6Y/4Q7Uc86vR3HajN9Q6DS3820avtJ0JLHpZ1O7iCTWSy99RVaWi7y8DFwuJ3l5GWRluXjppa+MZdLQKEmVdNzWZs9eTVaWh/z8TNxuF/n5mWRleZg9e7WxTHV1u9cu6SE/37Nb7akwdGgv6urCVFeHiEZjVFeHqKsLM3RoL2OZSkoKqK0NUVsbIhaLNd8uKSkwlknSU1KKUNu2/wGEkvHa6ergg/MpLi5g43E/YPo9L/L5OaPoU/YqQ+88D1580ciYksLCTJxOiMViRCJRYrEYTme8XUQSr6YmSFaWa5u2rCwXNTXmRkT4/Q1kZ2975kV2thu/XyMiJLHScVurro7/TrY8xz4ry0V1tbnfSWmfioqyKCjYdvsuKHBTVGSu1/Gkkw7kxhuPJSvLw4YN9WRlebjxxmM56aQDjWWKD3XvRmZmfAhuZqZbkxJJqzQ7boKUlBTg89XTq1c+2UcVUXnCg3w09EJKn3oA/ud/4Jln4C9/gZ49U5bpppv68dBD84GmAjiG0+ngppv6pSzD9jp0cFNVFW61XaS9KyzMoro6QF6eE6czfh52XV04LYZG5eRsPVqvoVGSDOm4rXXvnovfH8DphFAoitvtJBp10L17rrFMLle8GG76G9H00+Vq+7n7i6b3yONxEIvFR3CFQjGj71HXrjnk5nro12/r3/NNm+rJyckwlqmgwMvppx/MD39Y3NxWWxsiM9PsdyqT51xL+6HZcROktSM/R1x+Nu4Fn8DEifDee3DkkfHb4e8XYckwbtwgxo4dQFFRNm63m6KibMaOHcC4cYNSsv7WbNly6/cKzg4d3GzZcquRPK+88qPdak+FI45ofcjKjtpTITe39T8VO2pPheLivN1qT4WbbjqOcDhKTU2IYDBCTU2IcDjKTTcdZyyThkZJqqTjtjZ69LHU1YUIhSLk53sIhSLU1YUYPfpYY5nOO683sG0B2rLdhBNO6LJb7cnW9F6EQjGi0VjzhEkm36PRo49ly5YgmzbVEw5H2LSpni1bgka3pXT8nRPZVY5YkoaJWpZ1CPC8bdsDWmlfNWfOHHr06JGUdaelr7+Gn/0M3ngD+vWDJ56A/v1NpxJg5sxypkxZwrp1NXTvnst11/XlggtKjGY68sipfPnl1vOojjiigC++uNZgIsjLm7jNZBq5uU6qq283mAgOPXQyK1ZUNy8XF+exfPlPDSaCCRM+ZtKkxfh8DRQWehk9+ljuvPNEo5nSbcbSRFu7di1nnnkmQC/btlcbjtMuJWrfnI7bWjpe4zgdrwV94onP8MknG5qXTzihCx9/PMpYnnR8j9JxW0rH3zkRaHvfnLQidEf22yIU4ueFvvQS3HwzbNgAt9wC48dDrrlhQSIi7Z2K0L23X++bRUQk4draN2s4bio5HHDxxfDll3D99fDoo3DUUfD666aTiYiIiIiIpISKUBMKCmDSJPjgg3gv6HnnwYgRUFFhOpmIiIiIiCRQWVkZAwcOZOTIkVx++eVccsklrFixYrdf54UXXiAU2vMLkIwcOXKP1ttk3bp1/Otf/9rj57ekItSkQYPgv/+FBx+E116DI46Av/516ywFIiIiIiLS7g0YMIBp06bx7LPP8vOf/5zf/va3u/0akydPJmqwTpg/fz6LFi1KyGvpuhimZWTAvffGe0J/+lMYPRqmTYtPXHSU2ZPdRUREREQksaqqqjjwwPj1XG3b5sEHHwSgoKCAhx56iFAoxK233kosFiMUCvGrX/2KTz/9lI0bN3Lbbbfx+OOPN7/WwoULeeSRR3C73XTo0IEJEybw9ttvs3LlSu68804CgQBDhgxp7sF87LHH2Lx5MxkZGc2F8PbrsiyLadOm8frrr+NwOBg6dCiXXXYZTzzxBA0NDRx33HFN53vuMRWh6aKkBObMiV9P9I474Ljj4Be/gF/+Ery6np+IiIiISEI88ww89VRiX/Pqq2HUjmeUnj9/PiNHjiQYDGLbNpMnTwbgvvvu46GHHuLQQw/l73//O1OnTuW4444jLy+P3//+9yxfvpyamhouvvhiJk2axKOPPrrN67777rucddZZXHPNNfzrX/+iqqpqpzHPPvtshg0bxvTp05k8eTIDBw783rqWL1/OP//5T5577jkcDgdXXnklJ598Mtdffz0rV67c6wIUVISmF4cDrrgChg6NF6K/+Q288AJMngxnnGE6nYiIiIiI7IEBAwY0F5ArV67kkksu4f3332fFihX86le/AiAUCtGrVy9OOeUUVq9ezY033ojb7Wb06NE7fN0bbriBv/71r1xxxRV07dqVY445Zpv7t78SyvHHHw9Av379mDt3Lnfffff31vXVV1+xbt06rrzySgC2bNnCmjVrEvVWACpC01PnzvEjNKNGwQ03wJlnxovTCROgUyfT6URERERE2q9Ro3baa5lsnVp8n+/VqxePPPII3bt3Z+HChWzcuJGysjK6dOnCU089xX//+18mTpzItGnTcDgc3zsndNasWQwfPpy7776byZMn8+KLL9KrVy82btwIwOeff77N45cuXUrXrl1ZsGABJSUlra7r3nvv5dBDD2Xq1Kk4HA7+9re/cdhhh/Hxxx8n7JxUFaHpbPBgWLo0PnHRb38Lb7wBEyfC5ZfHe01FRERERCTtNQ3HdTqd1NbWMmbMGLxeLw888AB33303kUgEgN/85jcUFBRw22238fTTT+N0OvnZz34GxHsxr7/+ep555hkcjbXA0UcfzZgxY8jOzsbj8TB+/Hjy8/OZMWMGP/nJTzjqqKPIyclpzvHuu+/y9NNPk5OTwyOPPEI0Gv3eug4//HAGDhzIT37yE4LBIMcccwxdu3blsMMOY9KkSRx11FEMGzZsr94Px/ZdtMmmC2LvoaVL4xMXzZsX7xn961/h0ENNpxIRMa6tC2JL27RvFhGRRGpr36xLtLQXRx8dv67o44/DJ5/El//3f2EvrhUkIiIiIiKSaipC2xOnM34Jly+/hGHDYOxY6Ncv3jsqIiJimM9XT1lZBW+9tYqysgp8vnrTkZg27XNOOmk6xcVPcNJJ05k27fO2n5Rkw4e/jNs9AYdjAm73BIYPf9l0JE488RkcjgnN/0488RmjedLxPUrHbSkdf+dEdoWK0Paoe3d46SV47TXYsgUGDYIbb4zfFhERMaDpy3AgEKaoyEsgEDb+pXjatM+5774PqK0N0qNHDrW1Qe677wOjxcPw4S8zc+ZKIpH4seVIBGbOXGm0yDrxxGf45JMN27R98skGY4VoOr5H6bgtpePvnMiuUhHanp13Hnz+Odx8c/wyLkccAf/4B6T4PF8RETHLsiynZVl/tSxrnmVZ71mWdeh2919nWdYCy7LmW5b1w2RkKC/3k5PjISfHg8PhaL5dXu5Pxup2yaRJi8nPz6BTpyzcbhedOmWRn5/BpEmLjWWaNWslEJ9fMBrdOs9gU7sJ2xegbbUnW8v3ouVEnCbfo0mTFpOT48bjcbJlSwiPx0lOjtvotpSOv3Miu0qz47Z3eXnwhz/EZ8y97jr48Y/h/PPhz3+Ggw4ynU5ERFLjAsBr2/ZAy7IGAL8HfgRgWdYBwM3A8YAX+MCyrHds2w4kMoDf38D8+d/yj3+UU1lZT1FRFhddVMKAAQcmcjW7Zf36Wny+Oj79tLK5raDATWFhtrFMjRNgNh8vbvrZ1C47fi9Mvkfr1tWQm+smGo3hdjuIRmM4HPF2U/z+BoqKvNu0ZWe7qaxsMJRIZNepCN1XHH98fMKiP/wB7r8fjjwSHnyQFUMuY+4HFVRU1NCtWy6nntqD4uKORqNeccXrvPiiTUNDDK/XwYgRFk8/nZQD87skL28iNTVbD7Xm5jqprr7dWB4Ah2PC99pisTsNJNkqHTMdfPAkvvmmtnn5oINyWLNmxxd0ToUJEz5m0qTF+HwNFBZ6GT36WO6880SjmXy+esrL/fj9DRQUeCkpKaCwMMtoJkm4k4HZALZtz7cs6/gW950IfNhYdAYsy1oOHAN8ksgAH374LU88sYQOHTLo0iWL2towkyYtIRKBc87plchV7bJNm+qoqgpv0+b3h4lG64zkkfYrLy+DuroQWVkeAFwuB/X1QfLyMoxlKijwUlcXJifH09xWVxemoMC7k2eJpAcNx92XuN1w553xIbo/+AHceive039A1rJPOeigXGprg0yf/gUrVmw2FvGKK17nmWeW0dAQP4LY0BDjmWeWccUVrxvJs30BClBTEyUvb6KRPNB6sbez9lRIx0zbF6AA33xTy8EHTzKUKF6A3nXX+6xcWYXfH2Tlyiruuut9Jkz42Fgmn6+eu+56j+HDX+Gii2YyfPgr3HXXe0bPGdJEGknRAWg5MUDEsiz3Du6rBvITHWD27FV4vW5yczNxu13k5mbi9bqZPXtVole1y7YvQNtql/SQk9N6H8mO2lPh3HN7UVsbwu8PEIlE8fsD1NaGOPdcMwdYAEpKCqitDVFbGyIWizXfLikpMJZJdqysrIyBAwcycuRIRo4cyYUXXsjNN99MMBg0HW2nZsyYwZ/+9KeEv656QvdFhxwCb7zBv0dPoPS5h/mfCaOoKzqAiCeToNND7OlMOKgQvN7k/cvM3HqiSwvPP78MgIwMJw5HfBhSMBjl+eeXGekN3b4Abatd0sf2BWhb7alw113v77DdVG/o/fd/yPPPLyM720NhoZf6+kjz8p/+NDjleZoK0JwcD0VF8aP4ZWUVlJZ2U+/s3qkC8losO23bDu/gvjwg4SeNVVbW0717NsFgjFAoitvtpHv3bNav10EG2T0lJQWsXOnf5mBBhw5uevc2V1z9+McWGRkuZs1awYYN9RQWZjFixOGcf765a7YXFmZRWtqN8nI/lZXxkS59+nTS39I0NmDAAB599NHm5TvuuIN//etfnHvuuQZTmaEidF/lcPDRQSez/pHXOGr2M2T71uMKBXCGAoSq6+gC4PdDQ0Pr/wIJOFUoM/N7xWlZsIoGPIRCbqI4iOEgDMSCDjj77Xjh6nDEp8Nrur27bbvx2Mf5lBgOYtD409GYC7jt25TnwenkRj7cLlMLkyc3f747+tyT0X4VHxNjB4/929/2fp17kO9SFn2vuTnjc8/t1Wvvcvt2bT9mybY5WnrppaS/J62pevafDHfFyHK6IQA4oc4VZsuzNpxdv0uvkcjcG5b56BGK4PW6CBV1wWH1AeITbJSW6ovTXvgQOA94sfGc0KUt7vsY+I1lWV4gEzgC+CzRAbp2jc8Y2qnT1s9x06Z6unbNSfSqdpnLFT+PMDNz68CvQCCKy2UsUlrKz3ezZUsYlyu+a4pG4+9bfr6Zr4lnntmTmpoghx3mJSfHTW1tGL+/gTPP7GkkD8QL45NPPpBzzjmE7Gw3dXXhtOh1jBei+tuZDMk+lSUYDLJhwwby81sfmPL2228zZcoU3G43Bx54IL/97W/ZtGkTd9xxBwAlJSWUl5czbdo0zjjjDN58800yMzOZMGECvXv35kc/+hHjxo3ju+++Y/PmzZxyyinceuutjBkzBr/fj9/vZ/LkyUydOpVPPvmEWCzGlVdeyZAhQ1iwYAEPPfQQ+fn5OJ1Ojj322IT9v5uoCN2HdeuWy8baIEsuvrm5bfPmBnJyMii++uidPzkahWBwx0XqHv5bbX+GlxDZRHA1lnxuYjiJQXV1vGu06V80uu3y3ra10n4htTiby0+afzqJwZNLdm89CfKXnd15g5np6Z/a2Z1XvZiqGNuYvrM7L3tuZ/cmzd93dufF01IVYxtPN92obuXO8yenMEnc4S1ux5xOlsz5guzcDppIY++9ApxlWdZHgAO4yrKs24Hltm2/ZlnWY8B/iJ+Gc69t2wl/w0ePPpb77vsAgIKCDPz+IFu2BI2eE33eeb2ZOXMlgUC0ubhqajdl8OAevPvu2lbbTbn99hMYP35ec/HpcMQL+NtvP8FIntGjj2Xjxjq+/NLHhg115OZmctJJBzJ6dOK/CO8q9TruX5I1amf+/PmMHDmSyspKnE4nI0aMYODAga0+9vXXX+fKK69k2LBhzJw5k5qaGh5//HHOO+88RowYwaxZsygvL9/huioqKjj22GO5+OKLCQQCzUUoxHtkr7zySubOncvatWt5/vnnCQQCjBgxgkGDBvG///u//P73v6dXr17cf//9e/z/3RkVofuwU0/twfTpXwCQn5/Bli1BNm9uYOjQXdj5Op1bezAT6JGvpzF//nqIsc0XggEDujJv3siErmtXHLCTcxpjVXsw6c5eFsXEYnTp/OfGYvj7/WkV60bvuOBNYnvPnq0XKw5irF51/d6tcw/zlRw2dbssW31lX7NXr71L7a20HdXn/3bUX8xnn16xV6+9p+3Dhv2D2tpgi4krYtTVxieyeP31ixK7zl147OefbyIYjJCV5SZcUEgkL5+62pAm0thLtm1HgRu2a17W4v4pwJRkZhg58iggfimLtWtr6do1hzvvPLG53YRXXrmQ4cNfZtas+DUnXa54AfrKKxcay/TOO5dw1lnPb1OIDh7cg3feucRYpnHjBgEwefIStmwJkp+fwU9/2re5PdWKizsybtxJzJ27Nq0mVlSv4/6j5eVvgOafeztqp2k47ubNm7n66qvp0WPHB5/uueceJk+ezIwZM+jduzeDBw9m7dq1XHJJ/G9FaWkpL774/Y6AWOM+t6CggKVLlzJ//nxyc3O3Ofe0V6/4ucxfffUVn3/+OSNHxr+Dh8Nh1q1bx/r165sf069fP9asWbPH/+cdURG6Dysu7shllx3J3Llr+eab+B/xoUN7G/0j/uyzP2T48Ff44gtf8xeCI48s5NlnzcyOO2rU4TzzzLJW2/dI0+HjvVCf26HVc1Jzc53QrdtevfaeWsNOtplDDklZjpaW03nHdx52WOqCtFB9UHGr56QedFAOHN3G6IMkOf2OMOPHf0RGyEVmppNAIEqQCOPuOAn69095nm6HbT26nJ3tpq5xIo0+fTqlPIsk3siRRxktOltjsuDcEZMF546MGzfIWNHZmuLijsaLTtl/JfvyNx07duR3v/sdo0aNYubMmXTp0uV7j3nhhRe46aabKCoqYty4cbzzzjtYlsXChQs5/PDD+eyzrWdVZGRksGHDBnr06MGyZcsoLi7m5ZdfJi8vj/Hjx/P111/z4osvNheojsZTZHr37k1paSm//vWviUajPP744/To0YPOnTuzYsUKiouLWbp06Q6HDO8NFaH7uHT7I15c3JFXXhmeNkc3myZDSqdLxlRX3552l42Jxe5Mu0u0pGOmNWtGp91lY5qGQqbLZWM0pE1ERNJdKi5/c+ihhzJy5EgefPBBHnvsse/df8wxx3DVVVdRUFBATk4Op512GmeccQZjxozhrbfe2qYwvPbaa7n++us58MAD6dChAwADBw7k9ttvZ+HChWRlZdGzZ082bNiwzTrOOOMMPv74Yy699FLq6uoYPHgwubm5/O53v+Puu+8mJyeHnJycpBShjtiOhk8liWVZhwCr5syZs9MuaBERkV2xdu1azjzzTIBetm2vNhynXdK+WURkq5bnhLaciCqdZnJfsWIFDzzwANOmmZlzoi1t7ZvVEyoiIiIiItIoVaN2gsEg11xzzffae/Xqxfjx4xO6rnSjIlRERERERKSFVExElZGRscc9mcXFxWnbC7ornG0/RERERERERCQxVISKiIiIiIhIyqgIFRERERERkZRRESoiIiIiIiIpk5SJiSzLcgKPA32BAHCtbdvLk7EuERERERERaT+S1RN6AeC1bXsgMAb4fZLWIyIiIiIiIu1IsorQk4HZALZtzweOT9J6REREREREpB1J1nVCOwBbWixHLMty27YdBlwA3333XZJWLSIi+5MW+xOXyRztnPbNIiKSMG3tm5NVhFYBeS2WnY0FKEA3gMsuuyxJqxYRkf1UN2CF6RDtlPbNIiKSDK3um5NVhH4InAe8aFnWAGBpi/s+AX4AVACRJK1fRET2Hy7iO7lPTAdpx7RvFhGRRNrpvtkRi8USvsYWs+MeAziAq2zbXpbwFYmIiIiIiEi7kpQiVERERERERKQ1yRqOu9+xLMsDPAUcAmQCD9q2/ZrRUGnMsqwuwELgLPWSt86yrHuA84EM4HHbtp80HCmtNP7OPU38dy4CXKdtaVuWZZUCj9i2fZplWYcCfwNiwGfAz2zbjprMJ5Js2jfvHu2b26Z9885p39w27ZvjknWJlv3R5UClbds/AIYAfzacJ201/oGaDNSbzpKuLMs6DTgJGAScChxkNFB6Ggq4bds+CRgP/MZwnrRiWdYvgKmAt7FpIvDLxr9RDuBHprKJpJD2zbtI++a2ad+8S7Rv3gntm7dSEZo4fwfua7Ec3tEDhQnAX4F1poOksXOIT+j1CjALeN1snLT0FeBuPAe9AxAynCfdrAAubLHcH5jjLgXrAAAEa0lEQVTbePtNYHDKE4mknvbNu0775rZp39w27Zt3TvvmRipCE8S27Rrbtqsty8oDXgJ+aTpTOrIs60pgo23bb5nOkuY6AccDFwM3ANMty3KYjZR2aogP91kGTAEeM5omzdi2/Q+23fk7bNtumgSgGshPfSqR1NK+eddo37zLtG9um/bNO6F981YqQhPIsqyDgH8D02zbfs50njR1NXCWZVnvwf+3d38hUpVhHMe/RpYlQkJW3hVEvy6KhCCC8A+kQhAIVleFFAUFBmYFgtCl2B8wugoywsSLUrqJjLJCySAwMu/0uSgiErzI7A+FbOZ2cSZ2FbfZabYzJ/f7gWWHnT3vPGdg+PGc877zsgTYmeS60ZbUSSeBD6tqrKoKOA0sGnFNXbOR5j26CbgNeDPJvD7HzGaT15gsAH4aVSFSm8zmaTGbp8ds7s9sHsyszWa/mGiGJLkW2Ac8WVWfjLqerqqqZX8/7oXdE1V1YnQVddZnwIYk22j2WJpPE36acIqJq4k/AnNp9qTShX2VZEVVHaBZG7d/xPVI/zmzeXrM5mkzm/szmwcza7PZJnTmbAYWAs8l+Xv9yT1V5QJ/Dayq3kuyDDhEM2NhfVW5gfy5XgbeSHKQ5lsKN1fVbyOuqcueAbYnuQw4SjM1UbrYmc2aMWbztJjNg5m12ew+oZIkSZKk1rgmVJIkSZLUGptQSZIkSVJrbEIlSZIkSa2xCZUkSZIktcYmVJIkSZLUGrdokYbU29B7a1U9kuTjqlp53vMHgCuB3yf9eXVVjQ3wGrcCC6vq05moWZKki5nZLHWbTag0vDuBL5LMB36d4n/WVdWxIV7jPuAEYNBJktSf2Sx1mE2oNIQke4C7gO+A9cClSe6vqr6bDSdZDmwB/gS+Bh4HrgBeB64Crga2A+8CDwNjSQ4Du4Gbq+p0kueBY8C3wAvAGPBar57zx74B2AH8AZyhCd/jw74HkiR1idksdZ9rQqUhVNUDwBFgKfA28NgUIbczyYHez6NJ5tCE2NqqWg4cpwmzG4G3qmo1cC/wdC+MdgDbqurQP5Qzr6qWArumGHsV8CWwkiYEFw518pIkdZDZLHWfd0KlISR5B7gD+Ai4BViV5JULhN05U36SXAMsBnYngeYq6z5gL/BUkrXAL8DcPiXMmfS4er8XTTH2FmAT8AHwM7B5oJOVJOl/wGyWus87odJwtgLbq2oFcKSqlk5nug/wA/A9sKZ37BZgP/As8HlVPQTsYSLIzjLxeT0NLO5dsV0yacyzfcZeAxysqrt7Y28a+GwlSeo+s1nqOO+ESsO5HTic5Hrgm+keVFVnk2wA9ia5hObK6jpgHHg1yYPASeBMkstppuq8lOQo8CLwPs1ak1MDjL0A2JXkDE0obvx3pyxJUqeZzVLHzRkfHx91DZIkSZKkWcLpuJIkSZKk1tiESpIkSZJaYxMqSZIkSWqNTagkSZIkqTU2oZIkSZKk1tiESpIkSZJaYxMqSZIkSWqNTagkSZIkqTV/ASDFInbg2NgHAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1152x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize = (16,6))\n",
    "ax = fig.add_subplot(1, 2, 1)\n",
    "\n",
    "ax.scatter(df.numb_features,df.RSS, alpha = .2, color = 'darkblue')\n",
    "ax.set_xlabel('# Features')\n",
    "ax.set_ylabel('RSS')\n",
    "ax.set_title('RSS - Best subset selection')\n",
    "ax.plot(df.numb_features,df.min_RSS,color = 'r', label = 'Best subset')\n",
    "ax.legend()\n",
    "\n",
    "ax = fig.add_subplot(1, 2, 2)\n",
    "ax.scatter(df.numb_features,df.R_squared, alpha = .2, color = 'darkblue')\n",
    "ax.plot(df.numb_features,df.max_R_squared,color = 'r', label = 'Best subset')\n",
    "ax.set_xlabel('# Features')\n",
    "ax.set_ylabel('R squared')\n",
    "ax.set_title('R_squared - Best subset selection')\n",
    "ax.legend()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x1440 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize = (20,20))\n",
    "ax = fig.add_subplot(1, 1, 1)\n",
    "ax.scatter(df.numb_features, df.RSS/10000000, alpha = .1, color = 'darkblue')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='forward'></a>\n",
    "## Forward stepwise selection\n",
    "For computational reasons, the best subset cannot be applied for any large n due to the 2^n complexity. \n",
    "\n",
    "Forward Stepwise begins with a model containing no predictors, and then adds predictors to the model, one at the time. \n",
    "\n",
    "At each step, the variable that gives the greatest additional improvement to the fit is added to the model.\n",
    "\n",
    "### Algorithm\n",
    "Let M0 denote the null model which contains no predictors\n",
    "\n",
    "- For k=1,2,...,n−1\n",
    "    - Consider all n−k models that augment the predictors in Mk with one additional predictor\n",
    "    - Choose the 'best' among these n−k models, and call it Mk+1\n",
    "- Select the single best model among M0,M1,...,Mn using cross validated predicton error, Cp, BIC, adjusted R2 or any other method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Initialization variables\n",
    "Y = credit.Balance\n",
    "X = credit.drop(columns = 'Balance', axis = 1)\n",
    "k = 11\n",
    "\n",
    "remaining_features = list(X.columns.values)\n",
    "features = []\n",
    "RSS_list, R_squared_list = [np.inf], [np.inf] #Due to 1 indexing of the loop...\n",
    "features_list = dict()\n",
    "\n",
    "for i in range(1,k+1):\n",
    "    best_RSS = np.inf    \n",
    "    for combo in itertools.combinations(remaining_features,1):\n",
    "        RSS = fit_linear_reg(X[list(combo) + features],Y)   #Store temp result \n",
    "        if RSS[0] < best_RSS:\n",
    "            best_RSS = RSS[0]\n",
    "            best_R_squared = RSS[1] \n",
    "            best_feature = combo[0]\n",
    "\n",
    "    #Updating variables for next loop\n",
    "    features.append(best_feature)\n",
    "    remaining_features.remove(best_feature)\n",
    "    \n",
    "    #Saving values for plotting\n",
    "    RSS_list.append(best_RSS)\n",
    "    R_squared_list.append(best_R_squared)\n",
    "    features_list[i] = features.copy()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Displaying results of the first 4 steps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Forward stepwise subset selection\n",
      "Number of features | Features | RSS\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[(1, ['Rating'], 21435122.0),\n",
       " (2, ['Rating', 'Income'], 10532541.0),\n",
       " (3, ['Rating', 'Income', 'Student_Yes'], 4227219.0),\n",
       " (4, ['Rating', 'Income', 'Student_Yes', 'Limit'], 4032502.0)]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print('Forward stepwise subset selection')\n",
    "print('Number of features |', 'Features |', 'RSS')\n",
    "display([(i,features_list[i], round(RSS_list[i])) for i in range(1,5)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='compare'></a>\n",
    "## Comparing models: AIC, BIC, Mallows'CP\n",
    "The training set Mean Squared Error (MSE) is generally an underestimate of the test MSE. This is because when we fit a model to the training data using least squares, we specifically estimate the regression coefficients such that the training RSS is minimized. In particular, the training RSS decreases as we add more features to the model, but the test error may not. Therefore the training RSS and $R^2$ may not be used for selecting the best model unless we adjust for this underestimation. \n",
    "\n",
    "###  Theoretical justification\n",
    "$C_p$, AIC, BIC all have rigorous theoretical justification that rely on asymptotic arguments, i.e. when the sample size $m$ grows very large, whereas the adjusted $R^2$, although quite intuitive, is not as well motivated in statistical theory. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Combining forward stepwise results into a new DataFrame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "df1 = pd.concat([pd.DataFrame({'features':features_list}), pd.DataFrame({'RSS':RSS_list, 'R_squared': R_squared_list})], axis=1, join='inner')\n",
    "df1['numb_features'] = df1.index"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Computing the C_p, AIC, BIC and R-square adjusted\n",
    "### Estimation of $\\hat\\sigma^2$\n",
    "Using the RSS of the full model with $p$ features, (i.e.the smallest RSS) we estimate $\\hat\\sigma^2$ as: $$ \\hat\\sigma^2 = \\frac{RSS}{m - p -1} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "# sample number\n",
    "m = len(Y)\n",
    "# predictor number\n",
    "p = 11\n",
    "hat_sigma_squared = min(df1['RSS']) / (m - p -1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9759.613893499438"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hat_sigma_squared"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Mallow's $C_p$\n",
    "Mallow's $C_p$ is named after Colin Lingwood Mallows and is defined as: $$ C_p = \\frac{1}{m} (RSS + 2d\\hat\\sigma^2)$$ where $\\hat\\sigma^2$ is an estimate of the variance of the error $\\epsilon$ associated with each response measurement. Typically $\\hat\\sigma^2$ is estimated using the full model containing all predictors. Essentially,the $C_p$ statistic adds a penalty of $2d\\hat\\sigma^2$ to the training RSS in order to adjust for the fact that the training error tends to underestimate the test error. Clearly, the penalty increases as the number of predictors in the model increases, and this is intended to adjust for the corresponding decrease in training RSS. It can be shown that if $\\hat\\sigma^2$ is an unbiased estimate of $\\sigma^2$ then $C_p$ is an unbiased estimate of the test MSE, so we choose the model with the smallest $C_p$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "df1['C_p'] = (1/m) * (df1['RSS'] + 2 * df1['numb_features'] * hat_sigma_squared )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "        vertical-align: middle;\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>features</th>\n",
       "      <th>RSS</th>\n",
       "      <th>R_squared</th>\n",
       "      <th>numb_features</th>\n",
       "      <th>C_p</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>[Rating]</td>\n",
       "      <td>2.143512e+07</td>\n",
       "      <td>0.745848</td>\n",
       "      <td>1</td>\n",
       "      <td>53636.603151</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>[Rating, Income]</td>\n",
       "      <td>1.053254e+07</td>\n",
       "      <td>0.875118</td>\n",
       "      <td>2</td>\n",
       "      <td>26428.949364</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>[Rating, Income, Student_Yes]</td>\n",
       "      <td>4.227219e+06</td>\n",
       "      <td>0.949879</td>\n",
       "      <td>3</td>\n",
       "      <td>10714.442485</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>[Rating, Income, Student_Yes, Limit]</td>\n",
       "      <td>4.032502e+06</td>\n",
       "      <td>0.952188</td>\n",
       "      <td>4</td>\n",
       "      <td>10276.446437</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>[Rating, Income, Student_Yes, Limit, Cards]</td>\n",
       "      <td>3.866091e+06</td>\n",
       "      <td>0.954161</td>\n",
       "      <td>5</td>\n",
       "      <td>9909.218362</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>[Rating, Income, Student_Yes, Limit, Cards, Age]</td>\n",
       "      <td>3.821620e+06</td>\n",
       "      <td>0.954688</td>\n",
       "      <td>6</td>\n",
       "      <td>9846.837591</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>[Rating, Income, Student_Yes, Limit, Cards, Ag...</td>\n",
       "      <td>3.810759e+06</td>\n",
       "      <td>0.954817</td>\n",
       "      <td>7</td>\n",
       "      <td>9868.483418</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>[Rating, Income, Student_Yes, Limit, Cards, Ag...</td>\n",
       "      <td>3.804746e+06</td>\n",
       "      <td>0.954888</td>\n",
       "      <td>8</td>\n",
       "      <td>9902.248962</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>[Rating, Income, Student_Yes, Limit, Cards, Ag...</td>\n",
       "      <td>3.798367e+06</td>\n",
       "      <td>0.954964</td>\n",
       "      <td>9</td>\n",
       "      <td>9935.100415</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>[Rating, Income, Student_Yes, Limit, Cards, Ag...</td>\n",
       "      <td>3.791345e+06</td>\n",
       "      <td>0.955047</td>\n",
       "      <td>10</td>\n",
       "      <td>9966.344067</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>[Rating, Income, Student_Yes, Limit, Cards, Ag...</td>\n",
       "      <td>3.786730e+06</td>\n",
       "      <td>0.955102</td>\n",
       "      <td>11</td>\n",
       "      <td>10003.604241</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                             features           RSS  \\\n",
       "1                                            [Rating]  2.143512e+07   \n",
       "2                                    [Rating, Income]  1.053254e+07   \n",
       "3                       [Rating, Income, Student_Yes]  4.227219e+06   \n",
       "4                [Rating, Income, Student_Yes, Limit]  4.032502e+06   \n",
       "5         [Rating, Income, Student_Yes, Limit, Cards]  3.866091e+06   \n",
       "6    [Rating, Income, Student_Yes, Limit, Cards, Age]  3.821620e+06   \n",
       "7   [Rating, Income, Student_Yes, Limit, Cards, Ag...  3.810759e+06   \n",
       "8   [Rating, Income, Student_Yes, Limit, Cards, Ag...  3.804746e+06   \n",
       "9   [Rating, Income, Student_Yes, Limit, Cards, Ag...  3.798367e+06   \n",
       "10  [Rating, Income, Student_Yes, Limit, Cards, Ag...  3.791345e+06   \n",
       "11  [Rating, Income, Student_Yes, Limit, Cards, Ag...  3.786730e+06   \n",
       "\n",
       "    R_squared  numb_features           C_p  \n",
       "1    0.745848              1  53636.603151  \n",
       "2    0.875118              2  26428.949364  \n",
       "3    0.949879              3  10714.442485  \n",
       "4    0.952188              4  10276.446437  \n",
       "5    0.954161              5   9909.218362  \n",
       "6    0.954688              6   9846.837591  \n",
       "7    0.954817              7   9868.483418  \n",
       "8    0.954888              8   9902.248962  \n",
       "9    0.954964              9   9935.100415  \n",
       "10   0.955047             10   9966.344067  \n",
       "11   0.955102             11  10003.604241  "
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Akaike's Information Criteria (AIC)\n",
    "The AIC criterion is defiend for a large class of models fit by maximum likelihood. In the case of a linear model with Gaussian errors, MLE and least squares are the same thing and the AIC is given by $$ AIC = \\frac{1}{m\\hat \\sigma^2} (RSS + 2d\\hat\\sigma^2)$$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "df1['AIC'] = (1/(m*hat_sigma_squared)) * (df1['RSS'] + 2 * df1['numb_features'] * hat_sigma_squared )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bayesian Information Criteria (BIC)\n",
    "BIC is derived from a Bayesian point of view, and looks similar to the $C_p$ and $AIC$ - it is defined (up to irrelevant constants) as: $$ BIC = \\frac{1}{m\\hat \\sigma^2} (RSS + \\log(m) d \\hat\\sigma^2)$$ Like $C_p$ and AIC, the BIC will tend to take small values for a model with low test error. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "df1['BIC'] = (1/(m*hat_sigma_squared)) * (df1['RSS'] +  np.log(m) * df1['numb_features'] * hat_sigma_squared )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Adjusted $R^2$\n",
    "Since the $R^2$ always increases as more variables are added, the adjusted $R^2$ accounts for that fact and introduces a penalty. The intuition is that once all the correct variables have been included in the model,additional _noise_ variables will lead to a very small decrase in RSS, but an increase in $k$ and hence will decrease the adjusted $R^2$. In effect, we pay a price for the inclusion of unnecessary variables in the model. $$ R_{a}^2 = 1 - \\frac{RSS / (m - k -1)}{TSS / (m - 1)} = 1 - (1 - R^2) \\frac{m - 1}{m - k - 1} $$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "df1['R_squared_adj'] = 1 - ( (1 - df1['R_squared'])*(m-1)/(m-df1['numb_features'] -1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>features</th>\n",
       "      <th>RSS</th>\n",
       "      <th>R_squared</th>\n",
       "      <th>numb_features</th>\n",
       "      <th>C_p</th>\n",
       "      <th>AIC</th>\n",
       "      <th>BIC</th>\n",
       "      <th>R_squared_adj</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>[Rating]</td>\n",
       "      <td>2.143512e+07</td>\n",
       "      <td>0.745848</td>\n",
       "      <td>1</td>\n",
       "      <td>53636.603151</td>\n",
       "      <td>5.495771</td>\n",
       "      <td>5.505750</td>\n",
       "      <td>0.745210</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>[Rating, Income]</td>\n",
       "      <td>1.053254e+07</td>\n",
       "      <td>0.875118</td>\n",
       "      <td>2</td>\n",
       "      <td>26428.949364</td>\n",
       "      <td>2.707991</td>\n",
       "      <td>2.727949</td>\n",
       "      <td>0.874489</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>[Rating, Income, Student_Yes]</td>\n",
       "      <td>4.227219e+06</td>\n",
       "      <td>0.949879</td>\n",
       "      <td>3</td>\n",
       "      <td>10714.442485</td>\n",
       "      <td>1.097835</td>\n",
       "      <td>1.127771</td>\n",
       "      <td>0.949499</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>[Rating, Income, Student_Yes, Limit]</td>\n",
       "      <td>4.032502e+06</td>\n",
       "      <td>0.952188</td>\n",
       "      <td>4</td>\n",
       "      <td>10276.446437</td>\n",
       "      <td>1.052956</td>\n",
       "      <td>1.092871</td>\n",
       "      <td>0.951703</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>[Rating, Income, Student_Yes, Limit, Cards]</td>\n",
       "      <td>3.866091e+06</td>\n",
       "      <td>0.954161</td>\n",
       "      <td>5</td>\n",
       "      <td>9909.218362</td>\n",
       "      <td>1.015329</td>\n",
       "      <td>1.065222</td>\n",
       "      <td>0.953579</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>[Rating, Income, Student_Yes, Limit, Cards, Age]</td>\n",
       "      <td>3.821620e+06</td>\n",
       "      <td>0.954688</td>\n",
       "      <td>6</td>\n",
       "      <td>9846.837591</td>\n",
       "      <td>1.008937</td>\n",
       "      <td>1.068809</td>\n",
       "      <td>0.953996</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>[Rating, Income, Student_Yes, Limit, Cards, Ag...</td>\n",
       "      <td>3.810759e+06</td>\n",
       "      <td>0.954817</td>\n",
       "      <td>7</td>\n",
       "      <td>9868.483418</td>\n",
       "      <td>1.011155</td>\n",
       "      <td>1.081006</td>\n",
       "      <td>0.954010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>[Rating, Income, Student_Yes, Limit, Cards, Ag...</td>\n",
       "      <td>3.804746e+06</td>\n",
       "      <td>0.954888</td>\n",
       "      <td>8</td>\n",
       "      <td>9902.248962</td>\n",
       "      <td>1.014615</td>\n",
       "      <td>1.094444</td>\n",
       "      <td>0.953965</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>[Rating, Income, Student_Yes, Limit, Cards, Ag...</td>\n",
       "      <td>3.798367e+06</td>\n",
       "      <td>0.954964</td>\n",
       "      <td>9</td>\n",
       "      <td>9935.100415</td>\n",
       "      <td>1.017981</td>\n",
       "      <td>1.107789</td>\n",
       "      <td>0.953924</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>[Rating, Income, Student_Yes, Limit, Cards, Ag...</td>\n",
       "      <td>3.791345e+06</td>\n",
       "      <td>0.955047</td>\n",
       "      <td>10</td>\n",
       "      <td>9966.344067</td>\n",
       "      <td>1.021182</td>\n",
       "      <td>1.120969</td>\n",
       "      <td>0.953891</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>[Rating, Income, Student_Yes, Limit, Cards, Ag...</td>\n",
       "      <td>3.786730e+06</td>\n",
       "      <td>0.955102</td>\n",
       "      <td>11</td>\n",
       "      <td>10003.604241</td>\n",
       "      <td>1.025000</td>\n",
       "      <td>1.134765</td>\n",
       "      <td>0.953829</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                             features           RSS  \\\n",
       "1                                            [Rating]  2.143512e+07   \n",
       "2                                    [Rating, Income]  1.053254e+07   \n",
       "3                       [Rating, Income, Student_Yes]  4.227219e+06   \n",
       "4                [Rating, Income, Student_Yes, Limit]  4.032502e+06   \n",
       "5         [Rating, Income, Student_Yes, Limit, Cards]  3.866091e+06   \n",
       "6    [Rating, Income, Student_Yes, Limit, Cards, Age]  3.821620e+06   \n",
       "7   [Rating, Income, Student_Yes, Limit, Cards, Ag...  3.810759e+06   \n",
       "8   [Rating, Income, Student_Yes, Limit, Cards, Ag...  3.804746e+06   \n",
       "9   [Rating, Income, Student_Yes, Limit, Cards, Ag...  3.798367e+06   \n",
       "10  [Rating, Income, Student_Yes, Limit, Cards, Ag...  3.791345e+06   \n",
       "11  [Rating, Income, Student_Yes, Limit, Cards, Ag...  3.786730e+06   \n",
       "\n",
       "    R_squared  numb_features           C_p       AIC       BIC  R_squared_adj  \n",
       "1    0.745848              1  53636.603151  5.495771  5.505750       0.745210  \n",
       "2    0.875118              2  26428.949364  2.707991  2.727949       0.874489  \n",
       "3    0.949879              3  10714.442485  1.097835  1.127771       0.949499  \n",
       "4    0.952188              4  10276.446437  1.052956  1.092871       0.951703  \n",
       "5    0.954161              5   9909.218362  1.015329  1.065222       0.953579  \n",
       "6    0.954688              6   9846.837591  1.008937  1.068809       0.953996  \n",
       "7    0.954817              7   9868.483418  1.011155  1.081006       0.954010  \n",
       "8    0.954888              8   9902.248962  1.014615  1.094444       0.953965  \n",
       "9    0.954964              9   9935.100415  1.017981  1.107789       0.953924  \n",
       "10   0.955047             10   9966.344067  1.021182  1.120969       0.953891  \n",
       "11   0.955102             11  10003.604241  1.025000  1.134765       0.953829  "
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Find a best model based on a Adjusted $R^2$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7\n",
      "0.9540098163629882\n"
     ]
    }
   ],
   "source": [
    "print(df1['R_squared_adj'].idxmax())\n",
    "print(df1['R_squared_adj'].max())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting the computed values as a function of number of features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x432 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "variables = ['C_p', 'AIC','BIC','R_squared_adj']\n",
    "fig = plt.figure(figsize = (18,6))\n",
    "\n",
    "for i,v in enumerate(variables):\n",
    "    ax = fig.add_subplot(1, 4, i+1)\n",
    "    ax.plot(df1['numb_features'],df1[v], color = 'lightblue')\n",
    "    ax.scatter(df1['numb_features'],df1[v], color = 'darkblue')\n",
    "    if v == 'R_squared_adj':\n",
    "        ax.plot(df1[v].idxmax(),df1[v].max(), marker = 'x', markersize = 20)\n",
    "    else:\n",
    "        ax.plot(df1[v].idxmin(),df1[v].min(), marker = 'x', markersize = 20)\n",
    "    ax.set_xlabel('Number of predictors')\n",
    "    ax.set_ylabel(v)\n",
    "\n",
    "fig.suptitle('Forward stepwise selection using C_p, AIC, BIC, Adjusted R2', fontsize = 16)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lab 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Index: 263 entries, -Alan Ashby to -Willie Wilson\n",
      "Data columns (total 20 columns):\n",
      "AtBat        263 non-null int64\n",
      "Hits         263 non-null int64\n",
      "HmRun        263 non-null int64\n",
      "Runs         263 non-null int64\n",
      "RBI          263 non-null int64\n",
      "Walks        263 non-null int64\n",
      "Years        263 non-null int64\n",
      "CAtBat       263 non-null int64\n",
      "CHits        263 non-null int64\n",
      "CHmRun       263 non-null int64\n",
      "CRuns        263 non-null int64\n",
      "CRBI         263 non-null int64\n",
      "CWalks       263 non-null int64\n",
      "League       263 non-null object\n",
      "Division     263 non-null object\n",
      "PutOuts      263 non-null int64\n",
      "Assists      263 non-null int64\n",
      "Errors       263 non-null int64\n",
      "Salary       263 non-null float64\n",
      "NewLeague    263 non-null object\n",
      "dtypes: float64(1), int64(16), object(3)\n",
      "memory usage: 43.1+ KB\n"
     ]
    }
   ],
   "source": [
    "# In R, I exported the dataset from package 'ISLR' to a csv file.\n",
    "df = pd.read_csv('Data/Hitters.csv', index_col=0).dropna()\n",
    "df.index.name = 'Player'\n",
    "df.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AtBat</th>\n",
       "      <th>Hits</th>\n",
       "      <th>HmRun</th>\n",
       "      <th>Runs</th>\n",
       "      <th>RBI</th>\n",
       "      <th>Walks</th>\n",
       "      <th>Years</th>\n",
       "      <th>CAtBat</th>\n",
       "      <th>CHits</th>\n",
       "      <th>CHmRun</th>\n",
       "      <th>CRuns</th>\n",
       "      <th>CRBI</th>\n",
       "      <th>CWalks</th>\n",
       "      <th>League</th>\n",
       "      <th>Division</th>\n",
       "      <th>PutOuts</th>\n",
       "      <th>Assists</th>\n",
       "      <th>Errors</th>\n",
       "      <th>Salary</th>\n",
       "      <th>NewLeague</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Player</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>-Alan Ashby</th>\n",
       "      <td>315</td>\n",
       "      <td>81</td>\n",
       "      <td>7</td>\n",
       "      <td>24</td>\n",
       "      <td>38</td>\n",
       "      <td>39</td>\n",
       "      <td>14</td>\n",
       "      <td>3449</td>\n",
       "      <td>835</td>\n",
       "      <td>69</td>\n",
       "      <td>321</td>\n",
       "      <td>414</td>\n",
       "      <td>375</td>\n",
       "      <td>N</td>\n",
       "      <td>W</td>\n",
       "      <td>632</td>\n",
       "      <td>43</td>\n",
       "      <td>10</td>\n",
       "      <td>475.0</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-Alvin Davis</th>\n",
       "      <td>479</td>\n",
       "      <td>130</td>\n",
       "      <td>18</td>\n",
       "      <td>66</td>\n",
       "      <td>72</td>\n",
       "      <td>76</td>\n",
       "      <td>3</td>\n",
       "      <td>1624</td>\n",
       "      <td>457</td>\n",
       "      <td>63</td>\n",
       "      <td>224</td>\n",
       "      <td>266</td>\n",
       "      <td>263</td>\n",
       "      <td>A</td>\n",
       "      <td>W</td>\n",
       "      <td>880</td>\n",
       "      <td>82</td>\n",
       "      <td>14</td>\n",
       "      <td>480.0</td>\n",
       "      <td>A</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-Andre Dawson</th>\n",
       "      <td>496</td>\n",
       "      <td>141</td>\n",
       "      <td>20</td>\n",
       "      <td>65</td>\n",
       "      <td>78</td>\n",
       "      <td>37</td>\n",
       "      <td>11</td>\n",
       "      <td>5628</td>\n",
       "      <td>1575</td>\n",
       "      <td>225</td>\n",
       "      <td>828</td>\n",
       "      <td>838</td>\n",
       "      <td>354</td>\n",
       "      <td>N</td>\n",
       "      <td>E</td>\n",
       "      <td>200</td>\n",
       "      <td>11</td>\n",
       "      <td>3</td>\n",
       "      <td>500.0</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-Andres Galarraga</th>\n",
       "      <td>321</td>\n",
       "      <td>87</td>\n",
       "      <td>10</td>\n",
       "      <td>39</td>\n",
       "      <td>42</td>\n",
       "      <td>30</td>\n",
       "      <td>2</td>\n",
       "      <td>396</td>\n",
       "      <td>101</td>\n",
       "      <td>12</td>\n",
       "      <td>48</td>\n",
       "      <td>46</td>\n",
       "      <td>33</td>\n",
       "      <td>N</td>\n",
       "      <td>E</td>\n",
       "      <td>805</td>\n",
       "      <td>40</td>\n",
       "      <td>4</td>\n",
       "      <td>91.5</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-Alfredo Griffin</th>\n",
       "      <td>594</td>\n",
       "      <td>169</td>\n",
       "      <td>4</td>\n",
       "      <td>74</td>\n",
       "      <td>51</td>\n",
       "      <td>35</td>\n",
       "      <td>11</td>\n",
       "      <td>4408</td>\n",
       "      <td>1133</td>\n",
       "      <td>19</td>\n",
       "      <td>501</td>\n",
       "      <td>336</td>\n",
       "      <td>194</td>\n",
       "      <td>A</td>\n",
       "      <td>W</td>\n",
       "      <td>282</td>\n",
       "      <td>421</td>\n",
       "      <td>25</td>\n",
       "      <td>750.0</td>\n",
       "      <td>A</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   AtBat  Hits  HmRun  Runs  RBI  Walks  Years  CAtBat  CHits  \\\n",
       "Player                                                                          \n",
       "-Alan Ashby          315    81      7    24   38     39     14    3449    835   \n",
       "-Alvin Davis         479   130     18    66   72     76      3    1624    457   \n",
       "-Andre Dawson        496   141     20    65   78     37     11    5628   1575   \n",
       "-Andres Galarraga    321    87     10    39   42     30      2     396    101   \n",
       "-Alfredo Griffin     594   169      4    74   51     35     11    4408   1133   \n",
       "\n",
       "                   CHmRun  CRuns  CRBI  CWalks League Division  PutOuts  \\\n",
       "Player                                                                    \n",
       "-Alan Ashby            69    321   414     375      N        W      632   \n",
       "-Alvin Davis           63    224   266     263      A        W      880   \n",
       "-Andre Dawson         225    828   838     354      N        E      200   \n",
       "-Andres Galarraga      12     48    46      33      N        E      805   \n",
       "-Alfredo Griffin       19    501   336     194      A        W      282   \n",
       "\n",
       "                   Assists  Errors  Salary NewLeague  \n",
       "Player                                                \n",
       "-Alan Ashby             43      10   475.0         N  \n",
       "-Alvin Davis            82      14   480.0         A  \n",
       "-Andre Dawson           11       3   500.0         N  \n",
       "-Andres Galarraga       40       4    91.5         N  \n",
       "-Alfredo Griffin       421      25   750.0         A  "
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Index: 263 entries, -Alan Ashby to -Willie Wilson\n",
      "Data columns (total 6 columns):\n",
      "League_A       263 non-null uint8\n",
      "League_N       263 non-null uint8\n",
      "Division_E     263 non-null uint8\n",
      "Division_W     263 non-null uint8\n",
      "NewLeague_A    263 non-null uint8\n",
      "NewLeague_N    263 non-null uint8\n",
      "dtypes: uint8(6)\n",
      "memory usage: 3.6+ KB\n",
      "                   League_A  League_N  Division_E  Division_W  NewLeague_A  \\\n",
      "Player                                                                       \n",
      "-Alan Ashby               0         1           0           1            0   \n",
      "-Alvin Davis              1         0           0           1            1   \n",
      "-Andre Dawson             0         1           1           0            0   \n",
      "-Andres Galarraga         0         1           1           0            0   \n",
      "-Alfredo Griffin          1         0           0           1            1   \n",
      "\n",
      "                   NewLeague_N  \n",
      "Player                          \n",
      "-Alan Ashby                  1  \n",
      "-Alvin Davis                 0  \n",
      "-Andre Dawson                1  \n",
      "-Andres Galarraga            1  \n",
      "-Alfredo Griffin             0  \n"
     ]
    }
   ],
   "source": [
    "dummies = pd.get_dummies(df[['League', 'Division', 'NewLeague']])\n",
    "dummies.info()\n",
    "print(dummies.head())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Index: 263 entries, -Alan Ashby to -Willie Wilson\n",
      "Data columns (total 19 columns):\n",
      "AtBat          263 non-null float64\n",
      "Hits           263 non-null float64\n",
      "HmRun          263 non-null float64\n",
      "Runs           263 non-null float64\n",
      "RBI            263 non-null float64\n",
      "Walks          263 non-null float64\n",
      "Years          263 non-null float64\n",
      "CAtBat         263 non-null float64\n",
      "CHits          263 non-null float64\n",
      "CHmRun         263 non-null float64\n",
      "CRuns          263 non-null float64\n",
      "CRBI           263 non-null float64\n",
      "CWalks         263 non-null float64\n",
      "PutOuts        263 non-null float64\n",
      "Assists        263 non-null float64\n",
      "Errors         263 non-null float64\n",
      "League_N       263 non-null uint8\n",
      "Division_W     263 non-null uint8\n",
      "NewLeague_N    263 non-null uint8\n",
      "dtypes: float64(16), uint8(3)\n",
      "memory usage: 35.7+ KB\n"
     ]
    }
   ],
   "source": [
    "y = df.Salary\n",
    "\n",
    "# Drop the column with the independent variable (Salary), and columns for which we created dummy variables\n",
    "X_ = df.drop(['Salary', 'League', 'Division', 'NewLeague'], axis=1).astype('float64')\n",
    "# Define the feature set X.\n",
    "X = pd.concat([X_, dummies[['League_N', 'Division_W', 'NewLeague_N']]], axis=1)\n",
    "X.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AtBat</th>\n",
       "      <th>Hits</th>\n",
       "      <th>HmRun</th>\n",
       "      <th>Runs</th>\n",
       "      <th>RBI</th>\n",
       "      <th>Walks</th>\n",
       "      <th>Years</th>\n",
       "      <th>CAtBat</th>\n",
       "      <th>CHits</th>\n",
       "      <th>CHmRun</th>\n",
       "      <th>CRuns</th>\n",
       "      <th>CRBI</th>\n",
       "      <th>CWalks</th>\n",
       "      <th>PutOuts</th>\n",
       "      <th>Assists</th>\n",
       "      <th>Errors</th>\n",
       "      <th>League_N</th>\n",
       "      <th>Division_W</th>\n",
       "      <th>NewLeague_N</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Player</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>-Alan Ashby</th>\n",
       "      <td>315.0</td>\n",
       "      <td>81.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>38.0</td>\n",
       "      <td>39.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>3449.0</td>\n",
       "      <td>835.0</td>\n",
       "      <td>69.0</td>\n",
       "      <td>321.0</td>\n",
       "      <td>414.0</td>\n",
       "      <td>375.0</td>\n",
       "      <td>632.0</td>\n",
       "      <td>43.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-Alvin Davis</th>\n",
       "      <td>479.0</td>\n",
       "      <td>130.0</td>\n",
       "      <td>18.0</td>\n",
       "      <td>66.0</td>\n",
       "      <td>72.0</td>\n",
       "      <td>76.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1624.0</td>\n",
       "      <td>457.0</td>\n",
       "      <td>63.0</td>\n",
       "      <td>224.0</td>\n",
       "      <td>266.0</td>\n",
       "      <td>263.0</td>\n",
       "      <td>880.0</td>\n",
       "      <td>82.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-Andre Dawson</th>\n",
       "      <td>496.0</td>\n",
       "      <td>141.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>65.0</td>\n",
       "      <td>78.0</td>\n",
       "      <td>37.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>5628.0</td>\n",
       "      <td>1575.0</td>\n",
       "      <td>225.0</td>\n",
       "      <td>828.0</td>\n",
       "      <td>838.0</td>\n",
       "      <td>354.0</td>\n",
       "      <td>200.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-Andres Galarraga</th>\n",
       "      <td>321.0</td>\n",
       "      <td>87.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>39.0</td>\n",
       "      <td>42.0</td>\n",
       "      <td>30.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>396.0</td>\n",
       "      <td>101.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>48.0</td>\n",
       "      <td>46.0</td>\n",
       "      <td>33.0</td>\n",
       "      <td>805.0</td>\n",
       "      <td>40.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-Alfredo Griffin</th>\n",
       "      <td>594.0</td>\n",
       "      <td>169.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>74.0</td>\n",
       "      <td>51.0</td>\n",
       "      <td>35.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>4408.0</td>\n",
       "      <td>1133.0</td>\n",
       "      <td>19.0</td>\n",
       "      <td>501.0</td>\n",
       "      <td>336.0</td>\n",
       "      <td>194.0</td>\n",
       "      <td>282.0</td>\n",
       "      <td>421.0</td>\n",
       "      <td>25.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   AtBat   Hits  HmRun  Runs   RBI  Walks  Years  CAtBat  \\\n",
       "Player                                                                     \n",
       "-Alan Ashby        315.0   81.0    7.0  24.0  38.0   39.0   14.0  3449.0   \n",
       "-Alvin Davis       479.0  130.0   18.0  66.0  72.0   76.0    3.0  1624.0   \n",
       "-Andre Dawson      496.0  141.0   20.0  65.0  78.0   37.0   11.0  5628.0   \n",
       "-Andres Galarraga  321.0   87.0   10.0  39.0  42.0   30.0    2.0   396.0   \n",
       "-Alfredo Griffin   594.0  169.0    4.0  74.0  51.0   35.0   11.0  4408.0   \n",
       "\n",
       "                    CHits  CHmRun  CRuns   CRBI  CWalks  PutOuts  Assists  \\\n",
       "Player                                                                      \n",
       "-Alan Ashby         835.0    69.0  321.0  414.0   375.0    632.0     43.0   \n",
       "-Alvin Davis        457.0    63.0  224.0  266.0   263.0    880.0     82.0   \n",
       "-Andre Dawson      1575.0   225.0  828.0  838.0   354.0    200.0     11.0   \n",
       "-Andres Galarraga   101.0    12.0   48.0   46.0    33.0    805.0     40.0   \n",
       "-Alfredo Griffin   1133.0    19.0  501.0  336.0   194.0    282.0    421.0   \n",
       "\n",
       "                   Errors  League_N  Division_W  NewLeague_N  \n",
       "Player                                                        \n",
       "-Alan Ashby          10.0         1           1            1  \n",
       "-Alvin Davis         14.0         0           1            0  \n",
       "-Andre Dawson         3.0         1           0            1  \n",
       "-Andres Galarraga     4.0         1           0            1  \n",
       "-Alfredo Griffin     25.0         0           1            0  "
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.head(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### I executed the R code and downloaded the exact same training/test sets used in the book."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train = pd.read_csv('Data/Hitters_X_train.csv', index_col=0)\n",
    "y_train = pd.read_csv('Data/Hitters_y_train.csv', index_col=0)\n",
    "X_test = pd.read_csv('Data/Hitters_X_test.csv', index_col=0)\n",
    "y_test = pd.read_csv('Data/Hitters_y_test.csv', index_col=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.6.1 Ridge Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Scikit-learn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The __glmnet__ algorithms in R optimize the objective function using cyclical coordinate descent, while scikit-learn Ridge regression uses linear least squares with L2 regularization. They are rather different implementations, but the general principles are the same.\n",
    "\n",
    "The __glmnet() function in R__ optimizes:\n",
    "### $$ \\frac{1}{N}|| X\\beta-y||^2_2+\\lambda\\bigg(\\frac{1}{2}(1−\\alpha)||\\beta||^2_2 \\ +\\ \\alpha||\\beta||_1\\bigg) $$\n",
    "(See R documentation and https://cran.r-project.org/web/packages/glmnet/vignettes/glmnet_beta.pdf)<BR>\n",
    "The function supports L1 and L2 regularization. For just Ridge regression we need to use $\\alpha = 0 $. This reduces the above cost function to\n",
    "### $$ \\frac{1}{N}|| X\\beta-y||^2_2+\\frac{1}{2}\\lambda ||\\beta||^2_2 $$\n",
    "The __sklearn Ridge()__ function optimizes:\n",
    "### $$ ||X\\beta - y||^2_2 + \\alpha ||\\beta||^2_2 $$\n",
    "which is equivalent to optimizing\n",
    "### $$ \\frac{1}{N}||X\\beta - y||^2_2 + \\frac{\\alpha}{N} ||\\beta||^2_2 $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "alphas = 5**np.linspace(10,-2,100)*0.5 \n",
    "\n",
    "ridge = Ridge()\n",
    "coefs = []\n",
    "\n",
    "for a in alphas:\n",
    "    ridge.set_params(alpha=a)\n",
    "    ridge.fit(scale(X), y)\n",
    "    coefs.append(ridge.coef_)\n",
    "\n",
    "ax = plt.gca()\n",
    "ax.plot(alphas, coefs)\n",
    "ax.set_xscale('log')\n",
    "ax.set_xlim(ax.get_xlim()) \n",
    "plt.axis('tight')\n",
    "plt.xlabel('alpha')\n",
    "plt.ylabel('weights')\n",
    "plt.title('Ridge coefficients as a function of the regularization');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above plot shows that the Ridge coefficients get larger when we decrease alpha."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Alpha = 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "scaler = StandardScaler().fit(X_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "97383.68965102115"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ridge2 = Ridge(alpha=4)\n",
    "ridge2.fit(scaler.transform(X_train), y_train)\n",
    "pred = ridge2.predict(scaler.transform(X_test))\n",
    "mean_squared_error(y_test, pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "AtBat         -161.784058\n",
       "Hits           118.911404\n",
       "HmRun           52.645719\n",
       "Runs           -43.295947\n",
       "RBI             37.339573\n",
       "Walks          138.214992\n",
       "Years         -106.916784\n",
       "CAtBat         -21.080864\n",
       "CHits          115.933862\n",
       "CHmRun         -17.949420\n",
       "CRuns          239.723217\n",
       "CRBI           -17.945273\n",
       "CWalks         -59.754770\n",
       "PutOuts         21.752383\n",
       "Assists        -68.676906\n",
       "Errors          89.610291\n",
       "League_N        31.048268\n",
       "Division_W     -13.553466\n",
       "NewLeague_N      4.350305\n",
       "dtype: float64"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.Series(ridge2.coef_.flatten(), index=X.columns)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Alpha = $10^{10}$  (Alpha graph & find optimal alpha)\n",
    "This big penalty shrinks the coefficients to a very large degree and makes the model more biased, resulting in a higher MSE."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "193253.09741651407"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ridge2.set_params(alpha=10**10)\n",
    "ridge2.fit(scale(X_train), y_train)\n",
    "pred = ridge2.predict(scale(X_test))\n",
    "mean_squared_error(y_test, pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "AtBat          2.291553e-06\n",
       "Hits           2.428111e-06\n",
       "HmRun          2.051677e-06\n",
       "Runs           2.372252e-06\n",
       "RBI            2.538921e-06\n",
       "Walks          2.974270e-06\n",
       "Years          1.572334e-06\n",
       "CAtBat         2.507043e-06\n",
       "CHits          2.666936e-06\n",
       "CHmRun         2.280416e-06\n",
       "CRuns          2.839982e-06\n",
       "CRBI           2.526355e-06\n",
       "CWalks         2.544939e-06\n",
       "PutOuts        4.880225e-07\n",
       "Assists       -1.149268e-06\n",
       "Errors         2.067779e-06\n",
       "League_N       5.324293e-07\n",
       "Division_W     5.051366e-07\n",
       "NewLeague_N    5.291999e-07\n",
       "dtype: float64"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.Series(ridge2.coef_.flatten(), index=X.columns)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Training mse with different alpha value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Training mse with different alpha')"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "alphas = 5**np.linspace(10,-2,100)*0.5 \n",
    "mse = []\n",
    "for a in alphas:\n",
    "    ridge2 = Ridge(alpha=a)\n",
    "    ridge2.fit(scaler.transform(X_train), y_train)\n",
    "    pred = ridge2.predict(scaler.transform(X_train))\n",
    "    mse.append(mean_squared_error(y_train, pred))\n",
    "\n",
    "ax = plt.gca()\n",
    "ax.plot(alphas, mse)\n",
    "ax.set_xscale('log')\n",
    "ax.set_xlim(ax.get_xlim()) \n",
    "plt.axis('tight')\n",
    "plt.xlabel('alpha')\n",
    "plt.ylabel('mse')\n",
    "plt.title('Training mse with different alpha')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Training mse with different alpha value (Cross validation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "alphas = 5**np.linspace(10,-2,100)*0.5 \n",
    "mse = []\n",
    "# 10-fold CV, with shuffle\n",
    "kf_10 = KFold(n_splits=10, shuffle=False, random_state=1)\n",
    "for a in alphas:\n",
    "    ridge2 = Ridge(alpha=a)\n",
    "    mse.append(-1*cross_val_score(ridge2, scale(X_train), y_train, cv=kf_10, scoring='neg_mean_squared_error').mean())\n",
    "\n",
    "ax = plt.gca()\n",
    "ax.plot(alphas, mse)\n",
    "ax.set_xscale('log')\n",
    "ax.set_xlim(ax.get_xlim())  \n",
    "plt.axis('tight')\n",
    "plt.xlabel('alpha')\n",
    "plt.ylabel('mse')\n",
    "plt.title('Training mse with different alpha');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Test mse with different alpha value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Test mse with different alpha')"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "alphas = 5**np.linspace(10,-2,100)*0.5 \n",
    "mse = []\n",
    "for a in alphas:\n",
    "    ridge2 = Ridge(alpha=a)\n",
    "    ridge2.fit(scaler.transform(X_train), y_train)\n",
    "    pred = ridge2.predict(scaler.transform(X_test))\n",
    "    mse.append(mean_squared_error(y_test, pred))\n",
    "\n",
    "ax = plt.gca()\n",
    "ax.plot(alphas, mse)\n",
    "ax.set_xscale('log')\n",
    "ax.set_xlim(ax.get_xlim()) \n",
    "plt.axis('tight')\n",
    "plt.xlabel('alpha')\n",
    "plt.ylabel('mse')\n",
    "plt.title('Test mse with different alpha')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Compute the regularization path using RidgeCV\n",
    "Ridge regression with built-in cross-validation.\n",
    "\n",
    "Default cross validation method is \"Generalized Cross-Validation\" (efficient Leave-One-Out)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RidgeCV(alphas=array([4.88281250e+06, 4.01741235e+06, 3.30539050e+06, 2.71956308e+06,\n",
       "       2.23756418e+06, 1.84099184e+06, 1.51470558e+06, 1.24624833e+06,\n",
       "       1.02537082e+06, 8.43640297e+05, 6.94118595e+05, 5.71097214e+05,\n",
       "       4.69879399e+05, 3.86600818e+05, 3.18082028e+05, 2.61707094e+05,\n",
       "       2.15323712e+05, 1.77161040e+05, 1.45762089e+05, 1.19928098e+05,\n",
       "       9.86727677e+04, 8.11846033e+0...\n",
       "       3.73150948e-01, 3.07015931e-01, 2.52602285e-01, 2.07832585e-01,\n",
       "       1.70997595e-01, 1.40691016e-01, 1.15755791e-01, 9.52399351e-02,\n",
       "       7.83601852e-02, 6.44721001e-02, 5.30454551e-02, 4.36439996e-02,\n",
       "       3.59088012e-02, 2.95445425e-02, 2.43082465e-02, 2.00000000e-02]),\n",
       "        cv=None, fit_intercept=True, gcv_mode=None, normalize=False,\n",
       "        scoring='neg_mean_squared_error', store_cv_values=False)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ridgecv = RidgeCV(alphas=alphas, scoring='neg_mean_squared_error')\n",
    "ridgecv.fit(scale(X_train), y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "106.87349666729351"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Optimal alpha that RidgeCV found\n",
    "ridgecv.alpha_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "97171.90036529172"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ridge2.set_params(alpha=ridgecv.alpha_)\n",
    "ridge2.fit(scale(X_train), y_train)\n",
    "mean_squared_error(y_test, ridge2.predict(scale(X_test)))\n",
    "# Compare this mse value with an above graph (MSE with different alpha)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "AtBat           6.527403\n",
       "Hits           22.754323\n",
       "HmRun          19.213875\n",
       "Runs           20.029787\n",
       "RBI            21.072806\n",
       "Walks          57.407651\n",
       "Years          -5.790283\n",
       "CAtBat         20.637323\n",
       "CHits          29.977244\n",
       "CHmRun         14.050638\n",
       "CRuns          37.018236\n",
       "CRBI           20.284659\n",
       "CWalks         24.526594\n",
       "PutOuts        16.522197\n",
       "Assists       -45.652512\n",
       "Errors         56.322520\n",
       "League_N        6.000427\n",
       "Division_W     -0.571164\n",
       "NewLeague_N    11.210351\n",
       "dtype: float64"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.Series(ridge2.coef_.flatten(), index=X.columns)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.6.2 The Lasso"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Scikit-learn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "For both __glmnet__ in R and sklearn __Lasso()__ function the standard L1 penalty is:\n",
    "### $$ \\lambda |\\beta|_1 $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Lasso in Scikit-learn has a max iteration since it uses \"Coordinate descent solver\"\n",
    "lasso = Lasso(max_iter=10000)\n",
    "coefs = []\n",
    "for a in alphas:\n",
    "    lasso.set_params(alpha=a)\n",
    "    lasso.fit(scale(X_train), y_train)\n",
    "    coefs.append(lasso.coef_)\n",
    "\n",
    "ax = plt.gca()\n",
    "ax.plot(alphas*2, coefs)\n",
    "ax.set_xscale('log')\n",
    "ax.set_xlim(ax.get_xlim())  \n",
    "plt.axis('tight')\n",
    "plt.xlabel('alpha')\n",
    "plt.ylabel('weights')\n",
    "plt.title('Lasso coefficients as a function of the regularization');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Training mse with different alpha value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lasso = Lasso(max_iter=10000)\n",
    "mse = []\n",
    "for a in alphas:\n",
    "    lasso.set_params(alpha=a)\n",
    "    lasso.fit(scale(X_train), y_train)\n",
    "    mse.append(mean_squared_error(y_train, lasso.predict(scale(X_train))))\n",
    "\n",
    "ax = plt.gca()\n",
    "ax.plot(alphas, mse)\n",
    "ax.set_xscale('log')\n",
    "ax.set_xlim(ax.get_xlim())  \n",
    "plt.axis('tight')\n",
    "plt.xlabel('alpha')\n",
    "plt.ylabel('mse')\n",
    "plt.title('Training mse with different alpha');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Training mse with different alpha value (Cross validataion)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lasso = Lasso(max_iter=10000)\n",
    "mse = []\n",
    "# 10-fold CV, with shuffle\n",
    "kf_10 = KFold(n_splits=10, shuffle=False, random_state=1)\n",
    "for a in alphas:\n",
    "    lasso.set_params(alpha=a)\n",
    "    mse.append(-1*cross_val_score(lasso, scale(X_train), y_train, cv=kf_10, scoring='neg_mean_squared_error').mean())\n",
    "\n",
    "ax = plt.gca()\n",
    "ax.plot(alphas, mse)\n",
    "ax.set_xscale('log')\n",
    "ax.set_xlim(ax.get_xlim())  \n",
    "plt.axis('tight')\n",
    "plt.xlabel('alpha')\n",
    "plt.ylabel('mse')\n",
    "plt.title('Training mse with different alpha');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Test mse with different alpha value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lasso = Lasso(max_iter=10000)\n",
    "mse = []\n",
    "for a in alphas:\n",
    "    lasso.set_params(alpha=a)\n",
    "    lasso.fit(scale(X_train), y_train)  \n",
    "    mse.append(mean_squared_error(y_test, lasso.predict(scale(X_test))))\n",
    "\n",
    "ax = plt.gca()\n",
    "ax.plot(alphas, mse)\n",
    "ax.set_xscale('log')\n",
    "ax.set_xlim(ax.get_xlim())  \n",
    "plt.axis('tight')\n",
    "plt.xlabel('alpha')\n",
    "plt.ylabel('mse')\n",
    "plt.title('Training mse with different alpha');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Compute the regularization path using LassoCV\n",
    "Lasso regression with built-in cross-validation.\n",
    "\n",
    "Alphas are set automatically"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LassoCV(alphas=None, copy_X=True, cv=10, eps=0.001, fit_intercept=True,\n",
       "        max_iter=10000, n_alphas=100, n_jobs=None, normalize=False,\n",
       "        positive=False, precompute='auto', random_state=None,\n",
       "        selection='cyclic', tol=0.0001, verbose=False)"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lassocv = LassoCV(alphas=None, cv=10, max_iter=10000)\n",
    "lassocv.fit(scale(X_train), y_train.as_matrix().ravel())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "30.01382256446427"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lassocv.alpha_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "102924.90954696965"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lasso.set_params(alpha=lassocv.alpha_)\n",
    "lasso.fit(scale(X_train), y_train)\n",
    "mean_squared_error(y_test, lasso.predict(scale(X_test)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "AtBat            0.000000\n",
       "Hits             0.000000\n",
       "HmRun            2.154219\n",
       "Runs             0.000000\n",
       "RBI             30.835560\n",
       "Walks          104.071528\n",
       "Years           -0.000000\n",
       "CAtBat           0.000000\n",
       "CHits            0.000000\n",
       "CHmRun           0.000000\n",
       "CRuns          132.858095\n",
       "CRBI             0.000000\n",
       "CWalks           0.000000\n",
       "PutOuts          1.896185\n",
       "Assists        -51.058752\n",
       "Errors          76.779641\n",
       "League_N         0.000000\n",
       "Division_W       0.000000\n",
       "NewLeague_N      0.000000\n",
       "dtype: float64"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Some of the coefficients are now reduced to exactly zero.\n",
    "pd.Series(lasso.coef_, index=X.columns)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lab 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.7.1 Principal Components Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Scikit-klearn does not have an implementation of PCA and regression combined like the 'pls' package in R.\n",
    "https://cran.r-project.org/web/packages/pls/vignettes/pls-manual.pdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "pca = PCA()\n",
    "X_reduced = pca.fit_transform(scale(X))\n",
    "\n",
    "print(pca.components_.shape)\n",
    "pd.DataFrame(pca.components_.T).loc[:4,:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(263, 19)"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AtBat</th>\n",
       "      <th>Hits</th>\n",
       "      <th>HmRun</th>\n",
       "      <th>Runs</th>\n",
       "      <th>RBI</th>\n",
       "      <th>Walks</th>\n",
       "      <th>Years</th>\n",
       "      <th>CAtBat</th>\n",
       "      <th>CHits</th>\n",
       "      <th>CHmRun</th>\n",
       "      <th>CRuns</th>\n",
       "      <th>CRBI</th>\n",
       "      <th>CWalks</th>\n",
       "      <th>PutOuts</th>\n",
       "      <th>Assists</th>\n",
       "      <th>Errors</th>\n",
       "      <th>League_N</th>\n",
       "      <th>Division_W</th>\n",
       "      <th>NewLeague_N</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Player</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>-Alan Ashby</th>\n",
       "      <td>315.0</td>\n",
       "      <td>81.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>38.0</td>\n",
       "      <td>39.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>3449.0</td>\n",
       "      <td>835.0</td>\n",
       "      <td>69.0</td>\n",
       "      <td>321.0</td>\n",
       "      <td>414.0</td>\n",
       "      <td>375.0</td>\n",
       "      <td>632.0</td>\n",
       "      <td>43.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-Alvin Davis</th>\n",
       "      <td>479.0</td>\n",
       "      <td>130.0</td>\n",
       "      <td>18.0</td>\n",
       "      <td>66.0</td>\n",
       "      <td>72.0</td>\n",
       "      <td>76.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1624.0</td>\n",
       "      <td>457.0</td>\n",
       "      <td>63.0</td>\n",
       "      <td>224.0</td>\n",
       "      <td>266.0</td>\n",
       "      <td>263.0</td>\n",
       "      <td>880.0</td>\n",
       "      <td>82.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-Andre Dawson</th>\n",
       "      <td>496.0</td>\n",
       "      <td>141.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>65.0</td>\n",
       "      <td>78.0</td>\n",
       "      <td>37.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>5628.0</td>\n",
       "      <td>1575.0</td>\n",
       "      <td>225.0</td>\n",
       "      <td>828.0</td>\n",
       "      <td>838.0</td>\n",
       "      <td>354.0</td>\n",
       "      <td>200.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-Andres Galarraga</th>\n",
       "      <td>321.0</td>\n",
       "      <td>87.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>39.0</td>\n",
       "      <td>42.0</td>\n",
       "      <td>30.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>396.0</td>\n",
       "      <td>101.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>48.0</td>\n",
       "      <td>46.0</td>\n",
       "      <td>33.0</td>\n",
       "      <td>805.0</td>\n",
       "      <td>40.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   AtBat   Hits  HmRun  Runs   RBI  Walks  Years  CAtBat  \\\n",
       "Player                                                                     \n",
       "-Alan Ashby        315.0   81.0    7.0  24.0  38.0   39.0   14.0  3449.0   \n",
       "-Alvin Davis       479.0  130.0   18.0  66.0  72.0   76.0    3.0  1624.0   \n",
       "-Andre Dawson      496.0  141.0   20.0  65.0  78.0   37.0   11.0  5628.0   \n",
       "-Andres Galarraga  321.0   87.0   10.0  39.0  42.0   30.0    2.0   396.0   \n",
       "\n",
       "                    CHits  CHmRun  CRuns   CRBI  CWalks  PutOuts  Assists  \\\n",
       "Player                                                                      \n",
       "-Alan Ashby         835.0    69.0  321.0  414.0   375.0    632.0     43.0   \n",
       "-Alvin Davis        457.0    63.0  224.0  266.0   263.0    880.0     82.0   \n",
       "-Andre Dawson      1575.0   225.0  828.0  838.0   354.0    200.0     11.0   \n",
       "-Andres Galarraga   101.0    12.0   48.0   46.0    33.0    805.0     40.0   \n",
       "\n",
       "                   Errors  League_N  Division_W  NewLeague_N  \n",
       "Player                                                        \n",
       "-Alan Ashby          10.0         1           1            1  \n",
       "-Alvin Davis         14.0         0           1            0  \n",
       "-Andre Dawson         3.0         1           0            1  \n",
       "-Andres Galarraga     4.0         1           0            1  "
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.head(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.6029005 , -0.59567545, -0.5285512 , ...,  1.05875764,\n",
       "         0.98116592,  1.07505242],\n",
       "       [ 0.51254171,  0.49225957,  0.72996619, ..., -0.94450322,\n",
       "         0.98116592, -0.9301872 ],\n",
       "       [ 0.62816682,  0.73648988,  0.95878753, ...,  1.05875764,\n",
       "        -1.01919561,  1.07505242],\n",
       "       ...,\n",
       "       [ 0.48533581,  0.40344855, -0.98619389, ..., -0.94450322,\n",
       "         0.98116592, -0.9301872 ],\n",
       "       [ 1.15188054,  0.80309815, -0.29972986, ..., -0.94450322,\n",
       "        -1.01919561, -0.9301872 ],\n",
       "       [ 1.54636621,  1.38036979, -0.29972986, ..., -0.94450322,\n",
       "         0.98116592, -0.9301872 ]])"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scale(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-9.64871922e-03,  1.87052198e+00,  1.26514521e+00, ...,\n",
       "         8.02161532e-02,  3.81397452e-02, -1.92500795e-02],\n",
       "       [ 4.11433695e-01, -2.42942190e+00, -9.09193165e-01, ...,\n",
       "         4.43434707e-02,  1.48342246e-02, -3.39451856e-03],\n",
       "       [ 3.46682196e+00,  8.25946988e-01,  5.55469466e-01, ...,\n",
       "        -2.18282868e-01,  3.78251162e-02, -6.65007373e-02],\n",
       "       ...,\n",
       "       [-1.09460888e+00, -7.51385751e-01, -9.35936894e-01, ...,\n",
       "        -7.87381606e-02,  6.72009318e-02,  1.31936353e-02],\n",
       "       [ 1.97768180e+00, -2.18451741e+00, -2.82011929e-01, ...,\n",
       "        -1.44073449e-02,  2.29207125e-02, -1.05296972e-02],\n",
       "       [ 1.83300238e+00, -3.01096659e-01, -1.05532275e+00, ...,\n",
       "        -3.02569189e-01, -7.55286689e-02, -4.05988737e-02]])"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_reduced"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above loadings are the same as in R."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(263, 19)\n"
     ]
    }
   ],
   "source": [
    "print(X_reduced.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>10</th>\n",
       "      <th>11</th>\n",
       "      <th>12</th>\n",
       "      <th>13</th>\n",
       "      <th>14</th>\n",
       "      <th>15</th>\n",
       "      <th>16</th>\n",
       "      <th>17</th>\n",
       "      <th>18</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.009649</td>\n",
       "      <td>1.870522</td>\n",
       "      <td>1.265145</td>\n",
       "      <td>-0.935481</td>\n",
       "      <td>1.109636</td>\n",
       "      <td>1.211972</td>\n",
       "      <td>-0.065146</td>\n",
       "      <td>-0.098249</td>\n",
       "      <td>-0.252423</td>\n",
       "      <td>-0.637101</td>\n",
       "      <td>0.459341</td>\n",
       "      <td>0.615860</td>\n",
       "      <td>-0.478088</td>\n",
       "      <td>0.388407</td>\n",
       "      <td>0.063596</td>\n",
       "      <td>0.144790</td>\n",
       "      <td>0.080216</td>\n",
       "      <td>0.038140</td>\n",
       "      <td>-0.019250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.411434</td>\n",
       "      <td>-2.429422</td>\n",
       "      <td>-0.909193</td>\n",
       "      <td>-0.264212</td>\n",
       "      <td>1.232031</td>\n",
       "      <td>1.826617</td>\n",
       "      <td>0.359893</td>\n",
       "      <td>-1.199383</td>\n",
       "      <td>-0.371820</td>\n",
       "      <td>0.015215</td>\n",
       "      <td>0.176235</td>\n",
       "      <td>0.080529</td>\n",
       "      <td>0.403483</td>\n",
       "      <td>-0.019386</td>\n",
       "      <td>0.065149</td>\n",
       "      <td>0.161064</td>\n",
       "      <td>0.044343</td>\n",
       "      <td>0.014834</td>\n",
       "      <td>-0.003395</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3.466822</td>\n",
       "      <td>0.825947</td>\n",
       "      <td>0.555469</td>\n",
       "      <td>-1.616726</td>\n",
       "      <td>-0.857488</td>\n",
       "      <td>-1.028712</td>\n",
       "      <td>-0.999385</td>\n",
       "      <td>0.844247</td>\n",
       "      <td>0.197379</td>\n",
       "      <td>0.770490</td>\n",
       "      <td>0.055645</td>\n",
       "      <td>0.104938</td>\n",
       "      <td>0.021605</td>\n",
       "      <td>-0.376197</td>\n",
       "      <td>0.234291</td>\n",
       "      <td>0.011526</td>\n",
       "      <td>-0.218283</td>\n",
       "      <td>0.037825</td>\n",
       "      <td>-0.066501</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-2.558317</td>\n",
       "      <td>-0.230984</td>\n",
       "      <td>0.519642</td>\n",
       "      <td>-2.176251</td>\n",
       "      <td>-0.820301</td>\n",
       "      <td>1.491696</td>\n",
       "      <td>-0.276141</td>\n",
       "      <td>0.207094</td>\n",
       "      <td>0.414956</td>\n",
       "      <td>0.136842</td>\n",
       "      <td>-0.085375</td>\n",
       "      <td>-0.146217</td>\n",
       "      <td>0.142172</td>\n",
       "      <td>0.028975</td>\n",
       "      <td>0.042459</td>\n",
       "      <td>0.053043</td>\n",
       "      <td>-0.044443</td>\n",
       "      <td>0.010360</td>\n",
       "      <td>-0.013582</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.027702</td>\n",
       "      <td>-1.573537</td>\n",
       "      <td>1.331382</td>\n",
       "      <td>3.494004</td>\n",
       "      <td>0.983427</td>\n",
       "      <td>0.513675</td>\n",
       "      <td>0.140456</td>\n",
       "      <td>0.989707</td>\n",
       "      <td>-0.661933</td>\n",
       "      <td>-0.217565</td>\n",
       "      <td>0.111259</td>\n",
       "      <td>0.191244</td>\n",
       "      <td>-0.302426</td>\n",
       "      <td>-0.090770</td>\n",
       "      <td>0.043811</td>\n",
       "      <td>0.012300</td>\n",
       "      <td>-0.050593</td>\n",
       "      <td>0.126036</td>\n",
       "      <td>-0.071035</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>-3.980657</td>\n",
       "      <td>1.507279</td>\n",
       "      <td>-0.155479</td>\n",
       "      <td>0.369840</td>\n",
       "      <td>-1.209334</td>\n",
       "      <td>0.033514</td>\n",
       "      <td>0.013007</td>\n",
       "      <td>-0.540315</td>\n",
       "      <td>0.121838</td>\n",
       "      <td>0.411966</td>\n",
       "      <td>-1.198707</td>\n",
       "      <td>0.538882</td>\n",
       "      <td>0.106017</td>\n",
       "      <td>-0.238849</td>\n",
       "      <td>0.193108</td>\n",
       "      <td>-0.057444</td>\n",
       "      <td>0.052532</td>\n",
       "      <td>-0.024036</td>\n",
       "      <td>0.025065</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>-3.451719</td>\n",
       "      <td>0.599989</td>\n",
       "      <td>-0.626476</td>\n",
       "      <td>1.999776</td>\n",
       "      <td>0.807026</td>\n",
       "      <td>0.205971</td>\n",
       "      <td>-0.056137</td>\n",
       "      <td>0.395305</td>\n",
       "      <td>0.719654</td>\n",
       "      <td>0.421149</td>\n",
       "      <td>0.039300</td>\n",
       "      <td>-0.022136</td>\n",
       "      <td>0.178050</td>\n",
       "      <td>0.172087</td>\n",
       "      <td>-0.087011</td>\n",
       "      <td>-0.048078</td>\n",
       "      <td>-0.014070</td>\n",
       "      <td>-0.028050</td>\n",
       "      <td>0.000720</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>-3.432380</td>\n",
       "      <td>0.113542</td>\n",
       "      <td>1.999750</td>\n",
       "      <td>0.767813</td>\n",
       "      <td>1.016092</td>\n",
       "      <td>-0.272797</td>\n",
       "      <td>-1.204274</td>\n",
       "      <td>-0.098152</td>\n",
       "      <td>0.035413</td>\n",
       "      <td>0.359129</td>\n",
       "      <td>-0.010706</td>\n",
       "      <td>-0.201662</td>\n",
       "      <td>0.115068</td>\n",
       "      <td>0.284426</td>\n",
       "      <td>0.006564</td>\n",
       "      <td>0.064950</td>\n",
       "      <td>-0.059816</td>\n",
       "      <td>-0.067180</td>\n",
       "      <td>-0.004802</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>3.899707</td>\n",
       "      <td>1.947870</td>\n",
       "      <td>-1.820475</td>\n",
       "      <td>-0.026713</td>\n",
       "      <td>-1.137128</td>\n",
       "      <td>-0.821045</td>\n",
       "      <td>0.314217</td>\n",
       "      <td>-1.192292</td>\n",
       "      <td>0.444240</td>\n",
       "      <td>0.510195</td>\n",
       "      <td>0.217092</td>\n",
       "      <td>0.221224</td>\n",
       "      <td>0.130075</td>\n",
       "      <td>0.644068</td>\n",
       "      <td>-0.005987</td>\n",
       "      <td>-0.108769</td>\n",
       "      <td>0.131745</td>\n",
       "      <td>-0.057934</td>\n",
       "      <td>-0.022755</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>3.174812</td>\n",
       "      <td>-2.392365</td>\n",
       "      <td>0.794468</td>\n",
       "      <td>2.569006</td>\n",
       "      <td>-0.947328</td>\n",
       "      <td>-0.061251</td>\n",
       "      <td>-0.375009</td>\n",
       "      <td>-0.425686</td>\n",
       "      <td>-0.065025</td>\n",
       "      <td>-0.498544</td>\n",
       "      <td>-0.533286</td>\n",
       "      <td>-0.717679</td>\n",
       "      <td>-0.283230</td>\n",
       "      <td>-0.272698</td>\n",
       "      <td>-0.290593</td>\n",
       "      <td>-0.094599</td>\n",
       "      <td>0.054802</td>\n",
       "      <td>-0.028549</td>\n",
       "      <td>0.027711</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>-2.167606</td>\n",
       "      <td>1.864486</td>\n",
       "      <td>1.081053</td>\n",
       "      <td>-0.575818</td>\n",
       "      <td>0.935415</td>\n",
       "      <td>0.252217</td>\n",
       "      <td>-0.135862</td>\n",
       "      <td>-0.228715</td>\n",
       "      <td>-0.543103</td>\n",
       "      <td>-0.458606</td>\n",
       "      <td>0.130928</td>\n",
       "      <td>0.116231</td>\n",
       "      <td>-0.347348</td>\n",
       "      <td>-0.134637</td>\n",
       "      <td>-0.318234</td>\n",
       "      <td>0.008111</td>\n",
       "      <td>0.011816</td>\n",
       "      <td>0.003014</td>\n",
       "      <td>-0.012037</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>-0.933213</td>\n",
       "      <td>-0.435508</td>\n",
       "      <td>0.631417</td>\n",
       "      <td>-1.598076</td>\n",
       "      <td>-0.996468</td>\n",
       "      <td>-0.648208</td>\n",
       "      <td>-0.140635</td>\n",
       "      <td>-0.174776</td>\n",
       "      <td>-0.219926</td>\n",
       "      <td>0.036233</td>\n",
       "      <td>0.185101</td>\n",
       "      <td>0.200756</td>\n",
       "      <td>0.416675</td>\n",
       "      <td>0.268332</td>\n",
       "      <td>0.135570</td>\n",
       "      <td>0.057441</td>\n",
       "      <td>0.009851</td>\n",
       "      <td>-0.008454</td>\n",
       "      <td>-0.042310</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>-2.275324</td>\n",
       "      <td>1.666792</td>\n",
       "      <td>-0.922849</td>\n",
       "      <td>1.439654</td>\n",
       "      <td>-1.259431</td>\n",
       "      <td>0.436370</td>\n",
       "      <td>0.572372</td>\n",
       "      <td>0.129116</td>\n",
       "      <td>0.088152</td>\n",
       "      <td>0.005072</td>\n",
       "      <td>-0.163502</td>\n",
       "      <td>-0.320181</td>\n",
       "      <td>0.112925</td>\n",
       "      <td>-0.012291</td>\n",
       "      <td>0.081378</td>\n",
       "      <td>-0.015000</td>\n",
       "      <td>-0.110622</td>\n",
       "      <td>-0.004532</td>\n",
       "      <td>-0.029080</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>-1.046249</td>\n",
       "      <td>2.684710</td>\n",
       "      <td>0.959561</td>\n",
       "      <td>-0.517856</td>\n",
       "      <td>-1.119732</td>\n",
       "      <td>-0.335223</td>\n",
       "      <td>-0.337266</td>\n",
       "      <td>-0.203572</td>\n",
       "      <td>-0.361965</td>\n",
       "      <td>-0.917351</td>\n",
       "      <td>0.171027</td>\n",
       "      <td>0.152325</td>\n",
       "      <td>-0.468663</td>\n",
       "      <td>-0.322277</td>\n",
       "      <td>0.003972</td>\n",
       "      <td>-0.077642</td>\n",
       "      <td>-0.042167</td>\n",
       "      <td>0.025468</td>\n",
       "      <td>-0.007977</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>5.655999</td>\n",
       "      <td>0.402132</td>\n",
       "      <td>2.182295</td>\n",
       "      <td>0.201903</td>\n",
       "      <td>0.981668</td>\n",
       "      <td>-1.345032</td>\n",
       "      <td>0.466458</td>\n",
       "      <td>0.019188</td>\n",
       "      <td>0.337658</td>\n",
       "      <td>-0.342902</td>\n",
       "      <td>-0.300026</td>\n",
       "      <td>-0.306333</td>\n",
       "      <td>0.095752</td>\n",
       "      <td>-0.488056</td>\n",
       "      <td>0.120812</td>\n",
       "      <td>0.101775</td>\n",
       "      <td>0.248285</td>\n",
       "      <td>0.076392</td>\n",
       "      <td>0.044386</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>-3.577188</td>\n",
       "      <td>1.222869</td>\n",
       "      <td>-0.596820</td>\n",
       "      <td>2.074446</td>\n",
       "      <td>0.830985</td>\n",
       "      <td>0.417884</td>\n",
       "      <td>-0.300419</td>\n",
       "      <td>-0.571571</td>\n",
       "      <td>-0.466927</td>\n",
       "      <td>0.099572</td>\n",
       "      <td>0.024845</td>\n",
       "      <td>-0.194712</td>\n",
       "      <td>-0.334248</td>\n",
       "      <td>-0.055586</td>\n",
       "      <td>-0.064493</td>\n",
       "      <td>0.109564</td>\n",
       "      <td>-0.068115</td>\n",
       "      <td>-0.054926</td>\n",
       "      <td>-0.005152</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>-3.263406</td>\n",
       "      <td>2.478792</td>\n",
       "      <td>0.153300</td>\n",
       "      <td>-1.284811</td>\n",
       "      <td>0.892066</td>\n",
       "      <td>-0.234267</td>\n",
       "      <td>-0.463157</td>\n",
       "      <td>-0.089185</td>\n",
       "      <td>0.438550</td>\n",
       "      <td>-0.498858</td>\n",
       "      <td>0.044587</td>\n",
       "      <td>0.041791</td>\n",
       "      <td>-0.436226</td>\n",
       "      <td>-0.080805</td>\n",
       "      <td>-0.165206</td>\n",
       "      <td>0.093247</td>\n",
       "      <td>-0.127281</td>\n",
       "      <td>-0.042690</td>\n",
       "      <td>0.032801</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>-1.751013</td>\n",
       "      <td>-1.323168</td>\n",
       "      <td>0.342983</td>\n",
       "      <td>-2.147064</td>\n",
       "      <td>-1.036283</td>\n",
       "      <td>-0.624585</td>\n",
       "      <td>0.545461</td>\n",
       "      <td>-0.813632</td>\n",
       "      <td>-0.153811</td>\n",
       "      <td>-0.032113</td>\n",
       "      <td>-0.197054</td>\n",
       "      <td>-0.332331</td>\n",
       "      <td>-0.065527</td>\n",
       "      <td>-0.378001</td>\n",
       "      <td>0.233154</td>\n",
       "      <td>-0.212033</td>\n",
       "      <td>0.163025</td>\n",
       "      <td>-0.006707</td>\n",
       "      <td>0.019796</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>-2.152780</td>\n",
       "      <td>-0.916324</td>\n",
       "      <td>-0.520684</td>\n",
       "      <td>-1.047379</td>\n",
       "      <td>0.822729</td>\n",
       "      <td>-0.021434</td>\n",
       "      <td>1.782620</td>\n",
       "      <td>-0.045956</td>\n",
       "      <td>0.077066</td>\n",
       "      <td>0.396404</td>\n",
       "      <td>1.332914</td>\n",
       "      <td>-0.530436</td>\n",
       "      <td>0.289715</td>\n",
       "      <td>-0.047173</td>\n",
       "      <td>-0.063453</td>\n",
       "      <td>-0.063703</td>\n",
       "      <td>0.024051</td>\n",
       "      <td>0.030675</td>\n",
       "      <td>-0.014491</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>0.084279</td>\n",
       "      <td>-0.903456</td>\n",
       "      <td>0.582376</td>\n",
       "      <td>-2.126568</td>\n",
       "      <td>1.040489</td>\n",
       "      <td>-0.052544</td>\n",
       "      <td>0.882075</td>\n",
       "      <td>-0.605949</td>\n",
       "      <td>0.429003</td>\n",
       "      <td>-0.236362</td>\n",
       "      <td>0.161771</td>\n",
       "      <td>0.258728</td>\n",
       "      <td>-0.015689</td>\n",
       "      <td>-0.035607</td>\n",
       "      <td>0.278810</td>\n",
       "      <td>-0.035762</td>\n",
       "      <td>-0.023524</td>\n",
       "      <td>0.023124</td>\n",
       "      <td>0.009299</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>5.970981</td>\n",
       "      <td>-0.441813</td>\n",
       "      <td>0.055237</td>\n",
       "      <td>0.754230</td>\n",
       "      <td>-0.498954</td>\n",
       "      <td>2.649546</td>\n",
       "      <td>-1.184840</td>\n",
       "      <td>1.699355</td>\n",
       "      <td>-0.252054</td>\n",
       "      <td>-0.392732</td>\n",
       "      <td>0.448387</td>\n",
       "      <td>0.620552</td>\n",
       "      <td>0.276792</td>\n",
       "      <td>-0.802375</td>\n",
       "      <td>0.181051</td>\n",
       "      <td>-0.210927</td>\n",
       "      <td>0.163793</td>\n",
       "      <td>0.067497</td>\n",
       "      <td>0.061613</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>0.785418</td>\n",
       "      <td>-1.694971</td>\n",
       "      <td>-1.114628</td>\n",
       "      <td>-0.113931</td>\n",
       "      <td>-1.192531</td>\n",
       "      <td>0.430105</td>\n",
       "      <td>2.325016</td>\n",
       "      <td>0.747215</td>\n",
       "      <td>-0.644452</td>\n",
       "      <td>0.165261</td>\n",
       "      <td>-0.093634</td>\n",
       "      <td>0.082252</td>\n",
       "      <td>0.083503</td>\n",
       "      <td>0.105205</td>\n",
       "      <td>0.002900</td>\n",
       "      <td>-0.205277</td>\n",
       "      <td>-0.032735</td>\n",
       "      <td>0.040446</td>\n",
       "      <td>-0.016478</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>-2.054685</td>\n",
       "      <td>1.702366</td>\n",
       "      <td>0.644522</td>\n",
       "      <td>-1.146517</td>\n",
       "      <td>-1.121931</td>\n",
       "      <td>-0.098095</td>\n",
       "      <td>0.295297</td>\n",
       "      <td>0.642791</td>\n",
       "      <td>-0.168415</td>\n",
       "      <td>-0.066757</td>\n",
       "      <td>-0.106032</td>\n",
       "      <td>-0.144704</td>\n",
       "      <td>-0.138462</td>\n",
       "      <td>0.260333</td>\n",
       "      <td>0.384819</td>\n",
       "      <td>-0.147543</td>\n",
       "      <td>-0.116500</td>\n",
       "      <td>-0.033317</td>\n",
       "      <td>-0.030831</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>-0.083558</td>\n",
       "      <td>-0.465050</td>\n",
       "      <td>1.460094</td>\n",
       "      <td>-1.071268</td>\n",
       "      <td>1.217913</td>\n",
       "      <td>1.108492</td>\n",
       "      <td>-0.259328</td>\n",
       "      <td>0.444383</td>\n",
       "      <td>-0.357445</td>\n",
       "      <td>-0.130988</td>\n",
       "      <td>0.384545</td>\n",
       "      <td>0.580438</td>\n",
       "      <td>-0.490799</td>\n",
       "      <td>0.249610</td>\n",
       "      <td>0.049289</td>\n",
       "      <td>0.061389</td>\n",
       "      <td>-0.026856</td>\n",
       "      <td>-0.049776</td>\n",
       "      <td>-0.031107</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>0.165318</td>\n",
       "      <td>-1.919571</td>\n",
       "      <td>2.548135</td>\n",
       "      <td>0.365674</td>\n",
       "      <td>0.843075</td>\n",
       "      <td>-0.512586</td>\n",
       "      <td>1.820463</td>\n",
       "      <td>-0.646666</td>\n",
       "      <td>-0.212915</td>\n",
       "      <td>0.179016</td>\n",
       "      <td>-0.301681</td>\n",
       "      <td>-0.330036</td>\n",
       "      <td>-0.445375</td>\n",
       "      <td>-0.147088</td>\n",
       "      <td>0.012302</td>\n",
       "      <td>0.065606</td>\n",
       "      <td>-0.005114</td>\n",
       "      <td>0.040032</td>\n",
       "      <td>0.038938</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>4.620819</td>\n",
       "      <td>-0.418248</td>\n",
       "      <td>-1.524230</td>\n",
       "      <td>-0.343702</td>\n",
       "      <td>0.893863</td>\n",
       "      <td>-0.570270</td>\n",
       "      <td>1.240332</td>\n",
       "      <td>-0.890854</td>\n",
       "      <td>-0.097335</td>\n",
       "      <td>-0.581787</td>\n",
       "      <td>0.156429</td>\n",
       "      <td>0.371672</td>\n",
       "      <td>0.105426</td>\n",
       "      <td>0.217895</td>\n",
       "      <td>-0.590258</td>\n",
       "      <td>-0.246180</td>\n",
       "      <td>0.077626</td>\n",
       "      <td>0.000320</td>\n",
       "      <td>0.010350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>-2.521251</td>\n",
       "      <td>-0.104975</td>\n",
       "      <td>0.501976</td>\n",
       "      <td>-1.383434</td>\n",
       "      <td>0.894283</td>\n",
       "      <td>-0.669103</td>\n",
       "      <td>0.367361</td>\n",
       "      <td>0.938914</td>\n",
       "      <td>-0.190485</td>\n",
       "      <td>0.411693</td>\n",
       "      <td>-0.154348</td>\n",
       "      <td>-0.082384</td>\n",
       "      <td>-0.160951</td>\n",
       "      <td>0.272895</td>\n",
       "      <td>-0.044384</td>\n",
       "      <td>-0.168799</td>\n",
       "      <td>0.031520</td>\n",
       "      <td>-0.022980</td>\n",
       "      <td>0.012640</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>0.354564</td>\n",
       "      <td>-3.397236</td>\n",
       "      <td>0.281875</td>\n",
       "      <td>2.057036</td>\n",
       "      <td>-0.937166</td>\n",
       "      <td>-0.448480</td>\n",
       "      <td>-0.708541</td>\n",
       "      <td>-0.557818</td>\n",
       "      <td>-0.808419</td>\n",
       "      <td>-0.029795</td>\n",
       "      <td>0.248470</td>\n",
       "      <td>0.219563</td>\n",
       "      <td>-0.034651</td>\n",
       "      <td>0.062045</td>\n",
       "      <td>-0.041153</td>\n",
       "      <td>0.141306</td>\n",
       "      <td>-0.015472</td>\n",
       "      <td>0.003363</td>\n",
       "      <td>-0.002312</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>-2.592687</td>\n",
       "      <td>1.583279</td>\n",
       "      <td>-1.608218</td>\n",
       "      <td>0.492974</td>\n",
       "      <td>0.942963</td>\n",
       "      <td>1.070955</td>\n",
       "      <td>-0.262522</td>\n",
       "      <td>0.200542</td>\n",
       "      <td>0.156128</td>\n",
       "      <td>-0.148030</td>\n",
       "      <td>0.068683</td>\n",
       "      <td>0.016403</td>\n",
       "      <td>-0.180048</td>\n",
       "      <td>-0.075711</td>\n",
       "      <td>-0.100684</td>\n",
       "      <td>-0.013185</td>\n",
       "      <td>-0.038492</td>\n",
       "      <td>0.027780</td>\n",
       "      <td>0.001663</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>2.747322</td>\n",
       "      <td>2.051091</td>\n",
       "      <td>2.537480</td>\n",
       "      <td>1.169989</td>\n",
       "      <td>1.093201</td>\n",
       "      <td>-0.494353</td>\n",
       "      <td>-1.352609</td>\n",
       "      <td>-0.148083</td>\n",
       "      <td>-1.241667</td>\n",
       "      <td>-0.027185</td>\n",
       "      <td>0.276369</td>\n",
       "      <td>0.147246</td>\n",
       "      <td>0.394630</td>\n",
       "      <td>0.022914</td>\n",
       "      <td>-0.107401</td>\n",
       "      <td>0.113559</td>\n",
       "      <td>-0.083346</td>\n",
       "      <td>-0.065977</td>\n",
       "      <td>0.125582</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>233</th>\n",
       "      <td>-0.109403</td>\n",
       "      <td>-3.595129</td>\n",
       "      <td>0.328831</td>\n",
       "      <td>2.110736</td>\n",
       "      <td>-1.018090</td>\n",
       "      <td>-0.036488</td>\n",
       "      <td>0.127879</td>\n",
       "      <td>1.672294</td>\n",
       "      <td>0.778216</td>\n",
       "      <td>0.473452</td>\n",
       "      <td>-0.278535</td>\n",
       "      <td>-0.101508</td>\n",
       "      <td>-0.217234</td>\n",
       "      <td>0.490513</td>\n",
       "      <td>-0.061294</td>\n",
       "      <td>0.234649</td>\n",
       "      <td>0.023926</td>\n",
       "      <td>-0.004327</td>\n",
       "      <td>0.028981</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>234</th>\n",
       "      <td>-1.388562</td>\n",
       "      <td>0.507019</td>\n",
       "      <td>1.408651</td>\n",
       "      <td>-0.389585</td>\n",
       "      <td>0.762880</td>\n",
       "      <td>-0.469189</td>\n",
       "      <td>1.489471</td>\n",
       "      <td>0.037609</td>\n",
       "      <td>0.894924</td>\n",
       "      <td>-0.343701</td>\n",
       "      <td>0.021203</td>\n",
       "      <td>0.179872</td>\n",
       "      <td>-0.343351</td>\n",
       "      <td>-0.094061</td>\n",
       "      <td>0.051275</td>\n",
       "      <td>0.163308</td>\n",
       "      <td>0.003399</td>\n",
       "      <td>-0.013923</td>\n",
       "      <td>0.008760</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>235</th>\n",
       "      <td>-3.020961</td>\n",
       "      <td>1.265845</td>\n",
       "      <td>0.970229</td>\n",
       "      <td>-0.600885</td>\n",
       "      <td>-1.197369</td>\n",
       "      <td>-0.477105</td>\n",
       "      <td>0.363921</td>\n",
       "      <td>-0.009564</td>\n",
       "      <td>0.536636</td>\n",
       "      <td>0.214656</td>\n",
       "      <td>0.108463</td>\n",
       "      <td>0.097596</td>\n",
       "      <td>0.112119</td>\n",
       "      <td>-0.004623</td>\n",
       "      <td>0.073873</td>\n",
       "      <td>0.102982</td>\n",
       "      <td>0.004079</td>\n",
       "      <td>0.018228</td>\n",
       "      <td>0.003872</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>236</th>\n",
       "      <td>0.781617</td>\n",
       "      <td>-2.390912</td>\n",
       "      <td>0.844478</td>\n",
       "      <td>-1.733680</td>\n",
       "      <td>0.937689</td>\n",
       "      <td>-1.051724</td>\n",
       "      <td>1.319469</td>\n",
       "      <td>1.632639</td>\n",
       "      <td>-0.547856</td>\n",
       "      <td>0.249376</td>\n",
       "      <td>-0.496253</td>\n",
       "      <td>-0.267745</td>\n",
       "      <td>-0.329786</td>\n",
       "      <td>0.189796</td>\n",
       "      <td>-0.026396</td>\n",
       "      <td>0.361574</td>\n",
       "      <td>0.034998</td>\n",
       "      <td>0.005971</td>\n",
       "      <td>0.051550</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>237</th>\n",
       "      <td>-2.189986</td>\n",
       "      <td>1.491790</td>\n",
       "      <td>-0.748916</td>\n",
       "      <td>-0.398164</td>\n",
       "      <td>0.828383</td>\n",
       "      <td>-0.482312</td>\n",
       "      <td>0.125941</td>\n",
       "      <td>-0.129507</td>\n",
       "      <td>0.020562</td>\n",
       "      <td>-0.147126</td>\n",
       "      <td>-0.939160</td>\n",
       "      <td>1.055504</td>\n",
       "      <td>-0.021997</td>\n",
       "      <td>0.054808</td>\n",
       "      <td>0.264818</td>\n",
       "      <td>0.099630</td>\n",
       "      <td>-0.000486</td>\n",
       "      <td>-0.024495</td>\n",
       "      <td>0.015731</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>238</th>\n",
       "      <td>0.592365</td>\n",
       "      <td>-0.865376</td>\n",
       "      <td>2.584718</td>\n",
       "      <td>0.321967</td>\n",
       "      <td>-1.092681</td>\n",
       "      <td>0.116704</td>\n",
       "      <td>1.366193</td>\n",
       "      <td>-0.064725</td>\n",
       "      <td>1.163895</td>\n",
       "      <td>-0.281333</td>\n",
       "      <td>0.439612</td>\n",
       "      <td>0.645534</td>\n",
       "      <td>0.589866</td>\n",
       "      <td>0.151940</td>\n",
       "      <td>0.281523</td>\n",
       "      <td>-0.073101</td>\n",
       "      <td>0.013922</td>\n",
       "      <td>-0.140908</td>\n",
       "      <td>-0.065652</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>239</th>\n",
       "      <td>-1.597665</td>\n",
       "      <td>-1.283359</td>\n",
       "      <td>-1.123601</td>\n",
       "      <td>1.087963</td>\n",
       "      <td>0.963203</td>\n",
       "      <td>-0.675707</td>\n",
       "      <td>-0.531006</td>\n",
       "      <td>0.470310</td>\n",
       "      <td>-0.099342</td>\n",
       "      <td>0.048615</td>\n",
       "      <td>-0.127003</td>\n",
       "      <td>-0.219532</td>\n",
       "      <td>-0.196829</td>\n",
       "      <td>0.483594</td>\n",
       "      <td>0.649658</td>\n",
       "      <td>-0.067842</td>\n",
       "      <td>0.103283</td>\n",
       "      <td>-0.097836</td>\n",
       "      <td>0.018837</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>240</th>\n",
       "      <td>-4.800079</td>\n",
       "      <td>2.450296</td>\n",
       "      <td>-0.369400</td>\n",
       "      <td>-0.222979</td>\n",
       "      <td>1.041927</td>\n",
       "      <td>2.175340</td>\n",
       "      <td>-0.707603</td>\n",
       "      <td>-0.553520</td>\n",
       "      <td>0.179595</td>\n",
       "      <td>0.383583</td>\n",
       "      <td>-1.339508</td>\n",
       "      <td>0.279815</td>\n",
       "      <td>0.330387</td>\n",
       "      <td>-0.311184</td>\n",
       "      <td>-0.213661</td>\n",
       "      <td>0.103846</td>\n",
       "      <td>-0.071964</td>\n",
       "      <td>0.014540</td>\n",
       "      <td>0.000685</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>241</th>\n",
       "      <td>-3.135664</td>\n",
       "      <td>2.227943</td>\n",
       "      <td>0.330068</td>\n",
       "      <td>-1.249720</td>\n",
       "      <td>-1.183045</td>\n",
       "      <td>-0.289683</td>\n",
       "      <td>0.137301</td>\n",
       "      <td>0.220382</td>\n",
       "      <td>0.188673</td>\n",
       "      <td>-0.098804</td>\n",
       "      <td>0.098170</td>\n",
       "      <td>0.120756</td>\n",
       "      <td>-0.324512</td>\n",
       "      <td>-0.052014</td>\n",
       "      <td>-0.007587</td>\n",
       "      <td>-0.128203</td>\n",
       "      <td>0.009733</td>\n",
       "      <td>-0.087104</td>\n",
       "      <td>0.013466</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>242</th>\n",
       "      <td>-2.413200</td>\n",
       "      <td>1.452691</td>\n",
       "      <td>-1.843542</td>\n",
       "      <td>0.254280</td>\n",
       "      <td>0.924325</td>\n",
       "      <td>0.575997</td>\n",
       "      <td>-0.269624</td>\n",
       "      <td>-0.444990</td>\n",
       "      <td>0.083057</td>\n",
       "      <td>-0.171534</td>\n",
       "      <td>0.114226</td>\n",
       "      <td>-0.000244</td>\n",
       "      <td>-0.020904</td>\n",
       "      <td>-0.064370</td>\n",
       "      <td>0.058501</td>\n",
       "      <td>0.120618</td>\n",
       "      <td>-0.077355</td>\n",
       "      <td>0.015000</td>\n",
       "      <td>-0.022235</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>243</th>\n",
       "      <td>-0.204079</td>\n",
       "      <td>3.509632</td>\n",
       "      <td>-1.316145</td>\n",
       "      <td>1.286691</td>\n",
       "      <td>0.860525</td>\n",
       "      <td>0.464705</td>\n",
       "      <td>-0.358526</td>\n",
       "      <td>1.053932</td>\n",
       "      <td>0.006810</td>\n",
       "      <td>-0.540583</td>\n",
       "      <td>0.309471</td>\n",
       "      <td>0.466660</td>\n",
       "      <td>-0.691423</td>\n",
       "      <td>-0.077937</td>\n",
       "      <td>-0.004767</td>\n",
       "      <td>0.133906</td>\n",
       "      <td>-0.100601</td>\n",
       "      <td>-0.084431</td>\n",
       "      <td>0.030830</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>244</th>\n",
       "      <td>0.351533</td>\n",
       "      <td>-1.185396</td>\n",
       "      <td>1.963629</td>\n",
       "      <td>-0.910715</td>\n",
       "      <td>-0.701158</td>\n",
       "      <td>1.584364</td>\n",
       "      <td>-0.241614</td>\n",
       "      <td>0.108525</td>\n",
       "      <td>-0.872380</td>\n",
       "      <td>0.252505</td>\n",
       "      <td>0.308680</td>\n",
       "      <td>0.314099</td>\n",
       "      <td>-0.135031</td>\n",
       "      <td>-0.002908</td>\n",
       "      <td>0.437375</td>\n",
       "      <td>0.308657</td>\n",
       "      <td>0.005664</td>\n",
       "      <td>0.089902</td>\n",
       "      <td>0.021933</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>245</th>\n",
       "      <td>-1.477414</td>\n",
       "      <td>-1.727950</td>\n",
       "      <td>2.758495</td>\n",
       "      <td>1.034681</td>\n",
       "      <td>-1.015978</td>\n",
       "      <td>-0.476608</td>\n",
       "      <td>-0.243771</td>\n",
       "      <td>0.413158</td>\n",
       "      <td>-0.013014</td>\n",
       "      <td>0.595545</td>\n",
       "      <td>0.323686</td>\n",
       "      <td>0.379683</td>\n",
       "      <td>0.333726</td>\n",
       "      <td>0.331645</td>\n",
       "      <td>-0.016289</td>\n",
       "      <td>-0.372484</td>\n",
       "      <td>0.114977</td>\n",
       "      <td>-0.043971</td>\n",
       "      <td>-0.005596</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>246</th>\n",
       "      <td>-0.630399</td>\n",
       "      <td>-1.586506</td>\n",
       "      <td>-0.288104</td>\n",
       "      <td>1.521727</td>\n",
       "      <td>0.738338</td>\n",
       "      <td>-0.247005</td>\n",
       "      <td>1.677445</td>\n",
       "      <td>-0.929791</td>\n",
       "      <td>0.239943</td>\n",
       "      <td>-0.135456</td>\n",
       "      <td>0.122386</td>\n",
       "      <td>0.173333</td>\n",
       "      <td>-0.004062</td>\n",
       "      <td>-0.457810</td>\n",
       "      <td>-0.349633</td>\n",
       "      <td>-0.194709</td>\n",
       "      <td>0.007171</td>\n",
       "      <td>0.016611</td>\n",
       "      <td>0.012287</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>247</th>\n",
       "      <td>-0.897584</td>\n",
       "      <td>4.035288</td>\n",
       "      <td>0.526034</td>\n",
       "      <td>-0.744719</td>\n",
       "      <td>0.768556</td>\n",
       "      <td>-0.520411</td>\n",
       "      <td>0.325824</td>\n",
       "      <td>0.499430</td>\n",
       "      <td>0.067997</td>\n",
       "      <td>-0.237128</td>\n",
       "      <td>-0.259119</td>\n",
       "      <td>-0.374129</td>\n",
       "      <td>0.295988</td>\n",
       "      <td>0.019241</td>\n",
       "      <td>0.043372</td>\n",
       "      <td>-0.012748</td>\n",
       "      <td>-0.149269</td>\n",
       "      <td>0.043766</td>\n",
       "      <td>0.023824</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>248</th>\n",
       "      <td>3.620540</td>\n",
       "      <td>6.446612</td>\n",
       "      <td>1.221060</td>\n",
       "      <td>0.035406</td>\n",
       "      <td>0.976830</td>\n",
       "      <td>0.121677</td>\n",
       "      <td>-0.849409</td>\n",
       "      <td>0.172538</td>\n",
       "      <td>-0.161419</td>\n",
       "      <td>0.511081</td>\n",
       "      <td>0.054147</td>\n",
       "      <td>-0.067335</td>\n",
       "      <td>0.034614</td>\n",
       "      <td>-0.347053</td>\n",
       "      <td>-0.375775</td>\n",
       "      <td>0.150426</td>\n",
       "      <td>0.590764</td>\n",
       "      <td>-0.165173</td>\n",
       "      <td>0.011092</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>249</th>\n",
       "      <td>-2.284968</td>\n",
       "      <td>0.936929</td>\n",
       "      <td>1.293063</td>\n",
       "      <td>-0.344655</td>\n",
       "      <td>-1.112760</td>\n",
       "      <td>-0.314411</td>\n",
       "      <td>-0.077419</td>\n",
       "      <td>-0.355335</td>\n",
       "      <td>0.237324</td>\n",
       "      <td>0.238878</td>\n",
       "      <td>-0.001691</td>\n",
       "      <td>-0.121008</td>\n",
       "      <td>0.145642</td>\n",
       "      <td>-0.058436</td>\n",
       "      <td>-0.068894</td>\n",
       "      <td>-0.035495</td>\n",
       "      <td>-0.005386</td>\n",
       "      <td>0.023533</td>\n",
       "      <td>0.015773</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>250</th>\n",
       "      <td>0.547392</td>\n",
       "      <td>-0.647612</td>\n",
       "      <td>1.811970</td>\n",
       "      <td>0.017238</td>\n",
       "      <td>-0.878407</td>\n",
       "      <td>-0.900164</td>\n",
       "      <td>-1.301805</td>\n",
       "      <td>-0.590023</td>\n",
       "      <td>0.319471</td>\n",
       "      <td>0.061319</td>\n",
       "      <td>0.241541</td>\n",
       "      <td>0.147751</td>\n",
       "      <td>0.103426</td>\n",
       "      <td>0.008604</td>\n",
       "      <td>0.320342</td>\n",
       "      <td>-0.100091</td>\n",
       "      <td>0.035265</td>\n",
       "      <td>0.092641</td>\n",
       "      <td>0.033600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>251</th>\n",
       "      <td>-1.278682</td>\n",
       "      <td>-1.675352</td>\n",
       "      <td>1.312185</td>\n",
       "      <td>-1.193412</td>\n",
       "      <td>-1.162173</td>\n",
       "      <td>-0.358582</td>\n",
       "      <td>1.893501</td>\n",
       "      <td>0.589389</td>\n",
       "      <td>-1.172429</td>\n",
       "      <td>0.849564</td>\n",
       "      <td>-0.216406</td>\n",
       "      <td>-0.182394</td>\n",
       "      <td>-0.413834</td>\n",
       "      <td>-0.009702</td>\n",
       "      <td>0.182000</td>\n",
       "      <td>-0.538661</td>\n",
       "      <td>0.216921</td>\n",
       "      <td>0.009430</td>\n",
       "      <td>0.017272</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>252</th>\n",
       "      <td>2.158657</td>\n",
       "      <td>-3.540909</td>\n",
       "      <td>1.520838</td>\n",
       "      <td>-2.311067</td>\n",
       "      <td>-0.586303</td>\n",
       "      <td>1.939852</td>\n",
       "      <td>0.122533</td>\n",
       "      <td>0.181229</td>\n",
       "      <td>-0.355070</td>\n",
       "      <td>-0.124241</td>\n",
       "      <td>-0.088671</td>\n",
       "      <td>0.057992</td>\n",
       "      <td>-0.039064</td>\n",
       "      <td>-0.136403</td>\n",
       "      <td>-0.574147</td>\n",
       "      <td>-0.042708</td>\n",
       "      <td>-0.026300</td>\n",
       "      <td>0.059983</td>\n",
       "      <td>-0.041700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>253</th>\n",
       "      <td>-1.123708</td>\n",
       "      <td>0.878726</td>\n",
       "      <td>1.380280</td>\n",
       "      <td>-0.326076</td>\n",
       "      <td>-1.134957</td>\n",
       "      <td>-0.396786</td>\n",
       "      <td>0.282579</td>\n",
       "      <td>0.078545</td>\n",
       "      <td>1.334589</td>\n",
       "      <td>-0.107678</td>\n",
       "      <td>0.062599</td>\n",
       "      <td>0.114864</td>\n",
       "      <td>0.168243</td>\n",
       "      <td>0.032036</td>\n",
       "      <td>-0.017582</td>\n",
       "      <td>-0.228612</td>\n",
       "      <td>0.039463</td>\n",
       "      <td>-0.018130</td>\n",
       "      <td>-0.001618</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>254</th>\n",
       "      <td>-1.384083</td>\n",
       "      <td>-0.335374</td>\n",
       "      <td>2.419414</td>\n",
       "      <td>0.738687</td>\n",
       "      <td>-1.128251</td>\n",
       "      <td>-0.139383</td>\n",
       "      <td>0.392432</td>\n",
       "      <td>0.231712</td>\n",
       "      <td>-0.400073</td>\n",
       "      <td>0.070228</td>\n",
       "      <td>-0.217093</td>\n",
       "      <td>-0.221829</td>\n",
       "      <td>-0.570632</td>\n",
       "      <td>0.026902</td>\n",
       "      <td>-0.361100</td>\n",
       "      <td>0.173899</td>\n",
       "      <td>-0.086229</td>\n",
       "      <td>-0.019452</td>\n",
       "      <td>0.013676</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>255</th>\n",
       "      <td>2.002422</td>\n",
       "      <td>-3.408654</td>\n",
       "      <td>0.479667</td>\n",
       "      <td>1.746449</td>\n",
       "      <td>-1.215699</td>\n",
       "      <td>-0.511633</td>\n",
       "      <td>2.078599</td>\n",
       "      <td>-0.955298</td>\n",
       "      <td>-0.997283</td>\n",
       "      <td>0.055357</td>\n",
       "      <td>0.094822</td>\n",
       "      <td>0.174274</td>\n",
       "      <td>0.381985</td>\n",
       "      <td>-0.266720</td>\n",
       "      <td>-0.356703</td>\n",
       "      <td>0.646105</td>\n",
       "      <td>-0.053170</td>\n",
       "      <td>-0.010997</td>\n",
       "      <td>0.084750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>256</th>\n",
       "      <td>-2.108194</td>\n",
       "      <td>-1.463497</td>\n",
       "      <td>1.076021</td>\n",
       "      <td>-1.748447</td>\n",
       "      <td>1.234843</td>\n",
       "      <td>1.665103</td>\n",
       "      <td>-0.024078</td>\n",
       "      <td>0.290549</td>\n",
       "      <td>-0.254985</td>\n",
       "      <td>0.371372</td>\n",
       "      <td>-0.384419</td>\n",
       "      <td>-0.486727</td>\n",
       "      <td>-0.217575</td>\n",
       "      <td>0.009344</td>\n",
       "      <td>-0.179317</td>\n",
       "      <td>0.061824</td>\n",
       "      <td>0.008438</td>\n",
       "      <td>0.013965</td>\n",
       "      <td>-0.002319</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>257</th>\n",
       "      <td>-0.009269</td>\n",
       "      <td>-4.502827</td>\n",
       "      <td>-0.833417</td>\n",
       "      <td>-0.617503</td>\n",
       "      <td>1.447927</td>\n",
       "      <td>2.551487</td>\n",
       "      <td>-0.461301</td>\n",
       "      <td>-0.018018</td>\n",
       "      <td>-0.023161</td>\n",
       "      <td>-0.114303</td>\n",
       "      <td>0.090621</td>\n",
       "      <td>0.138423</td>\n",
       "      <td>0.461864</td>\n",
       "      <td>0.136953</td>\n",
       "      <td>-0.275722</td>\n",
       "      <td>0.033526</td>\n",
       "      <td>-0.087040</td>\n",
       "      <td>0.036939</td>\n",
       "      <td>-0.023555</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>258</th>\n",
       "      <td>-0.331167</td>\n",
       "      <td>-0.165663</td>\n",
       "      <td>0.775890</td>\n",
       "      <td>-1.536702</td>\n",
       "      <td>-1.035016</td>\n",
       "      <td>-0.306299</td>\n",
       "      <td>0.552371</td>\n",
       "      <td>1.184243</td>\n",
       "      <td>-0.246646</td>\n",
       "      <td>0.379402</td>\n",
       "      <td>-0.094963</td>\n",
       "      <td>-0.033645</td>\n",
       "      <td>0.216773</td>\n",
       "      <td>-0.161802</td>\n",
       "      <td>0.227441</td>\n",
       "      <td>-0.224885</td>\n",
       "      <td>0.126489</td>\n",
       "      <td>-0.055403</td>\n",
       "      <td>-0.009739</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>259</th>\n",
       "      <td>3.246183</td>\n",
       "      <td>-0.543315</td>\n",
       "      <td>1.209150</td>\n",
       "      <td>2.754023</td>\n",
       "      <td>-1.197520</td>\n",
       "      <td>0.834749</td>\n",
       "      <td>1.969884</td>\n",
       "      <td>-1.371907</td>\n",
       "      <td>-0.543945</td>\n",
       "      <td>-0.897725</td>\n",
       "      <td>-0.166160</td>\n",
       "      <td>-0.298189</td>\n",
       "      <td>0.510572</td>\n",
       "      <td>0.318121</td>\n",
       "      <td>-0.144807</td>\n",
       "      <td>0.008947</td>\n",
       "      <td>-0.152826</td>\n",
       "      <td>-0.053871</td>\n",
       "      <td>-0.062282</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>260</th>\n",
       "      <td>-1.094609</td>\n",
       "      <td>-0.751386</td>\n",
       "      <td>-0.935937</td>\n",
       "      <td>1.072347</td>\n",
       "      <td>0.705912</td>\n",
       "      <td>-0.644482</td>\n",
       "      <td>1.496147</td>\n",
       "      <td>0.287111</td>\n",
       "      <td>-0.304373</td>\n",
       "      <td>0.017862</td>\n",
       "      <td>0.221392</td>\n",
       "      <td>0.378174</td>\n",
       "      <td>0.016308</td>\n",
       "      <td>0.092282</td>\n",
       "      <td>0.056039</td>\n",
       "      <td>-0.103487</td>\n",
       "      <td>-0.078738</td>\n",
       "      <td>0.067201</td>\n",
       "      <td>0.013194</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>261</th>\n",
       "      <td>1.977682</td>\n",
       "      <td>-2.184517</td>\n",
       "      <td>-0.282012</td>\n",
       "      <td>-0.216874</td>\n",
       "      <td>-0.694872</td>\n",
       "      <td>3.514692</td>\n",
       "      <td>1.142097</td>\n",
       "      <td>-0.230697</td>\n",
       "      <td>-0.240990</td>\n",
       "      <td>0.324960</td>\n",
       "      <td>0.118597</td>\n",
       "      <td>0.162044</td>\n",
       "      <td>-0.347028</td>\n",
       "      <td>-0.232762</td>\n",
       "      <td>0.021050</td>\n",
       "      <td>-0.262275</td>\n",
       "      <td>-0.014407</td>\n",
       "      <td>0.022921</td>\n",
       "      <td>-0.010530</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>262</th>\n",
       "      <td>1.833002</td>\n",
       "      <td>-0.301097</td>\n",
       "      <td>-1.055323</td>\n",
       "      <td>0.492980</td>\n",
       "      <td>0.916396</td>\n",
       "      <td>0.275273</td>\n",
       "      <td>1.224192</td>\n",
       "      <td>2.427177</td>\n",
       "      <td>-0.717128</td>\n",
       "      <td>-0.192461</td>\n",
       "      <td>-0.303374</td>\n",
       "      <td>-0.165953</td>\n",
       "      <td>-0.023341</td>\n",
       "      <td>0.023766</td>\n",
       "      <td>0.660839</td>\n",
       "      <td>-0.186210</td>\n",
       "      <td>-0.302569</td>\n",
       "      <td>-0.075529</td>\n",
       "      <td>-0.040599</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>263 rows × 19 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           0         1         2         3         4         5         6   \\\n",
       "0   -0.009649  1.870522  1.265145 -0.935481  1.109636  1.211972 -0.065146   \n",
       "1    0.411434 -2.429422 -0.909193 -0.264212  1.232031  1.826617  0.359893   \n",
       "2    3.466822  0.825947  0.555469 -1.616726 -0.857488 -1.028712 -0.999385   \n",
       "3   -2.558317 -0.230984  0.519642 -2.176251 -0.820301  1.491696 -0.276141   \n",
       "4    1.027702 -1.573537  1.331382  3.494004  0.983427  0.513675  0.140456   \n",
       "5   -3.980657  1.507279 -0.155479  0.369840 -1.209334  0.033514  0.013007   \n",
       "6   -3.451719  0.599989 -0.626476  1.999776  0.807026  0.205971 -0.056137   \n",
       "7   -3.432380  0.113542  1.999750  0.767813  1.016092 -0.272797 -1.204274   \n",
       "8    3.899707  1.947870 -1.820475 -0.026713 -1.137128 -0.821045  0.314217   \n",
       "9    3.174812 -2.392365  0.794468  2.569006 -0.947328 -0.061251 -0.375009   \n",
       "10  -2.167606  1.864486  1.081053 -0.575818  0.935415  0.252217 -0.135862   \n",
       "11  -0.933213 -0.435508  0.631417 -1.598076 -0.996468 -0.648208 -0.140635   \n",
       "12  -2.275324  1.666792 -0.922849  1.439654 -1.259431  0.436370  0.572372   \n",
       "13  -1.046249  2.684710  0.959561 -0.517856 -1.119732 -0.335223 -0.337266   \n",
       "14   5.655999  0.402132  2.182295  0.201903  0.981668 -1.345032  0.466458   \n",
       "15  -3.577188  1.222869 -0.596820  2.074446  0.830985  0.417884 -0.300419   \n",
       "16  -3.263406  2.478792  0.153300 -1.284811  0.892066 -0.234267 -0.463157   \n",
       "17  -1.751013 -1.323168  0.342983 -2.147064 -1.036283 -0.624585  0.545461   \n",
       "18  -2.152780 -0.916324 -0.520684 -1.047379  0.822729 -0.021434  1.782620   \n",
       "19   0.084279 -0.903456  0.582376 -2.126568  1.040489 -0.052544  0.882075   \n",
       "20   5.970981 -0.441813  0.055237  0.754230 -0.498954  2.649546 -1.184840   \n",
       "21   0.785418 -1.694971 -1.114628 -0.113931 -1.192531  0.430105  2.325016   \n",
       "22  -2.054685  1.702366  0.644522 -1.146517 -1.121931 -0.098095  0.295297   \n",
       "23  -0.083558 -0.465050  1.460094 -1.071268  1.217913  1.108492 -0.259328   \n",
       "24   0.165318 -1.919571  2.548135  0.365674  0.843075 -0.512586  1.820463   \n",
       "25   4.620819 -0.418248 -1.524230 -0.343702  0.893863 -0.570270  1.240332   \n",
       "26  -2.521251 -0.104975  0.501976 -1.383434  0.894283 -0.669103  0.367361   \n",
       "27   0.354564 -3.397236  0.281875  2.057036 -0.937166 -0.448480 -0.708541   \n",
       "28  -2.592687  1.583279 -1.608218  0.492974  0.942963  1.070955 -0.262522   \n",
       "29   2.747322  2.051091  2.537480  1.169989  1.093201 -0.494353 -1.352609   \n",
       "..        ...       ...       ...       ...       ...       ...       ...   \n",
       "233 -0.109403 -3.595129  0.328831  2.110736 -1.018090 -0.036488  0.127879   \n",
       "234 -1.388562  0.507019  1.408651 -0.389585  0.762880 -0.469189  1.489471   \n",
       "235 -3.020961  1.265845  0.970229 -0.600885 -1.197369 -0.477105  0.363921   \n",
       "236  0.781617 -2.390912  0.844478 -1.733680  0.937689 -1.051724  1.319469   \n",
       "237 -2.189986  1.491790 -0.748916 -0.398164  0.828383 -0.482312  0.125941   \n",
       "238  0.592365 -0.865376  2.584718  0.321967 -1.092681  0.116704  1.366193   \n",
       "239 -1.597665 -1.283359 -1.123601  1.087963  0.963203 -0.675707 -0.531006   \n",
       "240 -4.800079  2.450296 -0.369400 -0.222979  1.041927  2.175340 -0.707603   \n",
       "241 -3.135664  2.227943  0.330068 -1.249720 -1.183045 -0.289683  0.137301   \n",
       "242 -2.413200  1.452691 -1.843542  0.254280  0.924325  0.575997 -0.269624   \n",
       "243 -0.204079  3.509632 -1.316145  1.286691  0.860525  0.464705 -0.358526   \n",
       "244  0.351533 -1.185396  1.963629 -0.910715 -0.701158  1.584364 -0.241614   \n",
       "245 -1.477414 -1.727950  2.758495  1.034681 -1.015978 -0.476608 -0.243771   \n",
       "246 -0.630399 -1.586506 -0.288104  1.521727  0.738338 -0.247005  1.677445   \n",
       "247 -0.897584  4.035288  0.526034 -0.744719  0.768556 -0.520411  0.325824   \n",
       "248  3.620540  6.446612  1.221060  0.035406  0.976830  0.121677 -0.849409   \n",
       "249 -2.284968  0.936929  1.293063 -0.344655 -1.112760 -0.314411 -0.077419   \n",
       "250  0.547392 -0.647612  1.811970  0.017238 -0.878407 -0.900164 -1.301805   \n",
       "251 -1.278682 -1.675352  1.312185 -1.193412 -1.162173 -0.358582  1.893501   \n",
       "252  2.158657 -3.540909  1.520838 -2.311067 -0.586303  1.939852  0.122533   \n",
       "253 -1.123708  0.878726  1.380280 -0.326076 -1.134957 -0.396786  0.282579   \n",
       "254 -1.384083 -0.335374  2.419414  0.738687 -1.128251 -0.139383  0.392432   \n",
       "255  2.002422 -3.408654  0.479667  1.746449 -1.215699 -0.511633  2.078599   \n",
       "256 -2.108194 -1.463497  1.076021 -1.748447  1.234843  1.665103 -0.024078   \n",
       "257 -0.009269 -4.502827 -0.833417 -0.617503  1.447927  2.551487 -0.461301   \n",
       "258 -0.331167 -0.165663  0.775890 -1.536702 -1.035016 -0.306299  0.552371   \n",
       "259  3.246183 -0.543315  1.209150  2.754023 -1.197520  0.834749  1.969884   \n",
       "260 -1.094609 -0.751386 -0.935937  1.072347  0.705912 -0.644482  1.496147   \n",
       "261  1.977682 -2.184517 -0.282012 -0.216874 -0.694872  3.514692  1.142097   \n",
       "262  1.833002 -0.301097 -1.055323  0.492980  0.916396  0.275273  1.224192   \n",
       "\n",
       "           7         8         9         10        11        12        13  \\\n",
       "0   -0.098249 -0.252423 -0.637101  0.459341  0.615860 -0.478088  0.388407   \n",
       "1   -1.199383 -0.371820  0.015215  0.176235  0.080529  0.403483 -0.019386   \n",
       "2    0.844247  0.197379  0.770490  0.055645  0.104938  0.021605 -0.376197   \n",
       "3    0.207094  0.414956  0.136842 -0.085375 -0.146217  0.142172  0.028975   \n",
       "4    0.989707 -0.661933 -0.217565  0.111259  0.191244 -0.302426 -0.090770   \n",
       "5   -0.540315  0.121838  0.411966 -1.198707  0.538882  0.106017 -0.238849   \n",
       "6    0.395305  0.719654  0.421149  0.039300 -0.022136  0.178050  0.172087   \n",
       "7   -0.098152  0.035413  0.359129 -0.010706 -0.201662  0.115068  0.284426   \n",
       "8   -1.192292  0.444240  0.510195  0.217092  0.221224  0.130075  0.644068   \n",
       "9   -0.425686 -0.065025 -0.498544 -0.533286 -0.717679 -0.283230 -0.272698   \n",
       "10  -0.228715 -0.543103 -0.458606  0.130928  0.116231 -0.347348 -0.134637   \n",
       "11  -0.174776 -0.219926  0.036233  0.185101  0.200756  0.416675  0.268332   \n",
       "12   0.129116  0.088152  0.005072 -0.163502 -0.320181  0.112925 -0.012291   \n",
       "13  -0.203572 -0.361965 -0.917351  0.171027  0.152325 -0.468663 -0.322277   \n",
       "14   0.019188  0.337658 -0.342902 -0.300026 -0.306333  0.095752 -0.488056   \n",
       "15  -0.571571 -0.466927  0.099572  0.024845 -0.194712 -0.334248 -0.055586   \n",
       "16  -0.089185  0.438550 -0.498858  0.044587  0.041791 -0.436226 -0.080805   \n",
       "17  -0.813632 -0.153811 -0.032113 -0.197054 -0.332331 -0.065527 -0.378001   \n",
       "18  -0.045956  0.077066  0.396404  1.332914 -0.530436  0.289715 -0.047173   \n",
       "19  -0.605949  0.429003 -0.236362  0.161771  0.258728 -0.015689 -0.035607   \n",
       "20   1.699355 -0.252054 -0.392732  0.448387  0.620552  0.276792 -0.802375   \n",
       "21   0.747215 -0.644452  0.165261 -0.093634  0.082252  0.083503  0.105205   \n",
       "22   0.642791 -0.168415 -0.066757 -0.106032 -0.144704 -0.138462  0.260333   \n",
       "23   0.444383 -0.357445 -0.130988  0.384545  0.580438 -0.490799  0.249610   \n",
       "24  -0.646666 -0.212915  0.179016 -0.301681 -0.330036 -0.445375 -0.147088   \n",
       "25  -0.890854 -0.097335 -0.581787  0.156429  0.371672  0.105426  0.217895   \n",
       "26   0.938914 -0.190485  0.411693 -0.154348 -0.082384 -0.160951  0.272895   \n",
       "27  -0.557818 -0.808419 -0.029795  0.248470  0.219563 -0.034651  0.062045   \n",
       "28   0.200542  0.156128 -0.148030  0.068683  0.016403 -0.180048 -0.075711   \n",
       "29  -0.148083 -1.241667 -0.027185  0.276369  0.147246  0.394630  0.022914   \n",
       "..        ...       ...       ...       ...       ...       ...       ...   \n",
       "233  1.672294  0.778216  0.473452 -0.278535 -0.101508 -0.217234  0.490513   \n",
       "234  0.037609  0.894924 -0.343701  0.021203  0.179872 -0.343351 -0.094061   \n",
       "235 -0.009564  0.536636  0.214656  0.108463  0.097596  0.112119 -0.004623   \n",
       "236  1.632639 -0.547856  0.249376 -0.496253 -0.267745 -0.329786  0.189796   \n",
       "237 -0.129507  0.020562 -0.147126 -0.939160  1.055504 -0.021997  0.054808   \n",
       "238 -0.064725  1.163895 -0.281333  0.439612  0.645534  0.589866  0.151940   \n",
       "239  0.470310 -0.099342  0.048615 -0.127003 -0.219532 -0.196829  0.483594   \n",
       "240 -0.553520  0.179595  0.383583 -1.339508  0.279815  0.330387 -0.311184   \n",
       "241  0.220382  0.188673 -0.098804  0.098170  0.120756 -0.324512 -0.052014   \n",
       "242 -0.444990  0.083057 -0.171534  0.114226 -0.000244 -0.020904 -0.064370   \n",
       "243  1.053932  0.006810 -0.540583  0.309471  0.466660 -0.691423 -0.077937   \n",
       "244  0.108525 -0.872380  0.252505  0.308680  0.314099 -0.135031 -0.002908   \n",
       "245  0.413158 -0.013014  0.595545  0.323686  0.379683  0.333726  0.331645   \n",
       "246 -0.929791  0.239943 -0.135456  0.122386  0.173333 -0.004062 -0.457810   \n",
       "247  0.499430  0.067997 -0.237128 -0.259119 -0.374129  0.295988  0.019241   \n",
       "248  0.172538 -0.161419  0.511081  0.054147 -0.067335  0.034614 -0.347053   \n",
       "249 -0.355335  0.237324  0.238878 -0.001691 -0.121008  0.145642 -0.058436   \n",
       "250 -0.590023  0.319471  0.061319  0.241541  0.147751  0.103426  0.008604   \n",
       "251  0.589389 -1.172429  0.849564 -0.216406 -0.182394 -0.413834 -0.009702   \n",
       "252  0.181229 -0.355070 -0.124241 -0.088671  0.057992 -0.039064 -0.136403   \n",
       "253  0.078545  1.334589 -0.107678  0.062599  0.114864  0.168243  0.032036   \n",
       "254  0.231712 -0.400073  0.070228 -0.217093 -0.221829 -0.570632  0.026902   \n",
       "255 -0.955298 -0.997283  0.055357  0.094822  0.174274  0.381985 -0.266720   \n",
       "256  0.290549 -0.254985  0.371372 -0.384419 -0.486727 -0.217575  0.009344   \n",
       "257 -0.018018 -0.023161 -0.114303  0.090621  0.138423  0.461864  0.136953   \n",
       "258  1.184243 -0.246646  0.379402 -0.094963 -0.033645  0.216773 -0.161802   \n",
       "259 -1.371907 -0.543945 -0.897725 -0.166160 -0.298189  0.510572  0.318121   \n",
       "260  0.287111 -0.304373  0.017862  0.221392  0.378174  0.016308  0.092282   \n",
       "261 -0.230697 -0.240990  0.324960  0.118597  0.162044 -0.347028 -0.232762   \n",
       "262  2.427177 -0.717128 -0.192461 -0.303374 -0.165953 -0.023341  0.023766   \n",
       "\n",
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       "21   0.002900 -0.205277 -0.032735  0.040446 -0.016478  \n",
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       "..        ...       ...       ...       ...       ...  \n",
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       "250  0.320342 -0.100091  0.035265  0.092641  0.033600  \n",
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       "253 -0.017582 -0.228612  0.039463 -0.018130 -0.001618  \n",
       "254 -0.361100  0.173899 -0.086229 -0.019452  0.013676  \n",
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       "261  0.021050 -0.262275 -0.014407  0.022921 -0.010530  \n",
       "262  0.660839 -0.186210 -0.302569 -0.075529 -0.040599  \n",
       "\n",
       "[263 rows x 19 columns]"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(X_reduced)"
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  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
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     "output_type": "stream",
     "text": [
      "(263, 19)\n"
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    "pd.DataFrame(X_reduced).loc[:4,:5]"
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above principal components are the same as in R."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "XtX = X_reduced.T@X_reduced"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [],
   "source": [
    "l=10"
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  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
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       "1  -9.592327e-14  6.039613e-14  6.816769e-14  4.440892e-15  2.353673e-14   \n",
       "2  -3.641532e-14  6.505907e-14  4.884981e-14 -1.776357e-14 -1.776357e-15   \n",
       "3   9.947598e-14 -1.243450e-14 -8.171241e-14 -3.108624e-14  4.818368e-14   \n",
       "4   8.704149e-14  4.973799e-14 -3.197442e-14  4.440892e-15 -1.776357e-15   \n",
       "5   2.170949e+02  1.687539e-13 -5.684342e-14 -8.881784e-15  3.641532e-14   \n",
       "6   1.687539e-13  1.812966e+02  4.024558e-15  1.965095e-14  4.005130e-14   \n",
       "7  -5.684342e-14  4.024558e-15  1.349268e+02  9.270362e-15 -1.776357e-15   \n",
       "8  -8.881784e-15  1.965095e-14  9.270362e-15  6.594281e+01  1.659783e-14   \n",
       "9   3.641532e-14  4.005130e-14 -1.776357e-15  1.659783e-14  4.860691e+01   \n",
       "10  1.185163e-14 -5.329071e-15  8.881784e-16  2.042810e-14 -9.742207e-15   \n",
       "\n",
       "              10  \n",
       "0  -2.087219e-14  \n",
       "1  -1.776357e-14  \n",
       "2  -3.885781e-14  \n",
       "3  -1.276756e-14  \n",
       "4   5.773160e-15  \n",
       "5   1.185163e-14  \n",
       "6  -5.329071e-15  \n",
       "7   8.881784e-16  \n",
       "8   2.042810e-14  \n",
       "9  -9.742207e-15  \n",
       "10  3.609539e+01  "
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(XtX).loc[:l,:l]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([38.31, 60.15, 70.84, 79.03, 84.29, 88.63, 92.26, 94.96, 96.28,\n",
       "       97.25, 97.97, 98.64, 99.14, 99.46, 99.73, 99.88, 99.95, 99.98,\n",
       "       99.99])"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Variance explained by the principal components\n",
    "np.cumsum(np.round(pca.explained_variance_ratio_, decimals=4)*100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Fitting PCA with training data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pca2 = PCA()\n",
    "X_reduced_train = pca2.fit_transform(scale(X_train))\n",
    "n = len(X_reduced_train)\n",
    "\n",
    "# 10-fold CV, with shuffle\n",
    "kf_10 = KFold(n_splits=10, shuffle=False, random_state=1)\n",
    "\n",
    "regr = LinearRegression()\n",
    "mse = []\n",
    "\n",
    "# Calculate MSE using CV for the 19 principle components, adding one component at the time.\n",
    "for i in np.arange(1, 20):\n",
    "    score = -1*cross_val_score(regr, X_reduced_train[:,:i], y_train, cv=kf_10, scoring='neg_mean_squared_error').mean()\n",
    "    mse.append(score)\n",
    "\n",
    "plt.plot(np.array(mse), '-v')\n",
    "plt.xlabel('Number of principal components in regression')\n",
    "plt.ylabel('MSE')\n",
    "plt.title('Salary')\n",
    "plt.xlim(xmin=-1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above plot indicates that the lowest training MSE is reached when doing regression on 6 components."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Transform test data with PCA & compute test result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "regr = LinearRegression()\n",
    "mse = []\n",
    "for i in np.arange(1, 20):\n",
    "    X_reduced_test = pca2.transform(scale(X_test))[:,:i]\n",
    "    # Train regression model on training data \n",
    "    regr = LinearRegression()\n",
    "    regr.fit(X_reduced_train[:,:i], y_train)\n",
    "    # Prediction with test data\n",
    "    pred = regr.predict(X_reduced_test)\n",
    "    mse.append(mean_squared_error(y_test, pred)) \n",
    "\n",
    "plt.plot(np.array(mse), '-v')\n",
    "plt.xlabel('Number of principal components in regression')\n",
    "plt.ylabel('MSE')\n",
    "plt.title('Salary')\n",
    "plt.xlim(xmin=-1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.7.2 Partial Least Squares"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Scikit-learn PLSRegression gives same results as the pls package in R when using 'method='oscorespls'. In the LAB excercise, the standard method is used which is 'kernelpls'. \n",
    "\n",
    "When doing a slightly different fitting in R, the result is close to the one obtained using scikit-learn.\n",
    "\n",
    "    pls.fit=plsr(Salary~., data=Hitters, subset=train, scale=TRUE, validation=\"CV\", method='oscorespls')\n",
    "    validationplot(pls.fit,val.type=\"MSEP\", intercept = FALSE)\n",
    "   \n",
    "See documentation:\n",
    "http://scikit-learn.org/dev/modules/generated/sklearn.cross_decomposition.PLSRegression.html#sklearn.cross_decomposition.PLSRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Select best # of components using CV\n",
    "n = len(X_train)\n",
    "mse = []\n",
    "for i in np.arange(1, 20):\n",
    "    pls = PLSRegression(n_components=i)\n",
    "    score = cross_val_score(pls, scale(X_train), y_train, cv=kf_10, scoring='neg_mean_squared_error').mean()\n",
    "    mse.append(-score)\n",
    "    # without cross validation\n",
    "    #pls.fit(scale(X_train), y_train)\n",
    "    #pred = pls.predict(X_train)\n",
    "    #mse.append(mean_squared_error(y_train, pred)) \n",
    "\n",
    "plt.plot(np.arange(1, 20), np.array(mse), '-v')\n",
    "plt.xlabel('Number of principal components in regression')\n",
    "plt.ylabel('MSE')\n",
    "plt.title('Salary')\n",
    "plt.xlim(xmin=-1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test mse with different # of principal components in regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "mse = []\n",
    "\n",
    "for i in np.arange(1, 20):\n",
    "    pls = PLSRegression(n_components=i)\n",
    "    pls.fit(scale(X_train), y_train)\n",
    "\n",
    "    mse.append(mean_squared_error(y_test, pls.predict(scale(X_test))))\n",
    "\n",
    "plt.plot(np.arange(1, 20), np.array(mse), '-v')\n",
    "plt.xlabel('Number of principal components in regression')\n",
    "plt.ylabel('MSE')\n",
    "plt.title('Salary')\n",
    "plt.xlim(xmin=-1);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}