week-3-polynomial-regression-assignment.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regression Week 3: Assessing Fit (polynomial regression)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook you will compare different regression models in order to assess which model fits best. We will be using polynomial regression as a means to examine this topic. In particular you will:\n",
    "* Write a function to take an SArray and a degree and return an SFrame where each column is the SArray to a polynomial value up to the total degree e.g. degree = 3 then column 1 is the SArray column 2 is the SArray squared and column 3 is the SArray cubed\n",
    "* Use matplotlib to visualize polynomial regressions\n",
    "* Use matplotlib to visualize the same polynomial degree on different subsets of the data\n",
    "* Use a validation set to select a polynomial degree\n",
    "* Assess the final fit using test data\n",
    "\n",
    "We will continue to use the House data from previous notebooks."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fire up graphlab create"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "A newer version of GraphLab Create (v1.8.1) is available! Your current version is v1.8.\n",
      "\n",
      "You can use pip to upgrade the graphlab-create package. For more information see https://dato.com/products/create/upgrade.\n"
     ]
    }
   ],
   "source": [
    "import graphlab"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we're going to write a polynomial function that takes an SArray and a maximal degree and returns an SFrame with columns containing the SArray to all the powers up to the maximal degree.\n",
    "\n",
    "The easiest way to apply a power to an SArray is to use the .apply() and lambda x: functions. \n",
    "For example to take the example array and compute the third power we can do as follows: (note running this cell the first time may take longer than expected since it loads graphlab)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[INFO] This non-commercial license of GraphLab Create is assigned to kcbighuge@gmail.com and will expire on October 25, 2016. For commercial licensing options, visit https://dato.com/buy/.\n",
      "\n",
      "[INFO] Start server at: ipc:///tmp/graphlab_server-9412 - Server binary: /Users/jjl/.graphlab/anaconda/lib/python2.7/site-packages/graphlab/unity_server - Server log: /tmp/graphlab_server_1454018474.log\n",
      "[INFO] GraphLab Server Version: 1.8\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.0, 2.0, 3.0]\n",
      "[1.0, 8.0, 27.0]\n"
     ]
    }
   ],
   "source": [
    "tmp = graphlab.SArray([1., 2., 3.])\n",
    "tmp_cubed = tmp.apply(lambda x: x**3)\n",
    "print tmp\n",
    "print tmp_cubed"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can create an empty SFrame using graphlab.SFrame() and then add any columns to it with ex_sframe['column_name'] = value. For example we create an empty SFrame and make the column 'power_1' to be the first power of tmp (i.e. tmp itself)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\"><table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">power_1</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3.0</td>\n",
       "    </tr>\n",
       "</table>\n",
       "[3 rows x 1 columns]<br/>\n",
       "</div>"
      ],
      "text/plain": [
       "Columns:\n",
       "\tpower_1\tfloat\n",
       "\n",
       "Rows: 3\n",
       "\n",
       "Data:\n",
       "+---------+\n",
       "| power_1 |\n",
       "+---------+\n",
       "|   1.0   |\n",
       "|   2.0   |\n",
       "|   3.0   |\n",
       "+---------+\n",
       "[3 rows x 1 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ex_sframe = graphlab.SFrame()\n",
    "ex_sframe['power_1'] = tmp\n",
    "ex_sframe"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Polynomial_sframe function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the hints above complete the following function to create an SFrame consisting of the powers of an SArray up to a specific degree:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def polynomial_sframe(feature, degree):\n",
    "    # assume that degree >= 1\n",
    "    # initialize the SFrame:\n",
    "    poly_sframe = graphlab.SFrame()\n",
    "    # and set poly_sframe['power_1'] equal to the passed feature\n",
    "    poly_sframe['power_1'] = feature\n",
    "    # first check if degree > 1\n",
    "    if degree > 1:\n",
    "        # then loop over the remaining degrees:\n",
    "        # range usually starts at 0 and stops at the endpoint-1. We want it to start at 2 and stop at degree\n",
    "        for power in range(2, degree+1): \n",
    "            # first we'll give the column a name:\n",
    "            name = 'power_' + str(power)\n",
    "            # then assign poly_sframe[name] to the appropriate power of feature\n",
    "            poly_sframe[name] = feature.apply(lambda x: x**power)\n",
    "\n",
    "    return poly_sframe"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To test your function consider the smaller tmp variable and what you would expect the outcome of the following call:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\"><table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">power_1</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">power_2</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">power_3</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">power_4</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">power_5</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">power_6</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">power_7</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">power_8</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">power_9</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">power_10</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">power_11</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.0</td>\n",
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       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.0</td>\n",
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       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.0</td>\n",
       "    </tr>\n",
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       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">8.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">16.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">32.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">64.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">128.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">256.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">512.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1024.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2048.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">9.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">27.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">81.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">243.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">729.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2187.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">6561.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">19683.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">59049.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">177147.0</td>\n",
       "    </tr>\n",
       "</table>\n",
       "[3 rows x 11 columns]<br/>\n",
       "</div>"
      ],
      "text/plain": [
       "Columns:\n",
       "\tpower_1\tfloat\n",
       "\tpower_2\tfloat\n",
       "\tpower_3\tfloat\n",
       "\tpower_4\tfloat\n",
       "\tpower_5\tfloat\n",
       "\tpower_6\tfloat\n",
       "\tpower_7\tfloat\n",
       "\tpower_8\tfloat\n",
       "\tpower_9\tfloat\n",
       "\tpower_10\tfloat\n",
       "\tpower_11\tfloat\n",
       "\n",
       "Rows: 3\n",
       "\n",
       "Data:\n",
       "+---------+---------+---------+---------+---------+---------+---------+---------+\n",
       "| power_1 | power_2 | power_3 | power_4 | power_5 | power_6 | power_7 | power_8 |\n",
       "+---------+---------+---------+---------+---------+---------+---------+---------+\n",
       "|   1.0   |   1.0   |   1.0   |   1.0   |   1.0   |   1.0   |   1.0   |   1.0   |\n",
       "|   2.0   |   4.0   |   8.0   |   16.0  |   32.0  |   64.0  |  128.0  |  256.0  |\n",
       "|   3.0   |   9.0   |   27.0  |   81.0  |  243.0  |  729.0  |  2187.0 |  6561.0 |\n",
       "+---------+---------+---------+---------+---------+---------+---------+---------+\n",
       "+---------+----------+----------+\n",
       "| power_9 | power_10 | power_11 |\n",
       "+---------+----------+----------+\n",
       "|   1.0   |   1.0    |   1.0    |\n",
       "|  512.0  |  1024.0  |  2048.0  |\n",
       "| 19683.0 | 59049.0  | 177147.0 |\n",
       "+---------+----------+----------+\n",
       "[3 rows x 11 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "polynomial_sframe(tmp, 11)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Visualizing polynomial regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's use matplotlib to visualize what a polynomial regression looks like on some real data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sales = graphlab.SFrame('kc_house_data.gl/')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As in Week 3, we will use the sqft_living variable. For plotting purposes (connecting the dots), you'll need to sort by the values of sqft_living. For houses with identical square footage, we break the tie by their prices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+-------------+----------+\n",
      "| sqft_living |  price   |\n",
      "+-------------+----------+\n",
      "|    290.0    | 142000.0 |\n",
      "|    370.0    | 276000.0 |\n",
      "|    380.0    | 245000.0 |\n",
      "+-------------+----------+\n",
      "[3 rows x 2 columns]\n",
      "\n"
     ]
    },
    {
     "data": {
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       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\"><table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">sqft_living</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">price</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">10040.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">7062500.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">12050.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">7700000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">13540.0</td>\n",
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       "    </tr>\n",
       "</table>\n",
       "[3 rows x 2 columns]<br/>\n",
       "</div>"
      ],
      "text/plain": [
       "Columns:\n",
       "\tsqft_living\tfloat\n",
       "\tprice\tfloat\n",
       "\n",
       "Rows: 3\n",
       "\n",
       "Data:\n",
       "+-------------+-----------+\n",
       "| sqft_living |   price   |\n",
       "+-------------+-----------+\n",
       "|   10040.0   | 7062500.0 |\n",
       "|   12050.0   | 7700000.0 |\n",
       "|   13540.0   | 2280000.0 |\n",
       "+-------------+-----------+\n",
       "[3 rows x 2 columns]"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sales = sales.sort(['sqft_living', 'price'], ascending=True)\n",
    "print sales.head(3)['sqft_living', 'price']\n",
    "sales.tail(3)['sqft_living', 'price']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's start with a degree 1 polynomial using 'sqft_living' (i.e. a line) to predict 'price' and plot what it looks like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "## use helper function\n",
    "poly1_data = polynomial_sframe(sales['sqft_living'], 1)\n",
    "poly1_data['price'] = sales['price'] # add price to the data since it's the target"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "NOTE: for all the models in this notebook use validation_set = None to ensure that all results are consistent across users."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PROGRESS: Linear regression:\n",
      "PROGRESS: --------------------------------------------------------\n",
      "PROGRESS: Number of examples          : 21613\n",
      "PROGRESS: Number of features          : 1\n",
      "PROGRESS: Number of unpacked features : 1\n",
      "PROGRESS: Number of coefficients    : 2\n",
      "PROGRESS: Starting Newton Method\n",
      "PROGRESS: --------------------------------------------------------\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: | Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: | 1         | 2        | 1.031056     | 4362074.696077     | 261440.790724 |\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: SUCCESS: Optimal solution found.\n",
      "PROGRESS:\n"
     ]
    }
   ],
   "source": [
    "model1 = graphlab.linear_regression.create(poly1_data, target = 'price', features = ['power_1'], validation_set = None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">(intercept)</td>\n",
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       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_1</td>\n",
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       "+-------------+-------+----------------+---------------+\n",
       "| (intercept) |  None | -43579.0852515 | 4402.68969743 |\n",
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      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#let's take a look at the weights before we plot\n",
    "model1.get(\"coefficients\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x11478f1d0>,\n",
       " <matplotlib.lines.Line2D at 0x1147a93d0>]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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FeOJi7jXDaENs3iIz7Lc4cTHRMYxjJBOBsXkLw2iMiY5hHCM2MW4YrcfmdAyjnTAXkmEc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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1145a6dd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(poly1_data['power_1'],poly1_data['price'],'+',\n",
    "        poly1_data['power_1'], model1.predict(poly1_data),'-')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's unpack that plt.plot() command. The first pair of SArrays we passed are the 1st power of sqft and the actual price we then ask it to print these as dots '.'. The next pair we pass is the 1st power of sqft and the predicted values from the linear model. We ask these to be plotted as a line '-'. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PROGRESS: Linear regression:\n",
      "PROGRESS: --------------------------------------------------------\n",
      "PROGRESS: Number of examples          : 21613\n",
      "PROGRESS: Number of features          : 3\n",
      "PROGRESS: Number of unpacked features : 3\n",
      "PROGRESS: Number of coefficients    : 4\n",
      "PROGRESS: Starting Newton Method\n",
      "PROGRESS: --------------------------------------------------------\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: | Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: | 1         | 2        | 0.044135     | 3261066.736006     | 249261.286346 |\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: SUCCESS: Optimal solution found.\n",
      "PROGRESS:\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\"><table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">name</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">index</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">value</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">stderr</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">(intercept)</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">336788.117952</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">10661.0153713</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_1</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-90.147623612</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">10.6222891844</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_2</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.087036715081</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.00296630623148</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_3</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-3.8398521196e-06</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.2417490959e-07</td>\n",
       "    </tr>\n",
       "</table>\n",
       "[4 rows x 4 columns]<br/>\n",
       "</div>"
      ],
      "text/plain": [
       "Columns:\n",
       "\tname\tstr\n",
       "\tindex\tstr\n",
       "\tvalue\tfloat\n",
       "\tstderr\tfloat\n",
       "\n",
       "Rows: 4\n",
       "\n",
       "Data:\n",
       "+-------------+-------+-------------------+------------------+\n",
       "|     name    | index |       value       |      stderr      |\n",
       "+-------------+-------+-------------------+------------------+\n",
       "| (intercept) |  None |   336788.117952   |  10661.0153713   |\n",
       "|   power_1   |  None |   -90.147623612   |  10.6222891844   |\n",
       "|   power_2   |  None |   0.087036715081  | 0.00296630623148 |\n",
       "|   power_3   |  None | -3.8398521196e-06 | 2.2417490959e-07 |\n",
       "+-------------+-------+-------------------+------------------+\n",
       "[4 rows x 4 columns]"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## use helper function to add higher powers of sqft\n",
    "poly3_data = polynomial_sframe(sales['sqft_living'], 3)\n",
    "poly3_data['price'] = sales['price'] # add price to the data since it's the target\n",
    "\n",
    "model3 = graphlab.linear_regression.create(poly3_data, target = 'price', \\\n",
    "                                           features = ['power_1', 'power_2', 'power_3'], validation_set = None)\n",
    "model3.get(\"coefficients\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see, not surprisingly, that the predicted values all fall on a line, specifically the one with slope 280 and intercept -43579. What if we wanted to plot a second degree polynomial?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PROGRESS: Linear regression:\n",
      "PROGRESS: --------------------------------------------------------\n",
      "PROGRESS: Number of examples          : 21613\n",
      "PROGRESS: Number of features          : 2\n",
      "PROGRESS: Number of unpacked features : 2\n",
      "PROGRESS: Number of coefficients    : 3\n",
      "PROGRESS: Starting Newton Method\n",
      "PROGRESS: --------------------------------------------------------\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: | Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: | 1         | 2        | 0.019158     | 5913020.984255     | 250948.368758 |\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: SUCCESS: Optimal solution found.\n",
      "PROGRESS:\n"
     ]
    }
   ],
   "source": [
    "poly2_data = polynomial_sframe(sales['sqft_living'], 2)\n",
    "my_features = poly2_data.column_names() # get the name of the features\n",
    "poly2_data['price'] = sales['price'] # add price to the data since it's the target\n",
    "model2 = graphlab.linear_regression.create(poly2_data, target = 'price', features = my_features, validation_set = None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\"><table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">name</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">index</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">value</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">stderr</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">(intercept)</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">199222.496445</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">7058.00483552</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_1</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">67.9940640677</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5.28787201316</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_2</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.0385812312789</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.000898246547032</td>\n",
       "    </tr>\n",
       "</table>\n",
       "[3 rows x 4 columns]<br/>\n",
       "</div>"
      ],
      "text/plain": [
       "Columns:\n",
       "\tname\tstr\n",
       "\tindex\tstr\n",
       "\tvalue\tfloat\n",
       "\tstderr\tfloat\n",
       "\n",
       "Rows: 3\n",
       "\n",
       "Data:\n",
       "+-------------+-------+-----------------+-------------------+\n",
       "|     name    | index |      value      |       stderr      |\n",
       "+-------------+-------+-----------------+-------------------+\n",
       "| (intercept) |  None |  199222.496445  |   7058.00483552   |\n",
       "|   power_1   |  None |  67.9940640677  |   5.28787201316   |\n",
       "|   power_2   |  None | 0.0385812312789 | 0.000898246547032 |\n",
       "+-------------+-------+-----------------+-------------------+\n",
       "[3 rows x 4 columns]"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model2.get(\"coefficients\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x11910d350>,\n",
       " <matplotlib.lines.Line2D at 0x11910d450>]"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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RtoH640Rkk69/SUDeR0TWiMhGEZkckOeKyEzfZpmIdA2cG+XrbxCRkQF5NxFZ7s89JSJm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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11616e710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(poly2_data['power_1'],poly2_data['price'],'.',\n",
    "        poly2_data['power_1'], model2.predict(poly2_data),'-')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The resulting model looks like half a parabola. Try on your own to see what the cubic looks like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x119951590>,\n",
       " <matplotlib.lines.Line2D at 0x119951690>]"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ZXJxcBBLLosk88/PDQ9YS99p42mLxvTn4z9caQhbNkN2crALxijiXPHEJJw06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\n+e+8pWHOLREQEx2jNYjH48R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GU7Rr95qIjAXKgC7A/ap6S5I6DW4O9fm8fvAD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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11968d950>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## power 3 polynomial\n",
    "plt.plot(poly3_data['power_1'],poly3_data['price'],'+',\n",
    "        poly3_data['power_1'], model3.predict(poly3_data),'-')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now try a 15th degree polynomial:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PROGRESS: Linear regression:\n",
      "PROGRESS: --------------------------------------------------------\n",
      "PROGRESS: Number of examples          : 21613\n",
      "PROGRESS: Number of features          : 15\n",
      "PROGRESS: Number of unpacked features : 15\n",
      "PROGRESS: Number of coefficients    : 16\n",
      "PROGRESS: Starting Newton Method\n",
      "PROGRESS: --------------------------------------------------------\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: | Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: | 1         | 2        | 0.040343     | 2662308.584338     | 245690.511190 |\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: SUCCESS: Optimal solution found.\n",
      "PROGRESS:\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\"><table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">name</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">index</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">value</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">stderr</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">(intercept)</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">73619.7522273</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">273149.979651</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_1</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">410.287462223</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1044.8547212</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_2</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-0.230450714115</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.54422074608</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_3</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">7.5884054095e-05</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.00100973407789</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_4</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-5.65701799055e-09</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">nan</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_5</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-4.57028134382e-13</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">nan</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_6</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.66360206665e-17</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">nan</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_7</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3.38584771349e-21</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">nan</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_8</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.14723103556e-25</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">nan</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_9</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-4.65293581684e-30</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">nan</td>\n",
       "    </tr>\n",
       "</table>\n",
       "[16 rows x 4 columns]<br/>Note: Only the head of the SFrame is printed.<br/>You can use print_rows(num_rows=m, num_columns=n) to print more rows and columns.\n",
       "</div>"
      ],
      "text/plain": [
       "Columns:\n",
       "\tname\tstr\n",
       "\tindex\tstr\n",
       "\tvalue\tfloat\n",
       "\tstderr\tfloat\n",
       "\n",
       "Rows: 16\n",
       "\n",
       "Data:\n",
       "+-------------+-------+--------------------+------------------+\n",
       "|     name    | index |       value        |      stderr      |\n",
       "+-------------+-------+--------------------+------------------+\n",
       "| (intercept) |  None |   73619.7522273    |  273149.979651   |\n",
       "|   power_1   |  None |   410.287462223    |   1044.8547212   |\n",
       "|   power_2   |  None |  -0.230450714115   |  1.54422074608   |\n",
       "|   power_3   |  None |  7.5884054095e-05  | 0.00100973407789 |\n",
       "|   power_4   |  None | -5.65701799055e-09 |       nan        |\n",
       "|   power_5   |  None | -4.57028134382e-13 |       nan        |\n",
       "|   power_6   |  None | 2.66360206665e-17  |       nan        |\n",
       "|   power_7   |  None | 3.38584771349e-21  |       nan        |\n",
       "|   power_8   |  None | 1.14723103556e-25  |       nan        |\n",
       "|   power_9   |  None | -4.65293581684e-30 |       nan        |\n",
       "+-------------+-------+--------------------+------------------+\n",
       "[16 rows x 4 columns]\n",
       "Note: Only the head of the SFrame is printed.\n",
       "You can use print_rows(num_rows=m, num_columns=n) to print more rows and columns."
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## use helper function to add higher powers of sqft\n",
    "poly15_data = polynomial_sframe(sales['sqft_living'], 15)\n",
    "features15 = poly15_data.column_names()\n",
    "poly15_data['price'] = sales['price'] # add price to the data since it's the target\n",
    "\n",
    "model15 = graphlab.linear_regression.create(poly15_data, target = 'price', \\\n",
    "                                           features = features15, validation_set = None)\n",
    "model15.get(\"coefficients\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x11a86fe90>,\n",
       " <matplotlib.lines.Line2D at 0x11a86ff90>]"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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YmensPbCXK/57BdN/O52qcS4+J1ZJSUyhiqnCF7lflEpqovAf5LfeemuJ+8yP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\n+xF/GRkakNCli7/V9aJFGmjRrp2+t7uoWpEaNkz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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11997ec50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## power 15 polynomial\n",
    "plt.plot(poly1_data['power_1'],poly1_data['price'],'x',\n",
    "        poly1_data['power_1'], model15.predict(poly15_data),'-')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What do you think of the 15th degree polynomial? Do you think this is appropriate? If we were to change the data do you think you'd get pretty much the same curve? Let's take a look."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Changing the data and re-learning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you’re using SFrames then create four subsets as follows:\n",
    "\n",
    "-    first split sales into 2 subsets with .random_split(.5) use seed = 0!\n",
    "-   next split these into 2 more subsets (4 total) using random_split(0.5) again set seed = 0!\n",
    "-   you should have 4 subsets of (approximately) equal size, call them set_1, set_2, set_3, and set_4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(5398, 21)\n",
      "(5402, 21)\n",
      "(5404, 21)\n",
      "(5409, 21)\n"
     ]
    }
   ],
   "source": [
    "set_1, set_2 = sales.random_split(0.5, seed=0)\n",
    "\n",
    "set_3, set_1 = set_1.random_split(0.5, seed=0)\n",
    "set_4, set_2 = set_2.random_split(0.5, seed=0)\n",
    "\n",
    "print set_1.shape\n",
    "print set_2.shape\n",
    "print set_3.shape\n",
    "print set_4.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit a 15th degree polynomial on set_1, set_2, set_3, and set_4 using sqft_living to predict prices. Print the coefficients and make a plot of the resulting model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "## helper function to add higher powers of sqft, create model, plot\n",
    "def create_poly(data, degree):\n",
    "    poly_data = polynomial_sframe(data['sqft_living'], degree)\n",
    "    features = poly_data.column_names()\n",
    "    poly_data['price'] = data['price']\n",
    "    \n",
    "    model = graphlab.linear_regression.create(poly_data, target = 'price', \\\n",
    "                                              features = features, validation_set = None, verbose = False)\n",
    "    print model.get(\"coefficients\").print_rows(num_rows=degree+1)\n",
    "    plt.plot(poly_data['power_1'],poly_data['price'],'x',\n",
    "        poly_data['power_1'], model.predict(poly_data),'-')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+-------------+-------+--------------------+-------------------+\n",
      "|     name    | index |       value        |       stderr      |\n",
      "+-------------+-------+--------------------+-------------------+\n",
      "| (intercept) |  None |   89836.5077327    |   1575072.52605   |\n",
      "|   power_1   |  None |   319.806946764    |   9306.12882948   |\n",
      "|   power_2   |  None |  -0.103315397042   |   23.4277359048   |\n",
      "|   power_3   |  None | 1.06682476069e-05  |  0.0331642866136  |\n",
      "|   power_4   |  None | 5.75577097718e-09  |  2.9410878859e-05 |\n",
      "|   power_5   |  None | -2.5466346476e-13  | 1.72262411743e-08 |\n",
      "|   power_6   |  None | -1.09641345061e-16 |  6.8337583788e-12 |\n",
      "|   power_7   |  None | -6.36458441713e-21 | 1.84750094523e-15 |\n",
      "|   power_8   |  None | 5.52560416991e-25  | 3.35734055021e-19 |\n",
      "|   power_9   |  None | 1.35082038963e-28  | 3.79203635463e-23 |\n",
      "|   power_10  |  None |  1.1840818825e-32  |        nan        |\n",
      "|   power_11  |  None | 1.98348000558e-37  |        nan        |\n",
      "|   power_12  |  None | -9.9253359041e-41  |        nan        |\n",
      "|   power_13  |  None | -1.60834847047e-44 |        nan        |\n",
      "|   power_14  |  None | -9.12006024287e-49 | 2.33825680386e-43 |\n",
      "|   power_15  |  None | 1.68636658328e-52  |  6.7296077272e-48 |\n",
      "+-------------+-------+--------------------+-------------------+\n",
      "[16 rows x 4 columns]\n",
      "\n",
      "None\n"
     ]
    },
    {
     "data": {
      "image/png": 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YcFclKqhImPHjABYT0T0AvoRErIGZPyOixZBIt1MAxloDZe4D8ByA2gCWM/MKpzwHwItE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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11517dd90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_poly(set_1, 15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+-------------+-------+--------------------+-------------------+\n",
      "|     name    | index |       value        |       stderr      |\n",
      "+-------------+-------+--------------------+-------------------+\n",
      "| (intercept) |  None |   259020.879454    |   1545198.28029   |\n",
      "|   power_1   |  None |   -31.7277162076   |    9987.4875763   |\n",
      "|   power_2   |  None |   0.109702769619   |    26.738101963   |\n",
      "|   power_3   |  None | -1.58383847337e-05 |  0.0392428614089  |\n",
      "|   power_4   |  None | -4.47660623786e-09 |  3.515833293e-05  |\n",
      "|   power_5   |  None | 1.13976573482e-12  | 2.00754862175e-08 |\n",
      "|   power_6   |  None | 1.97669120547e-16  | 7.24105980967e-12 |\n",
      "|   power_7   |  None | -6.15783678661e-21 | 1.43187601549e-15 |\n",
      "|   power_8   |  None | -4.88012304074e-24 |        nan        |\n",
      "|   power_9   |  None | -6.62186781351e-28 |        nan        |\n",
      "|   power_10  |  None | -2.70631583161e-32 | 5.65043690743e-27 |\n",
      "|   power_11  |  None | 6.72370411466e-36  | 9.67662635909e-31 |\n",
      "|   power_12  |  None | 1.74115646268e-39  |        nan        |\n",
      "|   power_13  |  None | 2.09188375728e-43  |        nan        |\n",
      "|   power_14  |  None | 4.78015566061e-48  | 2.37859778541e-43 |\n",
      "|   power_15  |  None | -4.74535333101e-51 | 1.16454261473e-47 |\n",
      "+-------------+-------+--------------------+-------------------+\n",
      "[16 rows x 4 columns]\n",
      "\n",
      "None\n"
     ]
    },
    {
     "data": {
      "image/png": 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E+1rfibpFU5sfKjSxo6apvebONz/fFRZjURjroLrn92ehGCvKXxXm0lKpdxaK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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114a94110>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_poly(set_2, 15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+-------------+-------+--------------------+-------------------+\n",
      "|     name    | index |       value        |       stderr      |\n",
      "+-------------+-------+--------------------+-------------------+\n",
      "| (intercept) |  None |   223312.750249    |   1256782.60077   |\n",
      "|   power_1   |  None |   118.086127587    |   6007.14384425   |\n",
      "|   power_2   |  None |  -0.0473482011344  |    11.969007003   |\n",
      "|   power_3   |  None | 3.25310342469e-05  |  0.0131429551736  |\n",
      "|   power_4   |  None | -3.32372152561e-09 | 8.85414511316e-06 |\n",
      "|   power_5   |  None | -9.75830457761e-14 | 3.83982596813e-09 |\n",
      "|   power_6   |  None | 1.15440303426e-17  |  1.0847728091e-12 |\n",
      "|   power_7   |  None | 1.05145869404e-21  | 1.93625236102e-16 |\n",
      "|   power_8   |  None | 3.46049616546e-26  |  1.8950619488e-20 |\n",
      "|   power_9   |  None | -1.09654454168e-30 |        nan        |\n",
      "|   power_10  |  None | -2.42031812009e-34 |  3.4981969864e-29 |\n",
      "|   power_11  |  None | -1.99601206824e-38 | 2.50800893225e-33 |\n",
      "|   power_12  |  None | -1.07709903827e-42 | 1.15429777633e-36 |\n",
      "|   power_13  |  None | -2.72862818141e-47 | 1.56910289863e-40 |\n",
      "|   power_14  |  None | 2.44782693088e-51  | 7.93831963225e-45 |\n",
      "|   power_15  |  None | 5.01975232933e-55  | 1.49249715723e-49 |\n",
      "+-------------+-------+--------------------+-------------------+\n",
      "[16 rows x 4 columns]\n",
      "\n",
      "None\n"
     ]
    },
    {
     "data": {
      "image/png": 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oGJWGeLEugnM4yckhMYwH4VmxaQUXzbqIZy96lpSkGJmBRpHodUSvcpWZwETH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\n48bQowesWuW+v9/+FjZsgI8+gsxMV75tG0ya5B7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      "text/plain": [
       "<matplotlib.figure.Figure at 0x114ce1950>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_poly(set_3, 15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+-------------+-------+--------------------+-------------------+\n",
      "|     name    | index |       value        |       stderr      |\n",
      "+-------------+-------+--------------------+-------------------+\n",
      "| (intercept) |  None |   87317.9795547    |        nan        |\n",
      "|   power_1   |  None |   356.304911045    |        nan        |\n",
      "|   power_2   |  None |  -0.164817442809   |        nan        |\n",
      "|   power_3   |  None | 4.40424992697e-05  |        nan        |\n",
      "|   power_4   |  None | 6.48234876179e-10  |        nan        |\n",
      "|   power_5   |  None | -6.75253226587e-13 |        nan        |\n",
      "|   power_6   |  None | -3.36842592661e-17 |        nan        |\n",
      "|   power_7   |  None | 3.60999704242e-21  |        nan        |\n",
      "|   power_8   |  None | 6.46999725625e-25  |        nan        |\n",
      "|   power_9   |  None | 4.23639388865e-29  |        nan        |\n",
      "|   power_10  |  None | -3.62149427043e-34 |        nan        |\n",
      "|   power_11  |  None | -4.27119527274e-37 |        nan        |\n",
      "|   power_12  |  None | -5.61445971705e-41 | 3.22504679661e-36 |\n",
      "|   power_13  |  None | -3.87452772861e-45 | 3.81940189807e-40 |\n",
      "|   power_14  |  None | 4.69430359483e-50  | 1.00042633659e-44 |\n",
      "|   power_15  |  None | 6.39045885992e-53  |        nan        |\n",
      "+-------------+-------+--------------------+-------------------+\n",
      "[16 rows x 4 columns]\n",
      "\n",
      "None\n"
     ]
    },
    {
     "data": {
      "image/png": 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w1MdPcU76OaUfbJSbaEVHgVdE5G0R+YXX1kJVtwOo6jagudfeGvg8dO4Wr601sDnUvtlr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\nHTgA9eu7zyKu2OfatdC8ubvvxRdDixb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      "text/plain": [
       "<matplotlib.figure.Figure at 0x114eb4590>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_poly(set_4, 15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some questions you will be asked on your quiz:\n",
    "\n",
    "**Quiz Question: Is the sign (positive or negative) for power_15 the same in all four models?**\n",
    "> pos\n",
    "\n",
    "**Quiz Question: (True/False) the plotted fitted lines look the same in all four plots**\n",
    "> False"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Selecting a Polynomial Degree"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Whenever we have a \"magic\" parameter like the degree of the polynomial there is one well-known way to select these parameters: validation set. (We will explore another approach in week 4).\n",
    "\n",
    "We split the sales dataset 3-way into training set, test set, and validation set as follows:\n",
    "\n",
    "* Split our sales data into 2 sets: `training_and_validation` and `testing`. Use `random_split(0.9, seed=1)`.\n",
    "* Further split our training data into two sets: `training` and `validation`. Use `random_split(0.5, seed=1)`.\n",
    "\n",
    "Again, we set `seed=1` to obtain consistent results for different users."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "training_and_validation, testing = sales.random_split(0.9, seed=1)\n",
    "training, validation = training_and_validation.random_split(0.5, seed=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next you should write a loop that does the following:\n",
    "* For degree in [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15] (to get this in python type range(1, 15+1))\n",
    "    * Build an SFrame of polynomial data of train_data['sqft_living'] at the current degree\n",
    "    * hint: my_features = poly_data.column_names() gives you a list e.g. ['power_1', 'power_2', 'power_3'] which you might find useful for graphlab.linear_regression.create( features = my_features)\n",
    "    * Add train_data['price'] to the polynomial SFrame\n",
    "    * Learn a polynomial regression model to sqft vs price with that degree on TRAIN data\n",
    "    * Compute the RSS on VALIDATION data (here you will want to use .predict()) for that degree and you will need to make a polynmial SFrame using validation data.\n",
    "* Report which degree had the lowest RSS on validation data (remember python indexes from 0)\n",
    "\n",
    "(Note you can turn off the print out of linear_regression.create() with verbose = False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "## helper function to add higher powers of sqft, create model, plot\n",
    "def choose_poly_train(train, degree, validation):\n",
    "    poly_train = polynomial_sframe(train['sqft_living'], degree)\n",
    "    features = poly_train.column_names()\n",
    "    poly_train['price'] = train['price']\n",
    "    \n",
    "    models[degree] = graphlab.linear_regression.create(poly_train, target = 'price', \\\n",
    "                                                       features = features, validation_set = None, verbose=False)\n",
    "    ## create polynomial validation sframe\n",
    "    poly_valid = polynomial_sframe(validation['sqft_living'], degree)\n",
    "    poly_valid['price'] = validation['price']\n",
    "    \n",
    "    ## get RSS\n",
    "    rss[degree] = sum((models[degree].predict(poly_valid) - poly_valid['price'])**2)\n",
    "    \n",
    "    print degree, ':', rss[degree]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 : 6.76709775198e+14\n",
      "2 : 6.07090530698e+14\n",
      "3 : 6.16714574533e+14\n",
      "4 : 6.09129230654e+14\n",
      "5 : 5.99177138584e+14\n",
      "6 : 5.89182477809e+14\n",
      "7 : 5.91717038418e+14\n",
      "8 : 6.01558237777e+14\n",
      "9 : 6.12563853988e+14\n",
      "10 : 6.21744288936e+14\n",
      "11 : 6.27012012704e+14\n",
      "12 : 6.27757914772e+14\n",
      "13 : 6.24738503262e+14\n",
      "14 : 6.19369705905e+14\n",
      "15 : 6.13089202414e+14\n"
     ]
    }
   ],
   "source": [
    "models = {}\n",
    "rss = {}\n",
    "for degree in xrange(1,16):\n",
    "    choose_poly_train(training, degree, validation)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Quiz Question: Which degree (1, 2, …, 15) had the lowest RSS on Validation data?**\n",
    "> 6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that you have chosen the degree of your polynomial using validation data, compute the RSS of this model on TEST data. Report the RSS on your quiz."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.25529337848e+14\n"
     ]
    }
   ],
   "source": [
    "poly_test = polynomial_sframe(testing['sqft_living'], 6)\n",
    "poly_test['price'] = testing['price']\n",
    "\n",
    "print sum((models[6].predict(poly_test) - poly_test['price'])**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Quiz Question: what is the RSS on TEST data for the model with the degree selected from Validation data?**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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