week-4-ridge-regression-assignment-1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regression Week 4: Ridge Regression (interpretation)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook, we will run ridge regression multiple times with different L2 penalties to see which one produces the best fit. We will revisit the example of polynomial regression as a means to see the effect of L2 regularization. In particular, we will:\n",
    "* Use a pre-built implementation of regression (GraphLab Create) to run polynomial regression\n",
    "* Use matplotlib to visualize polynomial regressions\n",
    "* Use a pre-built implementation of regression (GraphLab Create) to run polynomial regression, this time with L2 penalty\n",
    "* Use matplotlib to visualize polynomial regressions under L2 regularization\n",
    "* Choose best L2 penalty using cross-validation.\n",
    "* Assess the final fit using test data.\n",
    "\n",
    "We will continue to use the House data from previous notebooks.  (In the next programming assignment for this module, you will implement your own ridge regression learning algorithm using gradient descent.)"
   ]
  },
  {
   "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": [
    "# Polynomial regression, revisited"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We build on the material from Week 3, where we wrote the function to produce an SFrame with columns containing the powers of a given input. Copy and paste the function `polynomial_sframe` from Week 3:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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": [
    "Let's use matplotlib to visualize what a polynomial regression looks like on the house data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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-12034 - Server binary: /Users/jjl/.graphlab/anaconda/lib/python2.7/site-packages/graphlab/unity_server - Server log: /tmp/graphlab_server_1454277697.log\n",
      "[INFO] GraphLab Server Version: 1.8\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {
    "collapsed": false
   },
   "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": 136,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sales = sales.sort(['sqft_living','price'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us revisit the 15th-order polynomial model using the 'sqft_living' input. Generate polynomial features up to degree 15 using `polynomial_sframe()` and fit a model with these features. When fitting the model, use an L2 penalty of `1e-5`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "l2_small_penalty = 1e-5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note: When we have so many features and so few data points, the solution can become highly numerically unstable, which can sometimes lead to strange unpredictable results.  Thus, rather than using no regularization, we will introduce a tiny amount of regularization (`l2_penalty=1e-5`) to make the solution numerically stable.  (In lecture, we discussed the fact that regularization can also help with numerical stability, and here we are seeing a practical example.)\n",
    "\n",
    "With the L2 penalty specified above, fit the model and print out the learned weights.\n",
    "\n",
    "Hint: make sure to add 'price' column to the new SFrame before calling `graphlab.linear_regression.create()`. Also, make sure GraphLab Create doesn't create its own validation set by using the option `validation_set=None` in this call."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "## use helper function\n",
    "poly_data = polynomial_sframe(sales['sqft_living'], 15)\n",
    "my_features = poly_data.column_names()\n",
    "poly_data['price'] = sales['price'] # add price to the data since it's the target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "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          : 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        | 0.059613     | 2662555.738658     | 245656.462166 |\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: SUCCESS: Optimal solution found.\n",
      "PROGRESS:\n"
     ]
    },
    {
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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\">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\">167924.855861</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">932257.186892</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\">103.09095592</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4735.64035967</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\">0.13460454755</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">9.85916588414</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\">-0.000129071363621</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.0111681951166</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\">5.18928964915e-08</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">7.69612916365e-06</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\">-7.77169343059e-12</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3.40375275378e-09</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\">1.71144917832e-16</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">9.86487804671e-13</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\">4.51177946027e-20</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.85595593561e-16</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\">-4.78840959928e-25</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.13680012359e-20</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\">-2.33343401694e-28</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.22638025544e-24</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 |   167924.855861    |   932257.186892   |\n",
       "|   power_1   |  None |    103.09095592    |   4735.64035967   |\n",
       "|   power_2   |  None |   0.13460454755    |   9.85916588414   |\n",
       "|   power_3   |  None | -0.000129071363621 |  0.0111681951166  |\n",
       "|   power_4   |  None | 5.18928964915e-08  | 7.69612916365e-06 |\n",
       "|   power_5   |  None | -7.77169343059e-12 | 3.40375275378e-09 |\n",
       "|   power_6   |  None | 1.71144917832e-16  | 9.86487804671e-13 |\n",
       "|   power_7   |  None | 4.51177946027e-20  | 1.85595593561e-16 |\n",
       "|   power_8   |  None | -4.78840959928e-25 | 2.13680012359e-20 |\n",
       "|   power_9   |  None | -2.33343401694e-28 | 1.22638025544e-24 |\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": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = graphlab.linear_regression.create(poly_data, target = 'price', features = my_features, \\\n",
    "                                          validation_set = None, l2_penalty=l2_small_penalty)\n",
    "model.get(\"coefficients\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "[<matplotlib.lines.Line2D at 0x11485bf50>,\n",
       " <matplotlib.lines.Line2D at 0x11486d0d0>]"
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     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
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Xa16+hjUT1tCxbcf4DkapE2u2r+GHL/yQjbdujHnfIoIxJuY7g3VDpdLicNZF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\ntHU3bQIRKxpBXJaBRYusALios0OHbN0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//cA/RORnwCbgKm92XyMis4A1wCHgJm/wABOo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\nc/XAAeYAUYgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111edfb90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(poly_data['power_1'],poly_data['price'],'+',\n",
    "         poly_data['power_1'], model.predict(poly_data),'-')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***QUIZ QUESTION:  What's the learned value for the coefficient of feature `power_1`?***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Observe overfitting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Recall from Week 3 that the polynomial fit of degree 15 changed wildly whenever the data changed. In particular, when we split the sales data into four subsets and fit the model of degree 15, the result came out to be very different for each subset. The model had a *high variance*. We will see in a moment that ridge regression reduces such variance. But first, we must reproduce the experiment we did in Week 3."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, split the data into split the sales data into four subsets of roughly equal size and call them `set_1`, `set_2`, `set_3`, and `set_4`. Use `.random_split` function and make sure you set `seed=0`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "(semi_split1, semi_split2) = sales.random_split(.5,seed=0)\n",
    "(set_1, set_2) = semi_split1.random_split(0.5, seed=0)\n",
    "(set_3, set_4) = semi_split2.random_split(0.5, seed=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, fit a 15th degree polynomial on `set_1`, `set_2`, `set_3`, and `set_4`, using 'sqft_living' to predict prices. Print the weights and make a plot of the resulting model.\n",
    "\n",
    "Hint: When calling `graphlab.linear_regression.create()`, use the same L2 penalty as before (i.e. `l2_small_penalty`).  Also, make sure GraphLab Create doesn't create its own validation set by using the option `validation_set = None` in this call."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "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', features = features, \\\n",
    "                                              validation_set = None, verbose = False, l2_penalty=l2_small_penalty)\n",
    "    print model.get(\"coefficients\").print_rows(num_rows=5)\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": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+-------------+-------+--------------------+-------------------+\n",
      "|     name    | index |       value        |       stderr      |\n",
      "+-------------+-------+--------------------+-------------------+\n",
      "| (intercept) |  None |    9306.4606221    |   1255976.06157   |\n",
      "|   power_1   |  None |   585.865823394    |   6003.28876462   |\n",
      "|   power_2   |  None |  -0.397305895643   |   11.9613259026   |\n",
      "|   power_3   |  None | 0.000141470900599  |  0.0131345206929  |\n",
      "|   power_4   |  None | -1.52945989958e-08 | 8.84846297281e-06 |\n",
      "+-------------+-------+--------------------+-------------------+\n",
      "[16 rows x 4 columns]\n",
      "\n",
      "None\n"
     ]
    },
    {
     "data": {
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Aaqp9j8TlrP88/icD3xzIpEsm0apmq3Cbo+RCcSv+qaKjlBoixbvwjuE0a+YT\nw0gTnjHLxnB6rdO5ru114TZFyYOEJsUrmUBFRyk1RIp3sXJldi/L9cJWRkiERET471f/5e1Nb/Pf\n//uvpkdHOB0bdmT9nvUcOnoo3KYEhIqOUiqIJO+id++TvazYWNsebg4dPcR1717H1NVTWTJ4CdUr\nVA+3ScopqFCmAufWPbfYLOqmoqOUCiLdu4gENu7dSKcXOyEIq29YzRm1zgi3SUqAFKcQm4qOUiqI\nZO8iEpizfg4XzrqQv3f+O7OunEWlspXCbZKSD4rTom46OVRRSjF/Hv+TUYtHsTx1Oa//9XXOrXdu\nuE1SCsC+P/YR90wc+0fvJyYqOOtZ6uRQRcmDSJr8WVz4Yf8PdJnRhf2H97PmxjUqOMWYmhVr0rha\nY9btXhduU06Jio5SIoi0yZ+Rzlsb36LLjC6MaDeCedfMo2q5quE2SSkkxWVRNxUdpUQQaZM/I5Wj\nmUcZtXgUdy+9m4WDFnJbx9s0JbqEUFwWdVPRUUoMoZr8GWmhu4La8/OBn7nwpQv5Mf1HvrrxKzo0\n7BA6I5Uix81gi/QxbBUdpcQQqsmfkRa6K4g9C7cspMMLHbi69dW8O+BdalSoUTTGKkVG02pNiTbR\n/JD+Q7hNyRsRKdEve4tKSSc9XeSWW+x7Tp+D1X9qanD7DbU9xzKPyZgPxkijpxrJip9WFKmNStEz\n4I0B8tLal4LSl/PsDPozWT0dJSIobAgrlJM/XRu8oTtve377cu/T3fbeZ6D3HEgocefvO7n4lYv5\n6pev+PrGr0lokpB/g5ViRbFIJgiFkkXSC/V0igWh9lQKQ3q6yIgR9pWa6tsuiG3e+/L2634O9J5P\n5el8+tOnUv/J+vJo8qNyPPN4/g1ViiUpu1Kk1bRWQekL9XSUkkxpyT7z3qfXs8vP6qGnqiM3d/1c\nrpp3FTOumMGDf3mQ6KjokN2PElmcWftMdh/czZ5De8JtSq5oRQIlokhLsyGj1FT7QI0EFi60g/QZ\nGT7bYmNt6K6gZXS89wn5u2fXHq84ZWTAp58K31SdwAtfv8D7A9/nnLrnFMw4pVjTa3Yvbmh/A31b\n9y1UP2GrSGCMKWeMWW2MWWuMWW+Medhpr26MWWqM2WyMWWKMqeY5Z6wxZqsxZqMxpoenvb0xZp0x\nZosxZoqnvawxJsk553NjTBPPvmHO8ZuNMUM97c2MMaucfXONMcGp/aCEjUhZesAfV1i8tnnb84v3\nPv/5T/udZQH3AAAgAElEQVTKzz3nVEeuQuUjvH58OO9seodVI1ap4JRiIn5Rt0BicEBF5z0aWAV0\nBCYB9zrto4GJznYbYC0QAzQDvsfnUa0GOjjbi4CezvbNwHPOdn8gydmuDvwAVANi3W1n3zzgr872\ndGBkLrYHJb6phJa8xnQWLDh5zMJtD7dthemrMGM6XvYe2itdZ3aVPkl95OCRg/k3SilRfJL2iXT4\nb4dC90OIxnTyOyhfEVgDdAA2AXWd9nrAJmd7DDDac87/gE7OMRs87QOA6c72YqCT+IRtj/8x4hOX\n/s72XiDK2e4MLM7F5kJ/+UrocAXFKyzez+57OJMMFiwQSUrKfr30dNuWX+Hz3qe77RXQ/Irppr2b\npMUzLWT0B6MlMyszf8YoJZLDxw5LpQmV5Pcjvxeqn7CKDjYMtxb4DXjcaUv3O2a/8z4NGORpfxHo\nC5wHLPW0JwDvOdvrgQaefVuBGsDdwH2e9geAu4CawBZPeyNgXS62F+qLV0JLoIIS7nky4Ra+nFj+\n43Kp80QdmfH1jPAZoUQk8TPiZdkPywrVR6hEJ6BxEBHJAtoZY6oCbxtjzgT8R+eDOVofyOBVwANc\n48aNO7GdmJhIYmJi/i1STiK3Ae38DLB7s7nuuceOa+SUweWdl5Kaaq/hXtu1A3zXzq8dwbKzqJjx\n9QzuW34fSVcn0S2uW9D6DcbfVAk/bkmci5tfHPA5ycnJJCcnh84ol/yqFPAg1gPZSPbw2kbJOby2\nGF94baOnPdDw2vOec57HF17bQ/bw2v9ysbdQaq/kTjB//aemWr87NTXva6WmivTqJZKSkn1sZMgQ\nkR49Cjc2Egw7Q01mVqbcu/ReaTm1pWz+dXPQ+49Ej07JP+9vfl8ufvniQvVBuMJrQC18g/cVgE+A\nXthEgtFOe06JBGWBOLInErhJCAabSHCp034LvkSCAeScSOBuxzr75nkEaDpwUy72F+qLV/ImGGGv\nU/Xh/+BLSxM56yyf8KSkiLRubYUnlOG3cIf4Dh45KH2S+siFL10ovx76NWTXCfd9KoVn/x/7pfJj\nleXo8aMF7iOconM28DXwDbAOuN9prwEsAzYDS10xcPaNdcRmI9DD034edvxmK/CMp70cMN9pXwU0\n8+wb7rRvAYZ62uOw2XBbHAEqk4v9Bf7SlcAozK//QH5Z55S9lpYm0ru3yIoV9topKaH1QsLtAez4\nbYec95/zZNjbw+TPY3+G/Hrh9uiUwnPWc2fJF9u/KPD5YROd4v5S0Qkthf1VXJh06JQU+y94xYrs\nZWpCIQbhTNv+eufX0vipxvLYJ49JVlZWyK+nnk7J4OYFN8tTnz1V4PNVdFR0Io6cfv336mW9EP/j\ngv1w9obYRoywobXCzneJRN7c8KbUmlxL5n87P9djgimI4fbolOAxe91s6Tuvb4HPV9FR0Yk48gp7\nhXKSp7+4JSVZwUlLK/h8l0jjeOZxGfPBGGnydBP5cseXeR4bTKEI90RcJXj8lPGT1J5cu8DesYqO\nik6xIbfwTLAejiX9wfjroV+l+yvd5aKXL5I9B/cEdI6GxJScaPJ0kwJnOYZKdLTgp5IjhZ2vkVvh\nTrdCciTMdYlE1v6ylr7z+3JN62t4/JLHiYkKvKRgJBZLVcLLtW9dy8VxF3N9u+vzfW7YCn4qpZPC\nLNGcV+FO/8XHVq4s3OJtJYlXU16lx2s9mHTJJJ7o8US+BCdSi6Uq4SWhcQIrfo6wRd1C4T5F0gsN\nrxWYgoRsTpVc4O5PSbFjP2lpOnB99PhRuX3R7dJyaktZv3t9vs/XwX8lN9bvXi8tp7Ys0LnomI6K\nTjiYMUNOmq+R1/hJXskFaWnZqwm4guMKUCjGIyJ9/OenjJ+ky4tdpPfs3pJ+uGA3Hun3qISPzKxM\nqT6xuvzy+y/5PldFR0WnyHFL7w8eXPh0ZNfjWbHCpjq7no8rSO6cm8JORvR/ALv3kJTk+1zUFapz\nE4S3NrwldZ6oI5M/nawVopWQ0Xt2b3n9u9fzfZ6KjopOkeJ9OOckPgXBneXuejquZ+N6PMHwdHIK\nNYV64mh+7fnbrb/L0NdvkObPNJfPt31e6Guop6PkxcQVE+XO/92Z7/NUdFR0gkYgDyn/Y1zBmJHP\nKvreNWNcYRkxQmTq1OwCFMzxiJzGovIq6xLqh7bXnqvv+EJaTDlNhr8zXH7787eg9q9jOkpOfPrT\np3Lef87L93kqOio6QSO/lQQKMwfE62m44jN4sC3QmZISugoGXpFx7y8ngSuqReK+/+G4kPCY1JxY\nJ8/qAgVF5+koufHnsT+l0oRK+f6Ro6KjohNU/B9SuWWRBSO7zK0Y4Ho53uoBoZgg6u9Vudfz3k9u\n9xWKh/aaH7dI/fu6SufnE2XIbT+HTBC0SKeSG11ndpWl3y/N1zkqOio6Qcf/IZXTgze/oSfvMtPu\nEs/p6SJ33GGvNXJk9kF97/H5ITfvZMaM7ONOSUnWs3Jt8WbL+d9XsB/axzKPybgPJkn5h2rKY8uf\nluOZx0MW+lJPR8mNBQtE/r5grDy4/METbYH8n1PRUdEJKrk9pLxjNwUZ5/B6SG4hzsGDRfr3F2nR\nQqRVK7svkIfvqQQvJ6Hxr8Pmn72Wm7AE+6H9zS/fSPv/tJe2/7pEvkn7Mdd7CAY6pqPkRXq6SO9R\ni6Tri91OfA7k34eKjopO0MjtIeXNIvOOw7jH+I+/LFiQvcime1xSks+jaNVKpGVLkX79rPi4IpRb\nFpxXaLx25RaKc0Vk8GBfu/8ib3mF0Nx78F8kLidPKBAOHzss9394v9SeXFtmfj2zSJYi0Ow15VSk\n7UqXMg9Vli0/HA34B4mKjopO0Ai0OrR/qnFOD2fvnBuvKLhiMGmSffdfaM31pPwfjK64zZxpt91r\nrFhhl6N2PRbv9bwi6drqP+8nL6HNqWKCv5gGwrIflskZ/z5D+iT1kZ2/7czfyYoSYq6dc5NQeWfA\n4WMVHRWdoOIvPLl5Le5YjPfhPWKEFY3c5th4x05at7ahtX79rNfjLint70l57fCeN2KEyKJF1oZ+\n/XIPIblZcTnNAzrV2FRhQ2up6anSd15fiZsSJ29vfLtIvBtFyQ8F+TeuoqOiE1QCGQdwBWbwYJHu\n3X1jMd6H+4IFJ6cn+4/pjBjhC7W1auVbeC0n0XHPd5eh7tFDpFo1kT59sh+fW+WBadNEmja1714B\nTEuzXlJu3ktBkggOHT0kDy1/SGpMqiHjPx4vfxz9I/CTFaWIKOiYn4qOik7QyevXj/cfpis0rVpZ\nb8MVEe+4iduHmyXmn7328MP2we9OCnUFKicRcENqL70kJ0JzXkHLTajc/lxPacgQX4iuR4/cx5Hy\n+yswKytL5n87X5o83UT6v95ffs74OR/fuqIULQUd8wub6ACNgOXAd8B64A6nvTqwFNgMLAGqec4Z\nC2wFNgI9PO3tgXXAFmCKp70skOSc8znQxLNvmHP8ZmCop70ZsMrZNxeIycX+/Px9Sh25/cL3/4fq\nFv5s2NAnNCtWiNSubT+LnHo8JJCHe06ejhuWcwXMv+/cxqh69LBimVfiQn5/Ba79Za0kzkqUc6af\nI8mpyTkfpCglgHCKTj2grbNd2Xn4nwFMAu512kcDE53tNsBaIMYRhu/hxGJxq4EOzvYioKezfTPw\nnLPdH0gSn7D9AFQDYt1tZ9884K/O9nRgZC72h+QPUhII9Be+G7pKTBS56io5EVrr1csmCvTokT25\nwH/A3+0jkAH7nMZ0UlLy9lTc8/z3uckEeYXNAv0VuOXXLdL/9f5S78l68uwXz8qxzGM5d6goJYSI\nCa8B7wCXAJuAuuITpk3O9hhgtOf4/wGdnGM2eNoHANOd7cVAJ2c7Gtjjf4z4xKW/s70XiHK2OwOL\nc7E3uH+JEkJuv/DdkJj3OHeeS1qaFYOrrrLv7hiPN3MsrwSBQFKT/bPXAh2T8b8f19b+/QtXqHTb\ngW3yt/f+JrUm15IJn0yQg0cO5r+TAqBp0Eq4iQjRcTyXNMfjSffbt995nwYM8rS/CPQFzgOWetoT\ngPec7fVAA8++rUAN4G7gPk/7A8BdQE1gi6e9EbAuF5uD+ocoKeT2UHPn2Lj7vJMtvanIU6eePObj\nP18mJ07lXRXmYeufNecNyeUmhrmx99BeuWvxXVJ9YnUZ/cFo2ffHvsBODBIFHfxVlGARKtEJeD1c\nY0xl4A3gThE5aIwRv0P8PxeGQNblDnjt7nHjxp3YTkxMJDExMf8WFRMWLrRLSsfG+trmzbPv/fv7\n2uLj7VLRvXv72lauhJ497ev+++1y0h98AN27w7ffwr33wuTJviWR773XnpPbEtY52QJw3nl2uerU\n1JP3ee1xiY09uT2vvs89F6ZNg8GDffuffBKWLDn5nv37+e3Ibzz+0dM899U0Brftz3e3fEf9KvVz\nvsE8bMnIOPla+SE2FiZM8P0dnnjCfva/X0UJFsnJySQnJ4f+QoEoE3Z8ZjFWcNy2jWQPr22UnMNr\ni/GF1zZ62gMNrz3vOed5fOG1PWQPr/0vF9uDK/8RTk6/kHOqLnCqLDD/mf459etWbvaG1wYP9o3x\n5GVLYcvN5LfvU3l223b/LpM/nSy1J9WRVmMGy9q0HwplS7C8Ei3iqYQLwhleA14BnvJrm+SKCzkn\nEpQF4sieSLAK6Ij1UhYBlzrtt+BLJBhAzokE7nass2+eR4CmAzflYnsI/hyRTU4hrECTBtwCmd6s\nr7Q0m/KcU4ZYu3bZhcmd1+O/UmdupXWCITyB9J3b57Rd6XLf4kelwkO1pfesftL/9vUFsie/adfh\n6lNRAiVsogPEA5nAN46YfA1cih1zWYbNZlvqioFzzlhHbPxTps/Djt9sBZ7xtJcD5jvtq4Bmnn3D\nnfYtZE+ZjsNmw21xBKhMLvaH5A8SiXh/zXtX6XTHQwJZyCwtzaYou+fecYcvacDFnXfjegpuhYLE\nxOzlbdz9brr1jBki997rSxIQsfunTRMZPTp7Ic9AB8zzKlCalGSv5+8NTZ0qcsmVe+TvC8ZKjUk1\nZNjbw2TZN5sK7VEE0yvRMR0l3ITV0ynOr9IkOt5ML3dA3a2N5v+rObcstcsvtxNA+/e34tO/v31d\nc83J2WRuVpsrKi1aiHTrZvd558kMGeIrm+M/yJ+SIlK9ur1GTiE5kVOHxnLzBPxDi+npIv83aLvQ\nc5RUnVBdLnv2Jvkm7ceTPCb/dO/8fPfB8ko0e00JN6ESHTfsVWIxxkhJv0eXhQuhcWO49lqYPRv+\n8x8YOdIORDdubAfTY2PtIPc//mHP8bbdfjt88QW0a2dnt8yfD/36QdmyvmuUK2fPAdvHkSM2IWDX\nLjuID/D11/Dbb9C8OVSoAA0b2oH9t9+GpCR48EEYNAjOPx8+/xyaNYMzz4QHHvAlKHz7rW8QPiPD\nDqhfeKFNcnCvDbavl16C666zSQ7uYLs7kB8fb4/dl5nKuqqTSKs0n0FthhO1+m4e/UdDxo/3fQ/e\nft3vJRBc+7zX9n5WlOKIMQYRCThhK2BCoWSR9KKUeTq9evlm87uVA2bOzHmypr+nkJTkS4lu0MAW\n2mzd2nopbuioW7fsVafdVOl+/az34k4eBZHzz/eVzZk2zZ7btat9d4t4gq2rNnJkdptd+9y5Oa5n\n5Z4/c2Z276l375yXQNi4d6P0fXWocG8N4aL75KMv9py4f/e78U8+yK9HUVReiXo/SlGCejoFozR5\nOgA//QT/938wfTrcfDMsWABNm5583MKFcPAg7N1rPZzUVDDGegzHjsHx47BqFaxYAbNmwdGjViKO\nHrUeUGoqrF5tU6ofeABuvBHKlIFFi6B2bahY0dqSkACXX25/9V98sT3mq69sP7/+CnXq2OtGR9vt\nfftg6VKoVs16HUePQmKiPWfgQOja1aZbd+gAVapYT2fyZF86t5tePGBUCtO+mcBHqck02XUHf358\nG62axFKzps+L+ekn6yUNH+5L4W7WrGj/XvlBPSqlKFFPRz2dU+KdHOnvNYhk/6WclORbzbNrV5GE\nBJG4OJE2bbJ7LQ0binTpInL22b706MRE65106+bzoBYtEjHGXveqq+w5VarY88F6Iq7347a99JI9\ntlIl3/769W2bmzXnVqqeNEmkRg17nRYt7LErVuSw6mnDVXLxi5dL/Sfry/gPn5ShN/yerS9vRl5u\nSzP4f1fe7zcnr6IoPRDNaFOKCjSRQEXnVDz8sK8mmis4KSnZM83cB5WbpdaihRWQ2rVFypSxD3/v\nQ3r4cJ9otG5tw1ErVojUrGnPTUuz16ha1QpT3bpWvFwxA5tW3aKFSLNm9jgQefZZ+56QYIWkXTsb\nLnPDc+PG+UShXz/b5obk+vfPXgMuKytLHpqZLA3GXCINnmgiZw5/VjZ9fzhb9po3027qVF84LrcM\nMfdY/8y3nJIMijrTTOfuKEWBio6Kzkn4/8J2641Nm5Y9e80VopkzfQ/aGTPsw7xzZzkxtgI+j8Y/\nC65dO3u8uxhbQoJ9+E+dKtKokRWuIUN8IhUfLxITYzPYWrSwx/fqZfc1amTbOne2795yNUOGWG8I\nRObPtw/67t2t0LnXdTPinnkmS5peskjaTo2Xqve3lK53zJDdvx458T3kNLHV+8B2l1vwfo/unKQZ\nM6wn560pN2RI7pltReWBqKejFBUqOio6J+H/a/zee60H0KOHT3AWLbIPcddzcas2u6Guxo3tdpMm\nVjhcEVqx4uTlqxMTfeLUr58NoYFNAkhLs/vr1RO57DLbPnq0FUAQ6dDBekfjxtlj3DCcmxiQkmLf\nu3WzD/fRo+WEh+Xanphorzt4SKZcfNtbcu5z7aXVlDMl7oo58v2Px7I9kN3KCHlNkPUPsXnf3VBc\n//5ywrvKrXabK1r+i9kFO7ymc3eUokRFp5SLTl5rxnhL0LRu7ctec8NR3vVu3MXYuncXiYryjae0\naGEFqEoVK0aNGvnOc8/t18+Ox3i9lsqVrXj072/Hg6pXt+0XXWT7jIsTadvWej3jxlmhjI+3oba4\nOJGbbrIic/rpdjxnyBDfw3/cOGvfpEn2Hvftz5S7XnhTmjx+jpzzbDu5/9W3JTMrM9sD3vvgz2lF\n05MqEqSd7BX6hyDBvnsnyHrxzgfKq9J2YdHsNaUoUdEp4aKT1wMlp2UBZs60guOftjxtms/DqVHD\nCpC7jo0rOq63Uq+eSIUKVmS6d7djOmedZUNsI0dmr6HmhpfccZcyZawANWli+6pd23opZcqI1Kpl\nU67Ll7ev+vVtqKxxY5+o9O9v21u0sNcBKy7+97lihQgmU0Y8+YY0efxsaT7xPJnz1XuSlZV1Ulp1\nTmVxcpsM6/1+XXFyxdoVqREjAvN0ikp0FKUoCZXoRAU9HU4pEPHxNv01I8N+dtNh4+Pty00Lvv9+\nWLfOpgXXrQvLl9u0YrBpxV98YY/t1QvefRfmzoXHH7dp1GPG2GP794cGDaBLFzjjDFizxqY+t29v\nJ2U++KDtp1IlmDgRbrgB0tLsRFDXtmPH4MABiImBypVt6vXatXD33fDHH7BzJ/z5p32NHGnbK1eG\n9eut5FWubCeT/vCDTZFetMimMK9aZfcdOAD707P451tvUP/Rc0naMRGz/DG6fPslHz53OevXG/r3\nh+eft2nhZ53lSx82BrZts7a61Zo/+cT3XS9c6Ku8HR9vv8sVK+yE1alT7ee33rLfVeXKNpW6cmX7\necmSk/92K1faNOwHHrCp1w88YD+vXBmSfyqKUrwJhZJF0oti4umI+H6pz5jhy5Ryf6G7C56NGycn\nxlFSUmzYJy7Ohry6drVjMo0a+Twct/ZaSor1TOLifMkC/frZcFrlyrZPY0Suv16kbFnrmbgJAr16\niURHW69m0iR7rWbNrJfkThh1Q22NGvnaQaRlS3uNmBi7f/58ORH6q1TJbvfq5cuY69VL5ONPMqVh\nj3kSO/YsaT+9g0x6e4FUqpwlffpYT61PH5Fq1eTE5xEj7HiWu9Bb9+52e+ZMOzbkekTeenDe9Gm3\nNI87kTUtzfbhXRsor+w1799OB/iVkgI6ObRgFLfJoWlp9tfy4MHwz3/C+PH2F3bZsnD11daDadrU\nlrUBO4ly4ULo08d6Ih9/bL2T226znsNf/mInWdaubT+PHg09etgyNT/9ZM//9Vf7qlIFfv8dGjWy\nn3v3tl7I779D587WC6lUyfZVq5b1iqpXtxM6//MfO8n04EGoUcPa8scfVnqioqBePTsBdPduePpp\nuPNOyMqyZXGWLLHHlymXyRl932D8x+OpWbUSWcsf5vm7L2PIEMO779pJqq1a2XtwcdfkcUvygC3V\n8+CD2b87t8yN6w2BLfFTvTrs2WPvedo0275ypb0PyL4GUW5r5OikTaUkopNDS5Gnk5rq+6WdkmK9\nhx497ByXLl18v/ZjY22bd8LkokXZlyFISbFjKb172/dx43yeyPnn236jokQqVrRtsbE+LwVEypWz\n7xUr2uwzt71KFZFBg6yndcUVciIDrnx528eoUdn7OfNMO4enVi1fW0KCtfPXfcely9/mSsV72kiV\nv3eS+WsXyc23ZJ3wiubP990LWJsbNvR5Jt7MMfc7c5MC3JRr/4my6em+QqWFnfOiA/xKSQRNJCi5\nopNTosC0aXagHUTGjPE9HN2wWrNmciIV2Z3J7z6E77gje2jIDcm1aGGTAKpUseLgikirVjZ85g2L\nua8KFXwZaRUr+kSpUiVr46RJNmxWrpx9jRtnQ1pRUTakVr++DdeBTS5wqxGASKUqx2XYk3Ok/j9b\nS9lbOku5Notl2rQsEfFl3r30kq8SQevWViirVbPhQzdE1q+fLz3aTZTwJgV4KzSI+EJl/usGaUhM\nUXyESnQ0vBYBZGTYytDPPWdDZ/Pm2YHsr7+Gw4ft68gRG4666CI7GL9/vx2cf/llG5Lr3NmGuDZu\ntAPrbrXohAQbanL7ABg3DqZMsdc1jvPcsiVs3Zq7jZUqwaFDNlyUlWXDT/Xq2USCXbtsGOv88+0A\n/oEDNpTWuLENxaWlwY4dPimb9u9M7pszj9/bjSfqaHWqrR3Hb99054rLDTNn2rBdt24wZw4kJ9sk\niCuusCHDDz+ENm3swP6DD8L779vEiXHjoG9fG2b7/Xf47DObRDFrlrX/jjtgwABbjy4lxX4X/hWz\nIX/VpRWlJKPhtRLs6YhkD61559u44ahKlXypxcb4KgQ0aGC9lzZtbAp0Sorta+RI30B97dr25Xoj\nsbHWC/GGyvw9nJxebgmb+fNtKM2ttda8efY6azVr2oSGadN8JWyqVROJijkuTS9/TaLuOF1aP3mB\nxLZfKpB1ItTmVh6oWtVew50/c/75vrI57v25C8d508G9EzunTbPfoZvq7C2nM21azusJuckGiqKE\nztMJuyiE+lVcREck+yqYbgZV27ZyIrR19tm+h/o11/gewklJNsxVtaoNZ7ml/l1RaNjQhuHcLDX3\nFRWVc0gtKsq3XamS7ScmxobgevSwgvfSSz4BrF7d13eDBlaAOne2JXHOPlukU5djEt3uVYm+83Sp\n8Y946X37B9KgYdaJ893MN7cKwaJF2Sdszp9v93sLfPrXH3PHVbzjK+5cppQU3yRa97sp6lBaoOM+\nOj6kRAoqOsVcdE71MMmpRIv7y3zUKPvAd9OT+/SxHsuYMb41Ydq2tULgejfR0VYoate24zcVKpzs\n0ZQpc7LgNG16cptbKueSS+x2mzZWLBo1yn6cKyBVqlg7ylc8Judd/4rEPthKav4jQYhbJlWrZcl1\n1/nOadLEikp0tH2NGWOFZsUKn+C4YzTu9+Q/8TMvAfEmGISzfEygJWy01I0SKYRNdIAZwG5gnaet\nOrAU2AwsAap59o0FtgIbgR6e9vbAOmALMMXTXhZIcs75HGji2TfMOX4zMNTT3gxY5eybC8TkYX/w\n/xoFIK+qxTk9aBIT7QD/tGk2vOSGw6pUsQ/+unV9S0MPHixy2mlWRNzEAjcc1q6dnPBevB6Mf7KA\nK1T+Ho/rwdx8s00IcMNcYIWvYUOf2LiZbjFlj0nMeS8Lt58mFW/tKkPHfSjnts2S/v2tkHjt6d7d\nhsCaNLH2XnaZLSLqhvG8no+3OoI7Xyavh7L/vCf/cFpRew+BzuXROT9KJBBO0UkA2vqJziTgXmd7\nNDDR2W4DrAViHGH4Hk4kK6wGOjjbi4CezvbNwHPOdn8gSXzC9gNQDYh1t51984C/OtvTgZF52B+C\nP0dgeL0b/1Iy3lIp/l5Qerp9GM+YYcNBFStaofGO6cyf7xOyfv1s7TL3oe96MG4GWc2a2cdwcgql\n1ajha4uJ8XlFMTFW4IwRufZae3xCghUjV6TKlnWOjzomnDtLuL2lRF1/odTrslxq1MyS6GgrHG5G\nmWtfXJycCBeecYYNrzVvbu/dDalNnGgfvNOm2ft3RdrN+PMPq/l7jpHmMQS6LIEuX6CEm7CG14Cm\nfqKzCajrbNcDNjnbY4DRnuP+B3RyjtngaR8ATHe2FwOdnO1oYI//MeITl/7O9l4gytnuDCzOw/bg\n/iXygf+DzltAsl+/7A/L9PTs6964v+Q7drTeS0KCr+R/3bq+tGF3nKdTp+yejLttjM8TyetVtqzv\nuLp17cO/YkWfWJ1xhn1307hdW0CkcrWjQrsXJfrvzYVhiUKz5QJZUr++9V4aNbLjPlFRtkKBMb55\nQe6rVStrQ5cu9r4aNfIt5rZihRXd/v1930tamvWa3CKc/t91JI6NqKejFCciTXT2++3f77xPAwZ5\n2l8E+gLnAUs97QnAe872eqCBZ99WoAZwN3Cfp/0B4C6gJrDF097Ia1sOtgfz75Bv/ItQugUk3QXQ\nkpKs9zN4sM8DGjzY94s+MTF7Ucxnn7UPZ3ecpVYtm43mHew/lcDk9ipfPvtnN1vNfSUm2ms3b+60\nRR+Rchf8RxjVVBh6sdD045MSExo18pXJ8fZbvrxv/o4bwhs1yt57YqJviYYVK+w4k5swkdPSBHk9\nnDLbIpYAABNBSURBVCNFfHRMRyluRLro7JPgic73AYjOVk97RIuOiC9U4qbvujXTWrWyWWctWtjt\nlBTf0gNTp/rSgYcPt2LyxBM2hHbTTXIi9OV9z+1VGCHy95xiYkSI/lPo8KxE/6OxMLin0PjTbMfm\nZI+3rVw5m+Dg3V+/vh0fckNwLVpkX5rBvyK0G3Y6VRjK/6Htrc3mPSbU6dKavaYUN0IlOjEUjN3G\nmLoistsYUw/Y47TvABp7jmvktOXW7j1npzEmGqgqIvuNMTuARL9zPhKRfcaYasaYKBHJ8usrR8aN\nG3diOzExkcTExFyPDTYZGXDrrTB8uJ2wuHSpnfw4YwZcc42tI9aiha0pdu65dpJnjRp2MuOiRfa8\n9ettPbZ77rHVoZ9/3k5sPHIEype3lZzzIjOz8PeRlQXEHOZ4+xchYRLsakvm3NdhR6eTjhWxk0az\nspzzgOPH7XvZstbuvXt9E067dYOff7b33a+fb5Jpr162+vPUqfbcBx+0E0FTU20l6Hvvte/u55xq\nnblVpu+/335/H3xgq3OPH5/zxNBQ4V+vDWwdt/j47G3x8SfXd4uNzfl8RQkmycnJJCcnh/5CgSgT\nNilgvefzJJyxG3JOJCgLxJE9kWAV0BEw2ESCS532W/AlEgwg50QCdzvW2TcP3/jOdOCmPGwPrvzn\nA++ERTdLy/V0GjTwpRy3besbuC9Txra3bWs9gjZtTs46c8decppjE5JX+XQh4THh7nrCgCuEBl/m\neuypvC5/z+vss62H06uX7zto2dJ6Ps2aOSuFDrbjN336ZB/TadVK5M47s3/XuYWh/Bd085bBCVcJ\nHA2lKZEM4QqvAXOAncAR4GfgOkcElmFTmZe6YuAcP9YRG/+U6fOwobStwDOe9nLAfKd9FdDMs2+4\n076F7CnTcdhsuC2OAJXJw/5Q/D1yDYN4i216kwTcTDN3+YFmzexguhsqczO63HGVQKsEhPRVZbvQ\n/R/CvTWEPoOFOuuC2n/LllakunWz2XcVKtj7r1vXhh27drXHtWlji4tWqmTDbwsW2LlJrVrZd+/3\nn1MYKqeBeVeE8grNFQWaNKBEKqESHa29VkC85etXrrTl8efOhSuvtIunPfkkzJ5t65AtXmxDSOXK\n2fpoAM2b27pkq1f7+qxQwdZICzu1NsEFT0DrtyFlKHz+dzjQtNDdxsRAmTL2HmvXtnXkMjNtGPGP\nP+wxVavacFKTJnbZhaVLbY23li3h0Uft9/vaaza0tmCBrVXnz8KFNkzlXWbg3nttWDM+PvsyCOCr\nwRaummvuchapqdCsWXhsUBR/tPZaAV+EMLzmei/uImD9+9vX6afbDK3u3X0pw2XK2HCZNyTmzRYr\nslBZrq8sIe5DGz77Rx3hL48IFX4tVJ/uvCH/+3XDig0b2u/IDck1aGC/r0qVbHZe/fq2ZA3Y73TE\nCF9ygVuhICe8YSr/Ct7p6Tak5r8Ud7hDbOrpKJEG4QqvFfdXKETn4Yd9RSYTE+23OG6cDQO1aJF9\n3Zl69XwrZ7pt/vNm/FOTi/RV5qBw3vPCLWcKt7Sx22UOBa1/Y+z34ZbnqVHDty6Qe4wrMq4gecWq\nTx/fJNKHH85eIsebgeZPbg/zBQsip9injukokYyKTkFvMMii8/DDvoeem+LsPjDdiZP+r2CkLAf9\nFfujM15TUxhwpRC3TNyKz8F8Vahga8IZY+fbVK6cvVSP+7rqKvveuLGdSFqmjBWjKlWs97hokRUj\n18PxnxyaE5E+q1/To5VIJlSiExX0eF0J57rr7FLSvXtDYqJdtnmHk7D9yy++9Wm8BCNlOSjE/Aln\nJcGQ7nBjBzBZ8MIXkPQOpF6MTSwsHN77b9nSrntz0012jaBzz7Xf3f79dn/VqjYFvEIFmxa+aJEd\nAztyxKaZHzpkJQnsujrLltmluDMy7FjOXXfB9OnZr5+RYcd0MjKyp1NnZBT61oJO7945p3hrerRS\nktFEgnyycKEd4L7kEqhe3S5g5s6ZiVjqrIf2L8LZc2D3ufD1DbDpKjhePijdu3OFoqPt6+hR+/18\n841dgG3TJps4UKeOXWDtq6/s9r59dm7O7t0QFWW/x6pV7ZyeX36xc5X++1/o3t0KfOXK2eexeJM5\n/JMGJk8+uT2neTyKouRMqBIJ1NPJBffXsvdz585wyy0wcKB937XL7otIwYlNhYSJcNO5MPgyOFIV\nXlwNryyDbwcETXDA3n+NGtaji46Ghg1hzRo7GXPZMqhZ0x5zwQWwZQvceCN07Woz06pUgb/8BS68\nEDZsgEsvhd9+s9l9TZvaFVQXLsyekeZ6At6Jn2lpPmH59tvsAuMet3Jl0G5ZUZQCop5OLrhLSJ92\nmg0LHToE991nf6m7REX5ZtxHBFV2QJs34ay5UON72Hg1rB8IPyeARIf88jVrQqdOdsnsjAwrJtu3\nWwFKSbHte/fCpElWOCZOtOG0666zIcqBA+HppyEpCd5803pMInDsmE0lnjgx5+tqyrGiBJ9QeToq\nOjmwcCEcPAitW9uwjhsyqlrVPkQjB4H6a+H096DV+xCbBlt7W6H58RLIKlNklpQta0v5fPut9WLG\njrVlbM44w4r22rXQtq097uhRG3qrWxfq1/eFJ9evh0cegeuvh//9z85peu21vMXEDZ3dc0/upXAU\nRck/KjoFpCCik5Hhq8fVs6etBxYxVNoNzZKh+Ydw2iI4VhE2Xw6br4Bt8ZBV0HJ6BadaNeuxuPTu\nbevMValiJ4P+7W/wwgvwww+QkAC33WZDcF27WuHp0sUee9ZZthbd/Pn2Ox882NZIy01MchvTUeFR\nlMKjolNA8is67tjB44/b8Yf337cJA7/+GkIj86LSbmj8GcR9BM0+gmrbIO0vkNYNtl4G+04Pk2GO\neZVsiPHIEfteoYJNBIiNhY4dbbLAqlXQo4cdw+naFf79bxu6nDzZekNg31NTbeLAjTfCOefYxAG3\nCGdOYuId53HJyDi5YKaiKPlHRaeA5Fd03F/Lf/wBr7xSxGM2MYeh/tfQaDU0XG3fyx2AHR2tyPx4\nMexqFxZvxkvbtjY8Fh1tvZz9+22qdMuWsHWrPaZbN5u1VrGiraL92We+kNlXX/nEpXlz+PhjG85c\ntMiWtjn/fCscblXpCRNsnyomilJ0qOgUkEBFx/urefRoGw46cCBEohNzGGpthtrfQe0N9lXnO6i6\nDfaeCds72SUDtneC/aeBRE6SoZs8MWaMFQSwCQRnnw3Ll9sB/WbN4KOPbNjsqqvs97liha1Nd/75\nthbd3r02bXrePHsc2OUMFi60Xo7rseRU6l9RlNCjolNAAhGdhQt9BTsHDrQZa127BuHiZf6AWhuz\nC0vtDVB1O+xvCXvOhL1tnNeZti2zbBAuHBpiYuygf5kyVhTc+Tl33mm9mMxMOP1067Gcfz6kp9vC\nnVOmWA/HLbp58KD1fNxJouXKWa/mww9tivRrr+mYjKKEGxWdAhKI6MybZ8M6x47ZX+Tly9vxhYC/\nmpjDUHsj1PnWei+uuFT+xXoqJ4lLiyLNLCsIbpYZ2NBZzZp2XKtqVSsuhw7ZfQkJsG6dDYG1bQuD\nBlnPxRjYudOO8cybZ491x2Xc7QsvtIka/vvUs1GU8KOiU0BOJToLF9qsqfHjbXbVnj12kmKuVNlp\nx1vqr7UiU+dbGxbbfxrsOcsKy54zrbikNw/7+EtBcENolStbryY93YbNevb0rVpapYpNHqhc2Wab\nzZplV/984QU7zvP44zaJ4MEHrXfjVhBwJ2hqAoCiRDYqOgXkVKIzb55dwvjBB2HAAJtp5Ts504pL\n3HLfwH70ETuw/0t72HO2FZp9p0W85xIIFSpYwTl82FeKs0sXG3J85hkbSnPXw9m923qFI0bY9Och\nQ2zSQP/+vv5USBSl+KKiU0BOJTrunJzff7djCvsO74Uz3oUWS6zYHKwHqRfBtgvs4H56HMEojBkJ\nuJMyY2JsmnNcHDRqZNtTUnweTVKSTV1euRJGjrSTON3z77gD5syxY2AqLopScgiV6BS/2E+QiY2F\nqMr7WLj1TQ71eh0afgHfXwpb/g8WT4HfG4bbxKBQpYoV1jJlrEfz22/Wk1mxwq7IGR9vU8T79bPl\nagYNsp5L585wzTXwxhu2n1tvtQP9AEuW2AQBnYypKEqglHpPB+CiW9/hoz1z4bt+tCl7GRtSKhaR\ndaEjKsrOo8nMtOV8Nm2yA/e7dtmkgO+/twkTDz4Iffv6qjO/9BKMGpXzeAvoWIyilBY0vJYDxphL\ngSnYatkzRGRSDsfkKjpuEsHw4TaJICPDPqgjce2V3Khc2QrL8OEwY4adIxMbC+3bw+rVdpzqm29s\nhee33vr/9s4tNqsqi+O/fymdARGQGKiIFhydOCpe8AIRE414QSeBeTEVJ/WCTyTqxBgF9QGeVEyM\n+KAmJooGxXrDoZMoogHedKzBDljBgalRRK1MFBN9IKYuH9auPS0tavy+8327Wb/kJOesc/vtL+1Z\n5+y9z9lefXbccf6V7GIXZYjkEQTBANVKOhUfFa6sCU80e4EWYCzQBZw6zHY2Et98Y3b55WZtbT4C\n5ezZv3+kzMpPWwctNzaaTZtm1tBgduaZZjffbLZ6tdmSJV6GlSu9bMONStne7tPQ36BaI1Vu3bq1\nOgcuifCvLeFfW4iRQw/jAmCPmX1iZj8A7cDi33KAyZO991VTk78Nv3dvVTx/NY1DWthOOQWmT99G\nc7P3ILvqKli82KvK1q+H++7zBv7TT/fllhZYtcr3HW5UytbWwb3LoLojVW7btq06By6J8K8t4T86\nybkjwfHAvsLyZ3gi+k20tg588fi88/zC393tb81XsuZxzBhvwD/6aH9/pa/Pvzs2f76fa+lSWLbM\nv7rc1uYjbU6YAJ2dPt7M2rUDCaXfu5+oEguCIBdyTjoV4eBBuPVWv3D39Pi4LAcOeAP72LH+9ND/\nsmhDg8cOHRr4BMwZZ/jXC8aPh2OP9e3GjfNG+U2bfGpu9gHN1qzx823YABs3egN/cWCyrq7D21U6\nOwc/wQRBEORMth0JJM0DVpnZwrS8Aq+DXD1kuzwLGARBUGMseq8NIGkM8BGwAPgCeBdYYma7aioW\nBEEQjEi21Wtm1ifpFmAzA12mI+EEQRDUMdk+6QRBEAT5kXOX6SMiaaGk3ZL+K2l5rX36kTRD0hZJ\n3ZJ2SrotxY+RtFnSR5LekDSpsM/dkvZI2iXpikJ8jqQdqYxrSixDg6TtkjoydJ8k6aXk0y1pbmb+\nt0v6IJ37OUlN9ewv6UlJvZJ2FGIV803lb0/7vC3pxBL8H0x+XZJekTQxJ//Cujsk/ShpSqn+1Xj5\np9YTv/LF0Rq5NQNnp/kJeLvUqcBq4K4UXw48kOZPA97Hq0JnpnL1P6H+Gzg/zb8GXFlSGW4HngU6\n0nJO7k8DN6X5RmBSLv7AdKAHaErLLwA31LM/cBFwNrCjEKuYL7AMeCzNtwLtJfhfBjSk+QeA+3Py\nT/EZwCbgY2BKiv2lDP+q/5PXYgLmAa8XllcAy2vtNYLrP9Mf8W5gWoo1A7uHcwdeB+ambT4sxK8F\nHi/BdwbwJnAJA0knF/eJwP+GiefiPx34BDgmXRg6cvjbwW/+ihftivniF865aX4McKDa/kPW/Q1Y\nl5s/8BIwm8FJpxT/0Vq9NtyLo3X3uWhJM/G7kHfwf8JeADP7EpiaNhtalv0pdjxern7KKuPDwJ1A\nsTEwF/dZwP8lrU3Vg09IGk8m/mb2OfAQ8Gly+dbM3iIT/wJTK+j78z5m1gccLFYXlcBS/M5/kEui\nLv0lLQL2mdnOIatK8R+tSafukTQBeBn4h5l9x+CLOMMs1xxJfwV6zayLIw8qVHfuiUZgDvComc0B\nvsfv7ur+tweQNBn/1FML/tRzlKS/k4n/Eaikb2mDXUm6F/jBzJ6v5GEreKzDDy6NA+4BVlbrFL+0\nwWhNOvuBYoPWjBSrCyQ14glnnZltTOFeSdPS+mbgqxTfD5xQ2L2/LCPFq8l8YJGkHuB54FJJ64Av\nM3AHv0PbZ2bvpeVX8CSUw28PXpXWY2Zfp7vKV4ELyce/n0r6/rxO/u7eRDP7unrqjqQbgauB6wrh\nHPz/hLfX/EfSx8llu6SpjHzdrKj/aE06ncDJklokNeF1kB01diryFF5H+kgh1gHcmOZvADYW4tem\nXiKzgJOBd1O1xLeSLpAk4PrCPlXBzO4xsxPN7CT8N91iZm3Av+rdPfn3Avsk/TmFFgDdZPDbJz4F\n5kn6YzrvAuDDDPzF4DvgSvp2pGMAXANsqba/fEiVO4FFZnaosF3d+5vZB2bWbGYnmdks/EbsHDP7\nKrm0Vt2/0o1W9TIBC/GeYXuAFbX2KXjNB/rwHnXvA9uT6xTgreS8GZhc2OduvCfJLuCKQvxcYGcq\n4yMll+NiBjoSZOMOnIXflHQBG/Deazn5r0wuO4Bn8N6ZdesPrAc+Bw7hSfMmvCNERXyBPwAvpvg7\nwMwS/PfgHTq2p+mxnPyHrO8hdSQoyz9eDg2CIAhKY7RWrwVBEAR1SCSdIAiCoDQi6QRBEASlEUkn\nCIIgKI1IOkEQBEFpRNIJgiAISiOSThAEQVAakXSCIAiC0vgJMQM+jmZhHRkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114aa3a50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_poly(set_1, 15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+-------------+-------+--------------------+-------------------+\n",
      "|     name    | index |       value        |       stderr      |\n",
      "+-------------+-------+--------------------+-------------------+\n",
      "| (intercept) |  None |   -25115.9044254   |   1573017.12178   |\n",
      "|   power_1   |  None |    783.49380028    |   9293.98471763   |\n",
      "|   power_2   |  None |  -0.767759302942   |   23.3971636819   |\n",
      "|   power_3   |  None | 0.000438766369254  |  0.0331210085962  |\n",
      "|   power_4   |  None | -1.15169166858e-07 | 2.93724988829e-05 |\n",
      "+-------------+-------+--------------------+-------------------+\n",
      "[16 rows x 4 columns]\n",
      "\n",
      "None\n"
     ]
    },
    {
     "data": {
      "image/png": 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f+HzQr1tZCBv3GoDXAVwBYDuARmwL03ZreyqAKY793wLQ29pnq6N9JIBnrO0V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\n/ddEnrlyLt86/tR5teWcOGM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+aq4xpRlHXjqXo2NOnRPAAQOkv8YtNnq0iLNx99WrZ2fH\n1aol95iYKN937SrnSEuTZ/zUU9KfIUM8V0o1WWG+KkQUl71W3Po2xbnXArEiqFpASnGEm+hs83Kv\nbbO2vd1rKxzutW2Odn/da3Mcx8xxuNcOebnX3iqm7zx9+vRzr9WrVwf0D1MWvP+zZ2fbs++NSy0/\nX1xjaWl2yZicHHs5Ae8S/MaiuOQS291myugvX267kFq0kHiF9yBuft3XqSPCkZhoWzdGmKKjpd1Y\nQuZYE+cwNdSM1QPYrjUzv8ecy1hW5uVdNiciwhaeiAjb2nC+oqOZkbCdcf0IxqRG3Grk49zxohMe\nQtqrl/RnyhTJomvaVM7Vv7/dl+rV7TTrSy6x41DmeZg4lqlK3a2b75iOsUi8a+EZ16i3SPjKQnN+\n9j7OmZDg6zhzfX9rn6mFpDhZvXq1x1jptui0AvCl43OmERf4TiSoCSAJnokE6wH0AkCQRIIrrfbx\nsBMJRsJ3IoHZjrO+W+QQoGcA3FZM34Pw5yk7TveLGTxM2RhABCItzS4cmZEh1ktSkriH2rQR15b5\n5W5EqFYt+RWekCAD6uzZMgjdeqscYyZG1qkj13JaGc5Jk926eYqS2S821haaxERPC8lXzMZYIsat\nBUhdNG8XW1Evp3D5sohQfytj2BjGXfUZff/OzVr/6CFSTovKlIHp00fuo149uw8mgQBgvuIKuVa3\nbiKKPXpInCshwU6MACT9fPZsW2CcVklWVumXAi8qrlOSJeI8rqyVozWrTSkK10QHwMsAvgNwEsC3\nAG62ROAdSCrzKiMG1v7TLLHxTpm+2HKl7QLwD0d7JIDFVvt6AK0c391kte+EZ8p0EiQbbqclQDWK\n6X8w/h5lxpk1ZgpkmhnjGRkiHiaW8txz4qrKyJDAdbVqdizGDKr9+8ugmJoqA/XUqfYg36iRPafE\nOQg7X84B3RTCNC42X6/YWE+x8XVOXy9fwuTr5bSgfApU008Zw69lTGrI6PcAIyrfQzQjIuRlRMts\nN2smz9lkukVESJ+MQJlYkhHcjAzbNWmWZUhIkGdrZvebwd7bpVUWi6GsFZrNcc54T2mvr9WhFV+4\naulU5Fc4iI7zF6uxdAYNsrO+kpLkl7Nz7RgTrJ416/xCl3XrShzHzKd56imJnXTubMcjoqJkADfz\nXHxZC84BvnlzzwHeDMbeL+c+RYmT00oJzKuQ0XINY1Qa4/+aMXo/wahxnAFbUJ0vpwg5t6+4Qt4b\nN7afCyAuyOrV7X7PmiWDuKm5FhUl7cOG2UsymFI348bZK6U6CcUcmuLm+JQmvV4tHcUXKjplvcEw\nEB3vyYDjxtkxjOuvty0TUyQzPl4GfVNTrG5d+xd77dryecYMEZm0NNnHBO3NL3bvNWP8ERFfbi/T\n5hQYZ2wmqK9qvzC6LGD8/mLGH9sxuv2bUe1kiffhLYqxsXalhZgYEQ1jeZl9kpPluZoMufR0u0JB\nw4b28tKpqWLpPPkkn6tE7e3yKk0gvqxxlUDEYyp6TEcTIYKLik5Zb9BF0fEuQ2LSaPv2FWFZvFgG\nuubN5Rd527Z21WIzKJqVMo1oNGtmC9Z998kgahINjKvL+Su+uJevgdpn/CTUr5j/MS6fwfhzY8bo\nKxjJbzLobInHOYXW3Ie5R1PJ2ik0derYmXXVq4tVY8r4xMWJqDRp4jkHZ9w4ERzA/8Xz/P03YjBZ\nbU68B9NADLgVfdCu6KIZ7qjolPUGXRSdotKfL7nELpSZni7v7drZywA4Z/0DdqZXZKTsZwZMQFxB\nkZG2hePL3VQxXoWMVqsZ197ImBLHGPp7RoPNpTqHtzXnLb6XXuq5j3Gn9eghpW3i4yVGlpsryRdG\nWJx/x9IunheIfzc6mBaNugeDR7BEx2SWVVqIiEN5j8uWASkpQFycfC4oACZNAqpXBz74AOjdG1ix\nArjkEuDAASAvD+jeHdixA/jqK6BTJ+Cbb4BevYCcHODsWTlPvXrAzz8Dv/wC1KwJnD4t7ydPAtWq\nyX7JycDOnSG71cAQcwDo+jzQLQs4Gwl8/lsgdzRwIqFMp4uMlPeICHlWLVoAe/bIM2IG4uOl/aef\npG3gQPlbffcdcOgQ8Mc/Anv3ymdzvkceke2VK+VvOHOmHFNQANxzD3DrrcBFFwG7dwOtWnn2x/vf\nAyDHrV0LpKcXfR/m3HfdBcyaZV9TOZ+8PCApyffzV8oOEYGZKeAnDoaShdMLIbZ0fP1KNQkC/fpJ\nbKBNG7FIGjYUKyY+3p6w2bChWC2RkeIuMr/MiWTbuIu8XWNh4Rbz91X9BKP9fxkjholV86vfMhLX\ni7VTynN5Z885n0tCgnx2JmgAds221q1tK7JpUztu46z0PHmy/dksBeF0f+XmiqVkyt74cleV1Wox\nWWW+lr+uKC6wYKOWTvBAkCwd10Uh2K9Qiw6zZ1aRqeA8YoRd2n/iRDu+YFxAV1wh6dBxcZ4uoNhY\n/72HuoMAABF1SURBVNOSw/oVcZrRZiXjmpsYU+IZY/szuj/LqPlDqc9VVFJEtWrnTz694QZ5hsb9\nWLOmPGNTUdukQ6elyWvePHv+lHP+jWkzlSDGjbPrqjkLewZixU/nMUUtm6CDq7ohg42KTllvMMSi\nYwYq8yu1aVOJ32RlSckUM8iZNGjAji2YOEKleUWcllTnq/4g82p+14PR5zFGnX3lPrd3vMaZGm0S\nBZo0ke3ERNnu3FkswuhoqbGWni6CNGGC7N+1qwhPURW5nZMwc3Ml1dqsqePc15cVUpq5MN6Dp3fV\nah1UhYqeCBHuqOiU9QZDJDrTp8uv5AkT7OUEMjMl8B8d7Zl15vzVXb26fC5uQmaFetU4zrjwVcaw\nsYzJCYxbuzEuu49Rb2fAr2WsReeEVfOKixMxN+VzZsywl1S44QbJGGzSRMrjmDpxRGKFei+eNn26\nvRje7t22gJhkEH+XjvbX0vE1mDqLh3qfWwdZJRio6JT1BkMkOllZYtV06yaDYHq6VARwpuqaqsoR\nEXYMxvkLvcK+YveIq2zk1YxpdRhjBjJ6PcmIzQv6tVu2tKsLACLeUVH2pNmICHlPTpYYWUaGuDqv\nukrmRdWpY1chMKVuli/3dJfl5Ihb1MR8Ro+2F6wryfoI5HwadbUpoURFp6w3GALRMVUGhg8Xq8ZM\n7gTk13PNmp7uIO+4TYV71TjOaLeMceUExh0XSv2z637D6PICI+poUK/ta26REZymTe2266+Xd1PZ\noVs3qb2WlCRCk5RkFygFZM5Up07y3qCBvdy199IRpmzR6NG2KBUVyzH/NsrjAlJXm+IWKjplvcEQ\niI6znpopaukcJH1N1qxQ2WYRpyS7LOUhxpgBjLtrM266jNFvJqPJBr8mbpblVaOGLSjO+UdEIuze\ntdNM1p+pv/bUUyIcU6fKuQYMsKtJA2IR1akjZWzi40VojPAYIQJsl1ZWlnyePfv8JaOD5eYqztWm\ntdKUYKKiU9YbDKLoLF1qZzVlZ4ul4xzUgApq0VT7hdHiAymoOXqQuMxu7ywJARe8UaaMs7K8iOTV\nsuX539WrJ8Jdt6641MxzTkmR/c3Cc0ZIzITb5s3tlOkGDex1ioYMsatEmOUgWrY8PzPN7dRcTRFW\nQoWKTllvMIiiY1JoBw2SZaNNgkCFe0UdZbRZwUj9G+Omy8WS+f3FjLQ/MS54nRF9xJV+lVQ49Pbb\nRVhMsoApBzRxInPHjrKWDiCCU7euiI1JP586Vdxko0bZlsOUKfJuMtKcK4CGQyxFU4SVUKKiU9Yb\nDILoeFs49et7utBCUgyzrK+I04zGnzN6PCMZZndcyJgWI2IzcCqj7XJG5DH3+1nCy9RZM8H/5s3F\n3TZrlr2iaK1azDffLJ+nTrWtoCZNJCaTmytp1J07i9CYGM6gQeJCM64tMynU6T5zI2tMU4SVUBIs\n0dEyOH7iLGdSUAAMHy6lUsaMAd58E/jwwwB0NuAwEP8N0ORzIPFToNl6oPFG4IfmwL4+wL7e8n64\nI1BY3e3OnoNIpMV7GwCiooBatYCjR4GrrpLSNKak0KlTUsKmWzdg40YpC/TVV8Ds2cA//wnUrw80\naQL06wfs2wd8/z1w/Diwfz9w5AiQnQ08+aSUJPrmG+Ctt4AuXeS6BQVyrZiY4svXKEplIVhlcFR0\n/GTRIiArC3j2WRGam28Gxo2TAbFaNeDMmQB0tjxEnAHqbxeBabzRev8COBkL/K8b8F0PEZjvegK/\nVNwiXkRAgwZSE+3774E+fYAvvwQWLJC6aV9/Lfv17Al8+ikwYADw3nvAjBnA++8DrVtLLbW4OPmb\nGpYulfdTp4DDh4GGDYH8fHufSZPk3RyrKJUdFZ0yEijRKSiQQW3NGhnwvv4aaNrULgwZUmodBhpu\nARpsBRptEoFpsAX4oRlwoBvwv+4iNAe6AT/Xd6GDpadZM7E+iqJdO7FKDh4EmjcH2rYF3n0X6N8f\nuO8+ICNDCqfm5so+NWoATzwBTJ4sFuqqVcCIEcCcOb5FwxSNBKRwZFycCM3Jk9JmCn+q4ChVBRWd\nMlIe0fFVMfrGG4HlywPYwSJhoPZhEZMGW22RabBFrJrDHYHDHYCDnUVcDlwEnKoTio4FjZo1xdLw\nJjZWqkJ37izVtXfvlirc8+YBDzwA1K4tbrTly4G0NHGNnTghf6/nngN+9zvg2DFxt61aBbRs6Xl+\nUwncW2AKCjyFSCsYK1UJFZ0yUhrRcYrMsmWyzMDvfge0bw9ceimQmAgMGyb+/8DBQO1DnqJiRIbO\nirgc6miLzKGOwPHGAAJfcTxciIgACgtl2yzX0Ly5CEd0NNChA/Dqq57xtRMnxO32wQfACy8ADz8s\nSxhER4urrHFjiQMdPCguM++lJwB7CQOnABnU0lGqGio6ZaQ0ouOM28TGymBWowawbp0IzvbtQKNG\nEnguE7UPAQ03n2+9UOH5wnK4Q6URl/h4iY8UhbebMiJCrJ7ISLFs+veXuM233wJXXAH85z/ni0ZC\nAjBtmuxz0UXiZtuwQf6mRmTMvoMGiasNkB8Xx48Dgwfb59yzR2J2NWpoTEepuqjolJHSiI6J23z2\nmWQyzZwpAeYuXYD160sePM8RfVSEpeFmERYjNBFnbXExwnK4I3C8ESqDuBQFkWSc/fST/8fcdx/w\n6KMiEK+8ItZK7doiBE4XmXdWoVlU7e67gdGjPcUE8G8BNV9CpNlrSlVDRaeM+Cs6ZqDp00eCz4sX\nA0OHSoB582bg17+WX9jnEX0EaPoZ0HQD0MR6j853iEsne/vHJqjM4lISUVHi8jI4RbxGDVld1fn9\nvHnAgw+Kq+vMGYnZbNgAPP64/BhwxmaM4Hiv6qkrbipK2VDRKSP+io5xvZw6JYPc4sXSXqcOMGoU\n8MwzwAUXADsO7AFavQ+0fB9o+YG4zP7XXVKS/3cx8N3FQH4bgCOCfGcVg1q1ZJnt2Fh5thER9tyb\nU6dETGJj5fk3by7WzfDh4lqrVQu45hrg+efFXTZ3rojIsWOSIDBjhn2dsi4LrSiKb1R0ykhp3Gt7\n9kj20+nTwNmzMl8jPuEMzjb7ED8mvo6fmy1BRNRPKPzmciDvcmDP5eIiU4FBhPUIiOTZGVq0ALp2\nBZYskUB/y5ZirXTuDGzdKi6s77+X/VaulH0XLJC5UDVrinX0z38Cs2aJBbp5s4qIooQCFZ0yUtpE\ngkWLgNeWnALarsAVf3wN7+1diojjLRD5TQbqHb4Gezd0QlV2kXnTooVkjkVEiAVSs6aIjsn+atxY\nMtF+/3uZI9O2rWSXDRgAjB0LXHihxElSUoDbbhPL55VX5AfA0KG2G03dZYoSWoIlOvoT3YvN0U8h\nclpzNBg2C3s/6YbFV3yG+MWfof3hv6BZjc6oSoJTo4YE76tXF3cXIO8xMfIeESEpyHfcIVZMp04y\nyXPoUKnW0LWrJA+0bi2us0GDxGUWFwd8/jlw6JBYOunp4gabM0cEBxCLZulSeQfkmJkzZT9FUSou\naulYmJjO4Zqf4G93xaNNfDtMmiQpuH/7m8QWoqNlrseJEyHouMvExYm1kpEhz2DjRqBHD5mMOX68\nxGF+9Stg9Wpxj40fLynl3bvbWV+LFono1K4NbNsG3HmnnNvEWTTmoijhi7rXykhps9d8pckCMhnx\n1VfDoMZaOYmMFJfY7t1yLzVrShwmOlpm3G/ZIpbMoEHAxRcDTz8tYlyrlsxRAsQVBqh4KEplRkXH\nB0R0JYAnIG7CLGbO9LFPuWuvmeoEN94YPu4dkwFGJJWTv/tOROH4caBuXam6fOWV8jk/X4L2XbtK\nNYVJk0RAo6KkptnJkyJC7dtLzKVBA7lGTIzct3emmKIolZ9giU7A10oI1QsiNF8BaAmgBoAvAFzo\nYz8uL/n5sthXvXrMTZvK+i116gRnyWkiWUbZfI6Oluv06MEcGysLm8XFMV96qXwXFyfrwuTkyGqZ\nmZnMF14o7871V3JymLt0WX1ufZiqvi7L6tWr3e5C2KDPwkafhQ2CtJ5ORU4k6AVgFzPvYebTALIB\nXBOMC736qlQpuPdeqQXWty/w44/iqkpKkkmO0dFidRhMza/atT3PVceqyVmjhrxHRYl1cfnl8nny\nZFkf5uKLZb7K5ZfL+i+vvAJcdplkeH3xhWSKrV8v26++Kn1au1Y+b9sm50lPt12FffsCGRlrEBcn\nVot3BlhcXNVyj61Zs8btLoQN+ixs9FkEn/BZuav0JALY6/i8DyJEAefbb6Uszty5Mn9k4ULg+uuB\nFStEBN56C7juOsm0evVVCbLXry/C06AB8PHHkgLctq0UEJ0zRxYbmzhRSuwsWiSurwcekLTgN96w\nZ9WvXSsxlLVrZa6LwWR1Abbrq0sX4OWXg/EEFEVRAkNFFp2QMWOGxHUmT5bqxYsXiyjs2SPi88or\nMpdk2TLgoYck+eDzz6UA5cqVsk7Miy9KodBt2yTj6803gY8+Am65Bbj2WhGVvn1loTGD0/qoSlaI\noiiVlwqbSEBEfQDMYOYrrc9TIT7ITK/9KuYNKoqiuAxr9poNEVUDsAPAQAD/A/AJgN8w8zZXO6Yo\niqIUSYV1rzHzWSL6A4BVsFOmVXAURVHCmApr6SiKoigVj4qcMl0sRHQlEW0nop1ENMXt/gQDImpG\nRO8R0RYi+pKIJljt8US0ioh2ENFKIop1HDONiHYR0TYiSnO0dyeiTdbzesKN+ykvRBRBRJ8T0RLr\nc5V8DgBARLFE9B/r/rYQUe+q+jyI6P+IaLN1Hy8RUc2q8iyIKIuIDhLRJkdbwO7depbZ1jHriKhF\niZ0KxuQft1/wc+JoRX8BaAygq7UdA4lxXQggE8Bkq30KgIes7Q4ANkLcqq2sZ2Ss3Y8B9LS2lwMY\n7Pb9leF5/B+AFwEssT5Xyedg9f15ADdb29UBxFbF5wGgKYBvANS0Pi8CMLaqPAsAfQF0BbDJ0Raw\newdwO4Cnre0RALJL6lNltXRCNnHUTZj5ADN/YW0fB7ANQDPIvc63dpsPYJi1fTXkH8UZZs4DsAtA\nLyJqDKAOM39q7bfAcUyFgIiaARgC4N+O5ir3HACAiOoC6MfMzwGAdZ/HUEWfB4BqAGoTUXUA0QD2\no4o8C2b+EEC+V3Mg7915rlcgiV3FUllFx9fE0USX+hISiKgV5BfNegCNmPkgIMIEoKG1m/dz2W+1\nJUKekaEiPq/HAdwFwBmkrIrPAQCSAHxPRM9Z7sZ/EVEtVMHnwczfAXgUwLeQ+zrGzO+gCj4LBw0D\neO/njmHmswAKiKhecRevrKJTpSCiGMivjImWxeOdHVKps0WIKB3AQcvqK25eQaV+Dg6qA+gO4Clm\n7g7gJwBTUcX+XQAAEcVBfo23hLjaahPRjaiCz6IYAnnvJc7rqayisx+AM6DVzGqrdFgug1cAvMDM\nb1jNB4mokfV9YwCHrPb9AJo7DjfPpaj2ikIKgKuJ6BsACwEMIKIXAByoYs/BsA/AXmbeYH3+L0SE\nqtq/CwC4AsA3zHzU+iX+GoBLUTWfhSGQ937uO2vuZF1mPlrcxSur6HwKoC0RtSSimgBGAlhSwjEV\nlXkAtjLzPxxtSwDcZG2PBfCGo32klXGSBKAtgE8sE/sYEfUiIgIwxnFM2MPMdzNzC2ZuDflbv8fM\nowG8iSr0HAyW62QvESVbTQMBbEEV+3dh8S2APkQUZd3DQABbUbWeBcHTAgnkvS+xzgEAvwbwXom9\ncTu7IohZG1dCsrl2AZjqdn+CdI8pAM5CsvM2Avjcuu96AN6x7n8VgDjHMdMgWSnbAKQ52i8G8KX1\nvP7h9r2V45lcDjt77f/bt0MbBGIwAKOfIWg2YANmYhK2QSCYA0kYgh1wiJ7HkIZw78lT1998l7a3\n5jkcGh9f9+rauL22ynlUp2Vdj8ah92Yts6jO1bN6NQJ8rHbfWnu1rS7L81u1//ROfg4FYJp/3V4D\n4AeJDgDTiA4A04gOANOIDgDTiA4A04gOANOIDgDTvAGSFLGTGs636gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114bf23d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_poly(set_2, 15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+-------------+-------+--------------------+--------+\n",
      "|     name    | index |       value        | stderr |\n",
      "+-------------+-------+--------------------+--------+\n",
      "| (intercept) |  None |   462426.565731    |  nan   |\n",
      "|   power_1   |  None |   -759.251842854   |  nan   |\n",
      "|   power_2   |  None |    1.0286700473    |  nan   |\n",
      "|   power_3   |  None | -0.000528264527386 |  nan   |\n",
      "|   power_4   |  None | 1.15422908385e-07  |  nan   |\n",
      "+-------------+-------+--------------------+--------+\n",
      "[16 rows x 4 columns]\n",
      "\n",
      "None\n"
     ]
    },
    {
     "data": {
      "image/png": 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lbwJdQufGeuUbKBkynYGLhtuAi2RLKaP/cfgNYNQGyvqVn5PjLJvcXPeLPS+v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\nYxiGYdQY/x92JgwiOhkHjwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114c2c2d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_poly(set_3, 15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+-------------+-------+-------------------+-------------------+\n",
      "|     name    | index |       value       |       stderr      |\n",
      "+-------------+-------+-------------------+-------------------+\n",
      "| (intercept) |  None |   -170240.032842  |   1543796.62885   |\n",
      "|   power_1   |  None |   1247.59034541   |   9978.42791287   |\n",
      "|   power_2   |  None |   -1.22460912177  |   26.7138477947   |\n",
      "|   power_3   |  None | 0.000555254626344 |  0.0392072641565  |\n",
      "|   power_4   |  None | -6.3826237386e-08 | 3.51264407588e-05 |\n",
      "+-------------+-------+-------------------+-------------------+\n",
      "[16 rows x 4 columns]\n",
      "\n",
      "None\n"
     ]
    },
    {
     "data": {
      "image/png": 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Wfn5wve2Li6We3bqJME2YwJyRId/+khrCiTl2bm70+vKUVa/yLJryXlR2/bSL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\nIooKjaIoihJRVGgURVGUiPL/AR92236uG6LrAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114e866d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_poly(set_4, 15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The four curves should differ from one another a lot, as should the coefficients you learned.\n",
    "\n",
    "***QUIZ QUESTION:  For the models learned in each of these training sets, what are the smallest and largest values you learned for the coefficient of feature `power_1`?***  (For the purpose of answering this question, negative numbers are considered \"smaller\" than positive numbers. So -5 is smaller than -3, and -3 is smaller than 5 and so forth.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ridge regression comes to rescue"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generally, whenever we see weights change so much in response to change in data, we believe the variance of our estimate to be large. Ridge regression aims to address this issue by penalizing \"large\" weights. (Weights of `model15` looked quite small, but they are not that small because 'sqft_living' input is in the order of thousands.)\n",
    "\n",
    "With the argument `l2_penalty=1e5`, fit a 15th-order polynomial model on `set_1`, `set_2`, `set_3`, and `set_4`. Other than the change in the `l2_penalty` parameter, the code should be the same as the experiment above. Also, make sure GraphLab Create doesn't create its own validation set by using the option `validation_set = None` in this call."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "l2_small_penalty = 1e5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+-------------+-------+-------------------+-------------------+\n",
      "|     name    | index |       value       |       stderr      |\n",
      "+-------------+-------+-------------------+-------------------+\n",
      "| (intercept) |  None |   530317.024516   |   1890090.19151   |\n",
      "|   power_1   |  None |   2.58738875673   |   9034.21455077   |\n",
      "|   power_2   |  None |  0.00127414400592 |    18.000330944   |\n",
      "|   power_3   |  None | 1.74934226932e-07 |   0.019765845458  |\n",
      "|   power_4   |  None | 1.06022119097e-11 | 1.33158533722e-05 |\n",
      "+-------------+-------+-------------------+-------------------+\n",
      "[16 rows x 4 columns]\n",
      "\n",
      "None\n"
     ]
    },
    {
     "data": {
      "image/png": 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GN2HvYnHPAMcF2wuBMcH2hcAtwfYEoFQjYXsLyAcKwu1g3/3AOcH2rcAFddjf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\n0EM2SXXQILuHkNCrCEvdgPV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2mj307r3XHmh//7s9MA85xDycRNq1a5oMspZIbq4t2fCd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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114fefdd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_poly(set_1, 15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+-------------+-------+-------------------+------------------+\n",
      "|     name    | index |       value       |      stderr      |\n",
      "+-------------+-------+-------------------+------------------+\n",
      "| (intercept) |  None |   519216.897383   |  2167962.96521   |\n",
      "|   power_1   |  None |   2.04470474182   |  12809.1515268   |\n",
      "|   power_2   |  None |  0.0011314362684  |  32.2464286313   |\n",
      "|   power_3   |  None | 2.93074277549e-07 | 0.0456480218892  |\n",
      "|   power_4   |  None | 4.43540598453e-11 | 4.0481752482e-05 |\n",
      "+-------------+-------+-------------------+------------------+\n",
      "[16 rows x 4 columns]\n",
      "\n",
      "None\n"
     ]
    },
    {
     "data": {
      "image/png": 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lS4DzzgM+/hgYM0bqYydLVFfPhkh9sggjiZ300bOnm+Di72/P5jfFv0Hr5q0x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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x115153d90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_poly(set_2, 15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+-------------+-------+-------------------+--------+\n",
      "|     name    | index |       value       | stderr |\n",
      "+-------------+-------+-------------------+--------+\n",
      "| (intercept) |  None |   522911.518048   |  nan   |\n",
      "|   power_1   |  None |   2.26890421877   |  nan   |\n",
      "|   power_2   |  None |  0.00125905041842 |  nan   |\n",
      "|   power_3   |  None | 2.77552918155e-07 |  nan   |\n",
      "|   power_4   |  None |  3.2093309779e-11 |  nan   |\n",
      "+-------------+-------+-------------------+--------+\n",
      "[16 rows x 4 columns]\n",
      "\n",
      "None\n"
     ]
    },
    {
     "data": {
      "image/png": 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S0sTJeckSE7H4dadNs8i4ZCuqJismbB/vS7iUl4pVVtfvqaWGMtcHew/s1cv+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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1152afc50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_poly(set_3, 15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+-------------+-------+-------------------+-------------------+\n",
      "|     name    | index |       value       |       stderr      |\n",
      "+-------------+-------+-------------------+-------------------+\n",
      "| (intercept) |  None |   513667.087087   |   2041482.90233   |\n",
      "|   power_1   |  None |   1.91040938244   |   13195.2548642   |\n",
      "|   power_2   |  None |  0.00110058029175 |   35.3258081465   |\n",
      "|   power_3   |  None | 3.12753987879e-07 |   0.051846828738  |\n",
      "|   power_4   |  None | 5.50067886825e-11 | 4.64504371162e-05 |\n",
      "+-------------+-------+-------------------+-------------------+\n",
      "[16 rows x 4 columns]\n",
      "\n",
      "None\n"
     ]
    },
    {
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IM9vOe6sAfM/ZXgbghhB99+lnUBoDZWXMAwcyFxfLc1lZ5OeoTixKS+W/sLS0bv1UQVKi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\nMJ85dmby5MA+hbr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px5r8SevWIiyDB8uzqRbr21fOefbZrpAZocrIcAUuOVlCVF27Sp+N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\npMid9LFjbujLhMIM5nVqKnDkSKDhVGp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      "text/plain": [
       "<matplotlib.figure.Figure at 0x115433150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_poly(set_4, 15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These curves should vary a lot less, now that you applied a high degree of regularization.\n",
    "\n",
    "***QUIZ QUESTION:  For the models learned with the high level of regularization in each of these training sets, what are the smallest and largest values you learned for the coefficient of feature `power_1`?*** (For the purpose of answering this question, negative numbers are considered \"smaller\" than positive numbers. So -5 is smaller than -3, and -3 is smaller than 5 and so forth.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Selecting an L2 penalty via cross-validation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just like the polynomial degree, the L2 penalty is a \"magic\" parameter we need to select. We could use the validation set approach as we did in the last module, but that approach has a major disadvantage: it leaves fewer observations available for training. **Cross-validation** seeks to overcome this issue by using all of the training set in a smart way.\n",
    "\n",
    "We will implement a kind of cross-validation called **k-fold cross-validation**. The method gets its name because it involves dividing the training set into k segments of roughtly equal size. Similar to the validation set method, we measure the validation error with one of the segments designated as the validation set. The major difference is that we repeat the process k times as follows:\n",
    "\n",
    "Set aside segment 0 as the validation set, and fit a model on rest of data, and evalutate it on this validation set<br>\n",
    "Set aside segment 1 as the validation set, and fit a model on rest of data, and evalutate it on this validation set<br>\n",
    "...<br>\n",
    "Set aside segment k-1 as the validation set, and fit a model on rest of data, and evalutate it on this validation set\n",
    "\n",
    "After this process, we compute the average of the k validation errors, and use it as an estimate of the generalization error. Notice that  all observations are used for both training and validation, as we iterate over segments of data. \n",
    "\n",
    "To estimate the generalization error well, it is crucial to shuffle the training data before dividing them into segments. GraphLab Create has a utility function for shuffling a given SFrame. We reserve 10% of the data as the test set and shuffle the remainder. (Make sure to use `seed=1` to get consistent answer.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "(train_valid, test) = sales.random_split(.9, seed=1)\n",
    "train_valid_shuffled = graphlab.toolkits.cross_validation.shuffle(train_valid, random_seed=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once the data is shuffled, we divide it into equal segments. Each segment should receive `n/k` elements, where `n` is the number of observations in the training set and `k` is the number of segments. Since the segment 0 starts at index 0 and contains `n/k` elements, it ends at index `(n/k)-1`. The segment 1 starts where the segment 0 left off, at index `(n/k)`. With `n/k` elements, the segment 1 ends at index `(n*2/k)-1`. Continuing in this fashion, we deduce that the segment `i` starts at index `(n*i/k)` and ends at `(n*(i+1)/k)-1`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With this pattern in mind, we write a short loop that prints the starting and ending indices of each segment, just to make sure you are getting the splits right."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 (0, 1938) 1939\n",
      "1 (1939, 3878) 1940\n",
      "2 (3879, 5817) 1939\n",
      "3 (5818, 7757) 1940\n",
      "4 (7758, 9697) 1940\n",
      "5 (9698, 11636) 1939\n",
      "6 (11637, 13576) 1940\n",
      "7 (13577, 15515) 1939\n",
      "8 (15516, 17455) 1940\n",
      "9 (17456, 19395) 1940\n"
     ]
    }
   ],
   "source": [
    "n = len(train_valid_shuffled)\n",
    "k = 10 # 10-fold cross-validation\n",
    "\n",
    "for i in xrange(k):\n",
    "    start = (n*i)/k\n",
    "    end = (n*(i+1))/k - 1\n",
    "    print i, (start, end), end-start+1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Let us familiarize ourselves with array slicing with SFrame. To extract a continuous slice from an SFrame, use colon in square brackets. For instance, the following cell extracts rows 0 to 9 of `train_valid_shuffled`. Notice that the first index (0) is included in the slice but the last index (10) is omitted."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
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       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0475000510</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2014-11-18 00:00:00+00:00</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">594000.0</td>\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\">1.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1320.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5000</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0844001052</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2015-01-28 00:00:00+00:00</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">365000.0</td>\n",
       "        <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\">2.5</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1904.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">8200</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2658000373</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2015-01-22 00:00:00+00:00</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">305000.0</td>\n",
       "        <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\">2.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1610.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">6250</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3750603471</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2015-03-27 00:00:00+00:00</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">239950.0</td>\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\">2.5</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1560.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4800</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2114700540</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2014-10-21 00:00:00+00:00</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">366000.0</td>\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\">2.5</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1320.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4320</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2596400050</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2014-07-30 00:00:00+00:00</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">375000.0</td>\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\">1.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1960.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">7955</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4140900050</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2015-01-26 00:00:00+00:00</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">440000.0</td>\n",
       "        <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\">1.75</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2180.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">10200</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "    </tr>\n",
       "</table>\n",
       "<table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">view</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">condition</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">grade</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">sqft_above</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">sqft_basement</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">yr_built</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">yr_renovated</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">zipcode</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">lat</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">8</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1660</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1140</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1963</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">98115</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">47.68093246</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">9</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2490</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2003</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">98074</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">47.62984888</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">7</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1170</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1170</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1917</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">98144</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">47.57587004</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">7</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1090</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">230</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1920</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">98107</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">47.66737217</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">7</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1904</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1999</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">98010</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">47.31068733</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">7</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1610</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1952</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">98118</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">47.52930128</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">7</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1560</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1974</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">98001</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">47.26533057</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">6</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">660</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">660</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1918</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">98106</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">47.53271982</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">7</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1260</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">700</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1963</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">98177</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">47.76407345</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">8</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2000</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">180</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1966</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">98028</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">47.76382378</td>\n",
       "    </tr>\n",
       "</table>\n",
       "<table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">long</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">sqft_living15</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">sqft_lot15</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-122.28583258</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2580.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5900.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-122.02177564</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2710.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">6629.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-122.28796</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1360.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4725.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-122.36472902</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1700.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-122.0012452</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1560.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">12426.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-122.27097145</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1310.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">6000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-122.28506088</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1510.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">12240.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-122.34716948</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1190.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4200.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-122.36361517</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1850.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">8219.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-122.27022456</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2590.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">10445.0</td>\n",
       "    </tr>\n",
       "</table>\n",
       "[10 rows x 21 columns]<br/>\n",
       "</div>"
      ],
      "text/plain": [
       "Columns:\n",
       "\tid\tstr\n",
       "\tdate\tdatetime\n",
       "\tprice\tfloat\n",
       "\tbedrooms\tfloat\n",
       "\tbathrooms\tfloat\n",
       "\tsqft_living\tfloat\n",
       "\tsqft_lot\tint\n",
       "\tfloors\tstr\n",
       "\twaterfront\tint\n",
       "\tview\tint\n",
       "\tcondition\tint\n",
       "\tgrade\tint\n",
       "\tsqft_above\tint\n",
       "\tsqft_basement\tint\n",
       "\tyr_built\tint\n",
       "\tyr_renovated\tint\n",
       "\tzipcode\tstr\n",
       "\tlat\tfloat\n",
       "\tlong\tfloat\n",
       "\tsqft_living15\tfloat\n",
       "\tsqft_lot15\tfloat\n",
       "\n",
       "Rows: 10\n",
       "\n",
       "Data:\n",
       "+------------+---------------------------+----------+----------+-----------+\n",
       "|     id     |            date           |  price   | bedrooms | bathrooms |\n",
       "+------------+---------------------------+----------+----------+-----------+\n",
       "| 2780400035 | 2014-05-05 00:00:00+00:00 | 665000.0 |   4.0    |    2.5    |\n",
       "| 1703050500 | 2015-03-21 00:00:00+00:00 | 645000.0 |   3.0    |    2.5    |\n",
       "| 5700002325 | 2014-06-05 00:00:00+00:00 | 640000.0 |   3.0    |    1.75   |\n",
       "| 0475000510 | 2014-11-18 00:00:00+00:00 | 594000.0 |   3.0    |    1.0    |\n",
       "| 0844001052 | 2015-01-28 00:00:00+00:00 | 365000.0 |   4.0    |    2.5    |\n",
       "| 2658000373 | 2015-01-22 00:00:00+00:00 | 305000.0 |   4.0    |    2.0    |\n",
       "| 3750603471 | 2015-03-27 00:00:00+00:00 | 239950.0 |   3.0    |    2.5    |\n",
       "| 2114700540 | 2014-10-21 00:00:00+00:00 | 366000.0 |   3.0    |    2.5    |\n",
       "| 2596400050 | 2014-07-30 00:00:00+00:00 | 375000.0 |   3.0    |    1.0    |\n",
       "| 4140900050 | 2015-01-26 00:00:00+00:00 | 440000.0 |   4.0    |    1.75   |\n",
       "+------------+---------------------------+----------+----------+-----------+\n",
       "+-------------+----------+--------+------------+------+-----------+-------+------------+\n",
       "| sqft_living | sqft_lot | floors | waterfront | view | condition | grade | sqft_above |\n",
       "+-------------+----------+--------+------------+------+-----------+-------+------------+\n",
       "|    2800.0   |   5900   |   1    |     0      |  0   |     3     |   8   |    1660    |\n",
       "|    2490.0   |   5978   |   2    |     0      |  0   |     3     |   9   |    2490    |\n",
       "|    2340.0   |   4206   |   1    |     0      |  0   |     5     |   7   |    1170    |\n",
       "|    1320.0   |   5000   |   1    |     0      |  0   |     4     |   7   |    1090    |\n",
       "|    1904.0   |   8200   |   2    |     0      |  0   |     5     |   7   |    1904    |\n",
       "|    1610.0   |   6250   |   1    |     0      |  0   |     4     |   7   |    1610    |\n",
       "|    1560.0   |   4800   |   2    |     0      |  0   |     4     |   7   |    1560    |\n",
       "|    1320.0   |   4320   |   1    |     0      |  0   |     3     |   6   |    660     |\n",
       "|    1960.0   |   7955   |   1    |     0      |  0   |     4     |   7   |    1260    |\n",
       "|    2180.0   |  10200   |   1    |     0      |  2   |     3     |   8   |    2000    |\n",
       "+-------------+----------+--------+------------+------+-----------+-------+------------+\n",
       "+---------------+----------+--------------+---------+-------------+\n",
       "| sqft_basement | yr_built | yr_renovated | zipcode |     lat     |\n",
       "+---------------+----------+--------------+---------+-------------+\n",
       "|      1140     |   1963   |      0       |  98115  | 47.68093246 |\n",
       "|       0       |   2003   |      0       |  98074  | 47.62984888 |\n",
       "|      1170     |   1917   |      0       |  98144  | 47.57587004 |\n",
       "|      230      |   1920   |      0       |  98107  | 47.66737217 |\n",
       "|       0       |   1999   |      0       |  98010  | 47.31068733 |\n",
       "|       0       |   1952   |      0       |  98118  | 47.52930128 |\n",
       "|       0       |   1974   |      0       |  98001  | 47.26533057 |\n",
       "|      660      |   1918   |      0       |  98106  | 47.53271982 |\n",
       "|      700      |   1963   |      0       |  98177  | 47.76407345 |\n",
       "|      180      |   1966   |      0       |  98028  | 47.76382378 |\n",
       "+---------------+----------+--------------+---------+-------------+\n",
       "+---------------+---------------+-----+\n",
       "|      long     | sqft_living15 | ... |\n",
       "+---------------+---------------+-----+\n",
       "| -122.28583258 |     2580.0    | ... |\n",
       "| -122.02177564 |     2710.0    | ... |\n",
       "|   -122.28796  |     1360.0    | ... |\n",
       "| -122.36472902 |     1700.0    | ... |\n",
       "|  -122.0012452 |     1560.0    | ... |\n",
       "| -122.27097145 |     1310.0    | ... |\n",
       "| -122.28506088 |     1510.0    | ... |\n",
       "| -122.34716948 |     1190.0    | ... |\n",
       "| -122.36361517 |     1850.0    | ... |\n",
       "| -122.27022456 |     2590.0    | ... |\n",
       "+---------------+---------------+-----+\n",
       "[10 rows x 21 columns]"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_valid_shuffled[0:10] # rows 0 to 9"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let us extract individual segments with array slicing. Consider the scenario where we group the houses in the `train_valid_shuffled` dataframe into k=10 segments of roughly equal size, with starting and ending indices computed as above.\n",
    "Extract the fourth segment (segment 3) and assign it to a variable called `validation4`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "n = len(train_valid_shuffled)\n",
    "k = 10 # 10-fold cross-validation\n",
    "\n",
    "def k_cross_val(data, k):\n",
    "    n = len(data)\n",
    "    indices = {}\n",
    "    \n",
    "    for i in xrange(k):\n",
    "        start = (n*i)/k\n",
    "        end = (n*(i+1))/k - 1\n",
    "        print i, (start, end+1)\n",
    "        indices[i+1] = [start, end+1]\n",
    "    return indices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 (0, 1939)\n",
      "1 (1939, 3879)\n",
      "2 (3879, 5818)\n",
      "3 (5818, 7758)\n",
      "4 (7758, 9698)\n",
      "5 (9698, 11637)\n",
      "6 (11637, 13577)\n",
      "7 (13577, 15516)\n",
      "8 (15516, 17456)\n",
      "9 (17456, 19396)\n"
     ]
    }
   ],
   "source": [
    "my_indices = k_cross_val(train_valid_shuffled, 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5818 7758\n"
     ]
    }
   ],
   "source": [
    "validation4 = train_valid_shuffled[my_indices[4][0]:my_indices[4][1]]\n",
    "print my_indices[4][0], my_indices[4][1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To verify that we have the right elements extracted, run the following cell, which computes the average price of the fourth segment. When rounded to nearest whole number, the average should be $536,234."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "536234\n"
     ]
    }
   ],
   "source": [
    "print int(round(validation4['price'].mean(), 0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After designating one of the k segments as the validation set, we train a model using the rest of the data. To choose the remainder, we slice (0:start) and (end+1:n) of the data and paste them together. SFrame has `append()` method that pastes together two disjoint sets of rows originating from a common dataset. For instance, the following cell pastes together the first and last two rows of the `train_valid_shuffled` dataframe."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+------------+---------------------------+-----------+----------+-----------+\n",
      "|     id     |            date           |   price   | bedrooms | bathrooms |\n",
      "+------------+---------------------------+-----------+----------+-----------+\n",
      "| 2780400035 | 2014-05-05 00:00:00+00:00 |  665000.0 |   4.0    |    2.5    |\n",
      "| 1703050500 | 2015-03-21 00:00:00+00:00 |  645000.0 |   3.0    |    2.5    |\n",
      "| 4139480190 | 2014-09-16 00:00:00+00:00 | 1153000.0 |   3.0    |    3.25   |\n",
      "| 7237300290 | 2015-03-26 00:00:00+00:00 |  338000.0 |   5.0    |    2.5    |\n",
      "+------------+---------------------------+-----------+----------+-----------+\n",
      "+-------------+----------+--------+------------+------+-----------+-------+------------+\n",
      "| sqft_living | sqft_lot | floors | waterfront | view | condition | grade | sqft_above |\n",
      "+-------------+----------+--------+------------+------+-----------+-------+------------+\n",
      "|    2800.0   |   5900   |   1    |     0      |  0   |     3     |   8   |    1660    |\n",
      "|    2490.0   |   5978   |   2    |     0      |  0   |     3     |   9   |    2490    |\n",
      "|    3780.0   |  10623   |   1    |     0      |  1   |     3     |   11  |    2650    |\n",
      "|    2400.0   |   4496   |   2    |     0      |  0   |     3     |   7   |    2400    |\n",
      "+-------------+----------+--------+------------+------+-----------+-------+------------+\n",
      "+---------------+----------+--------------+---------+-------------+\n",
      "| sqft_basement | yr_built | yr_renovated | zipcode |     lat     |\n",
      "+---------------+----------+--------------+---------+-------------+\n",
      "|      1140     |   1963   |      0       |  98115  | 47.68093246 |\n",
      "|       0       |   2003   |      0       |  98074  | 47.62984888 |\n",
      "|      1130     |   1999   |      0       |  98006  | 47.55061236 |\n",
      "|       0       |   2004   |      0       |  98042  | 47.36923712 |\n",
      "+---------------+----------+--------------+---------+-------------+\n",
      "+---------------+---------------+-----+\n",
      "|      long     | sqft_living15 | ... |\n",
      "+---------------+---------------+-----+\n",
      "| -122.28583258 |     2580.0    | ... |\n",
      "| -122.02177564 |     2710.0    | ... |\n",
      "| -122.10144844 |     3850.0    | ... |\n",
      "| -122.12606473 |     1880.0    | ... |\n",
      "+---------------+---------------+-----+\n",
      "[4 rows x 21 columns]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "n = len(train_valid_shuffled)\n",
    "first_two = train_valid_shuffled[0:2]\n",
    "last_two = train_valid_shuffled[n-2:n]\n",
    "print first_two.append(last_two)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Extract the remainder of the data after *excluding* fourth segment (segment 3) and assign the subset to `train4`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "17456\n"
     ]
    }
   ],
   "source": [
    "first_two = train_valid_shuffled[0:2]\n",
    "last_two = train_valid_shuffled[n-2:n]\n",
    "\n",
    "train4 = train_valid_shuffled[my_indices[1][0]:my_indices[3][1]].append(\\\n",
    "    train_valid_shuffled[my_indices[5][0]:my_indices[10][1]])\n",
    "print len(train4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To verify that we have the right elements extracted, run the following cell, which computes the average price of the data with fourth segment excluded. When rounded to nearest whole number, the average should be $539,450."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "539450\n"
     ]
    }
   ],
   "source": [
    "print int(round(train4['price'].mean(), 0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we are ready to implement k-fold cross-validation. Write a function that computes k validation errors by designating each of the k segments as the validation set. It accepts as parameters (i) `k`, (ii) `l2_penalty`, (iii) dataframe, (iv) name of output column (e.g. `price`) and (v) list of feature names. The function returns the average validation error using k segments as validation sets.\n",
    "\n",
    "* For each i in [0, 1, ..., k-1]:\n",
    "  * Compute starting and ending indices of segment i and call 'start' and 'end'\n",
    "  * Form validation set by taking a slice (start:end+1) from the data.\n",
    "  * Form training set by appending slice (end+1:n) to the end of slice (0:start).\n",
    "  * Train a linear model using training set just formed, with a given l2_penalty\n",
    "  * Compute validation error using validation set just formed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def k_cross_val(data, k):\n",
    "    n = len(data)\n",
    "    indices = {}\n",
    "    \n",
    "    for i in xrange(k):\n",
    "        start = (n*i)/k\n",
    "        end = (n*(i+1))/k - 1\n",
    "        #print i, (start, end+1)\n",
    "        indices[i+1] = [start, end+1]\n",
    "    return indices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{1: [0, 1939],\n",
       " 2: [1939, 3879],\n",
       " 3: [3879, 5818],\n",
       " 4: [5818, 7758],\n",
       " 5: [7758, 9698],\n",
       " 6: [9698, 11637],\n",
       " 7: [11637, 13577],\n",
       " 8: [13577, 15516],\n",
       " 9: [15516, 17456],\n",
       " 10: [17456, 19396]}"
      ]
     },
     "execution_count": 170,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "my_indices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def k_fold_cross_validation(k, l2_penalty, data, output_name, features_list):\n",
    "    indices = k_cross_val(data, k)\n",
    "    error = []\n",
    "    for i in xrange(1,k+1):\n",
    "        valid_data = data[indices[i][0]:indices[i][1]]\n",
    "        train_data = data[0:indices[i][0]].append(data[indices[i][1]:])\n",
    "        model = graphlab.linear_regression.create(train_data, target = output_name, features = features_list, \\\n",
    "                                                  validation_set = None, verbose = False, l2_penalty=l2_penalty)\n",
    "        e = sum((model.predict(valid_data[features_list]) - valid_data[output_name])**2)\n",
    "        #print i, 'error:', e\n",
    "        error.append(e)\n",
    "    error = graphlab.SArray(error).mean()\n",
    "    print 'L2=', l2_penalty, ':', error\n",
    "    return error"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once we have a function to compute the average validation error for a model, we can write a loop to find the model that minimizes the average validation error. Write a loop that does the following:\n",
    "* We will again be aiming to fit a 15th-order polynomial model using the `sqft_living` input\n",
    "* For `l2_penalty` in [10^1, 10^1.5, 10^2, 10^2.5, ..., 10^7] (to get this in Python, you can use this Numpy function: `np.logspace(1, 7, num=13)`.)\n",
    "    * Run 10-fold cross-validation with `l2_penalty`\n",
    "* Report which L2 penalty produced the lowest average validation error.\n",
    "\n",
    "Note: since the degree of the polynomial is now fixed to 15, to make things faster, you should generate polynomial features in advance and re-use them throughout the loop. Make sure to use `train_valid_shuffled` when generating polynomial features!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "poly_data = polynomial_sframe(train_valid_shuffled['sqft_living'], 15)\n",
    "my_features = poly_data.column_names()\n",
    "poly_data['price'] = train_valid_shuffled['price']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "l2_search = np.logspace(1, 7, num=13)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "L2= 10.0 : 4.91826427769e+14\n",
      "L2= 31.6227766017 : 2.87504229919e+14\n",
      "L2= 100.0 : 1.60908965822e+14\n",
      "L2= 316.227766017 : 1.22090967326e+14\n",
      "L2= 1000.0 : 1.21192264451e+14\n",
      "L2= 3162.27766017 : 1.2395000929e+14\n",
      "L2= 10000.0 : 1.36837175248e+14\n",
      "L2= 31622.7766017 : 1.71728094842e+14\n",
      "L2= 100000.0 : 2.2936143126e+14\n",
      "L2= 316227.766017 : 2.52940568729e+14\n",
      "L2= 1000000.0 : 2.58682548441e+14\n",
      "L2= 3162277.66017 : 2.62819399742e+14\n",
      "L2= 10000000.0 : 2.64889015378e+14\n"
     ]
    }
   ],
   "source": [
    "y = []\n",
    "for i in l2_search:\n",
    "    y.append(k_fold_cross_validation(10, i, poly_data, 'price', my_features))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***QUIZ QUESTIONS:  What is the best value for the L2 penalty according to 10-fold validation?***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You may find it useful to plot the k-fold cross-validation errors you have obtained to better understand the behavior of the method.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x115321f50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the l2_penalty values in the x axis and the cross-validation error in the y axis.\n",
    "# Using plt.xscale('log') will make your plot more intuitive.\n",
    "\n",
    "plt.plot(l2_search, y)\n",
    "plt.xscale('log')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once you found the best value for the L2 penalty using cross-validation, it is important to retrain a final model on all of the training data using this value of `l2_penalty`.  This way, your final model will be trained on the entire dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1000.0\n"
     ]
    }
   ],
   "source": [
    "lowest_l2 = l2_search[np.argmin(y)]\n",
    "print lowest_l2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "model = graphlab.linear_regression.create(poly_data, target = 'price', features = my_features, \n",
    "                                          validation_set = None, verbose = False, l2_penalty=lowest_l2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***QUIZ QUESTION: Using the best L2 penalty found above, train a model using all training data. What is the RSS on the TEST data of the model you learn with this L2 penalty? ***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "poly_test = polynomial_sframe(test['sqft_living'], 15)\n",
    "poly_test['price'] = test['price']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.28780855058e+14\n"
     ]
    }
   ],
   "source": [
    "print sum((model.predict(poly_test[my_features]) - poly_test['price'])**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
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    "name": "ipython",
    "version": 2
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   "file_extension": ".py",
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