Week 3 - Polynomial Regression Assignment.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regression Week 3: Assessing Fit (polynomial regression)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook you will compare different regression models in order to assess which model fits best. We will be using polynomial regression as a means to examine this topic. In particular you will:\n",
    "* Write a function to take an SArray and a degree and return an SFrame where each column is the SArray to a polynomial value up to the total degree e.g. degree = 3 then column 1 is the SArray column 2 is the SArray squared and column 3 is the SArray cubed\n",
    "* Use matplotlib to visualize polynomial regressions\n",
    "* Use matplotlib to visualize the same polynomial degree on different subsets of the data\n",
    "* Use a validation set to select a polynomial degree\n",
    "* Assess the final fit using test data\n",
    "\n",
    "We will continue to use the House data from previous notebooks."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fire up graphlab create"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import graphlab"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we're going to write a polynomial function that takes an SArray and a maximal degree and returns an SFrame with columns containing the SArray to all the powers up to the maximal degree.\n",
    "\n",
    "The easiest way to apply a power to an SArray is to use the .apply() and lambda x: functions. \n",
    "For example to take the example array and compute the third power we can do as follows: (note running this cell the first time may take longer than expected since it loads graphlab)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "This non-commercial license of GraphLab Create for academic use is assigned to amitha353@gmail.com and will expire on May 07, 2019.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[INFO] graphlab.cython.cy_server: GraphLab Create v2.1 started. Logging: C:\\Users\\Amitha\\AppData\\Local\\Temp\\graphlab_server_1531577262.log.0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.0, 2.0, 3.0]\n",
      "[1.0, 8.0, 27.0]\n"
     ]
    }
   ],
   "source": [
    "tmp = graphlab.SArray([1., 2., 3.])\n",
    "tmp_cubed = tmp.apply(lambda x: x**3)\n",
    "print tmp\n",
    "print tmp_cubed"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can create an empty SFrame using graphlab.SFrame() and then add any columns to it with ex_sframe['column_name'] = value. For example we create an empty SFrame and make the column 'power_1' to be the first power of tmp (i.e. tmp itself)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+---------+\n",
      "| power_1 |\n",
      "+---------+\n",
      "|   1.0   |\n",
      "|   2.0   |\n",
      "|   3.0   |\n",
      "+---------+\n",
      "[3 rows x 1 columns]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "ex_sframe = graphlab.SFrame()\n",
    "ex_sframe['power_1'] = tmp\n",
    "print ex_sframe"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Polynomial_sframe function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the hints above complete the following function to create an SFrame consisting of the powers of an SArray up to a specific degree:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def polynomial_sframe(feature, degree):\n",
    "    # assume that degree >= 1\n",
    "    # initialize the SFrame:\n",
    "    poly_sframe = graphlab.SFrame()\n",
    "    # and set poly_sframe['power_1'] equal to the passed feature\n",
    "    poly_sframe['power_1'] = feature\n",
    "    # first check if degree > 1\n",
    "    if degree > 1:\n",
    "        # then loop over the remaining degrees:\n",
    "        # range usually starts at 0 and stops at the endpoint-1. We want it to start at 2 and stop at degree\n",
    "        for power in range(2, degree+1): \n",
    "            # first we'll give the column a name:\n",
    "            name = 'power_' + str(power)\n",
    "            # then assign poly_sframe[name] to the appropriate power of feature\n",
    "            poly_sframe[name] = feature ** power\n",
    "    return poly_sframe"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To test your function consider the smaller tmp variable and what you would expect the outcome of the following call:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+---------+---------+---------+\n",
      "| power_1 | power_2 | power_3 |\n",
      "+---------+---------+---------+\n",
      "|   1.0   |   1.0   |   1.0   |\n",
      "|   2.0   |   4.0   |   8.0   |\n",
      "|   3.0   |   9.0   |   27.0  |\n",
      "+---------+---------+---------+\n",
      "[3 rows x 3 columns]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print polynomial_sframe(tmp, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Visualizing polynomial regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's use matplotlib to visualize what a polynomial regression looks like on some real data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sales = graphlab.SFrame('kc_house_data.gl/')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As in Week 3, we will use the sqft_living variable. For plotting purposes (connecting the dots), you'll need to sort by the values of sqft_living. For houses with identical square footage, we break the tie by their prices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sales = sales.sort(['sqft_living', 'price'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's start with a degree 1 polynomial using 'sqft_living' (i.e. a line) to predict 'price' and plot what it looks like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "poly1_data = polynomial_sframe(sales['sqft_living'], 1)\n",
    "poly1_data['price'] = sales['price'] # add price to the data since it's the target"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "NOTE: for all the models in this notebook use validation_set = None to ensure that all results are consistent across users."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre>Linear regression:</pre>"
      ],
      "text/plain": [
       "Linear regression:"
      ]
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     "data": {
      "text/html": [
       "<pre>--------------------------------------------------------</pre>"
      ],
      "text/plain": [
       "--------------------------------------------------------"
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     "data": {
      "text/html": [
       "<pre>Number of examples          : 21613</pre>"
      ],
      "text/plain": [
       "Number of examples          : 21613"
      ]
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    {
     "data": {
      "text/html": [
       "<pre>Number of features          : 1</pre>"
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      "text/plain": [
       "Number of features          : 1"
      ]
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     "data": {
      "text/html": [
       "<pre>Number of unpacked features : 1</pre>"
      ],
      "text/plain": [
       "Number of unpacked features : 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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    {
     "data": {
      "text/html": [
       "<pre>Number of coefficients    : 2</pre>"
      ],
      "text/plain": [
       "Number of coefficients    : 2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Starting Newton Method</pre>"
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       "Starting Newton Method"
      ]
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     "data": {
      "text/html": [
       "<pre>--------------------------------------------------------</pre>"
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      "text/plain": [
       "--------------------------------------------------------"
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     "data": {
      "text/html": [
       "<pre>+-----------+----------+--------------+--------------------+---------------+</pre>"
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      "text/plain": [
       "+-----------+----------+--------------+--------------------+---------------+"
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     "output_type": "display_data"
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     "data": {
      "text/html": [
       "<pre>| Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |</pre>"
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      "text/plain": [
       "| Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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    {
     "data": {
      "text/html": [
       "<pre>+-----------+----------+--------------+--------------------+---------------+</pre>"
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      "text/plain": [
       "+-----------+----------+--------------+--------------------+---------------+"
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     "metadata": {},
     "output_type": "display_data"
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    {
     "data": {
      "text/html": [
       "<pre>| 1         | 2        | 1.028082     | 4362074.696077     | 261440.790724 |</pre>"
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      "text/plain": [
       "| 1         | 2        | 1.028082     | 4362074.696077     | 261440.790724 |"
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     "data": {
      "text/html": [
       "<pre>+-----------+----------+--------------+--------------------+---------------+</pre>"
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      "text/plain": [
       "+-----------+----------+--------------+--------------------+---------------+"
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     "data": {
      "text/html": [
       "<pre>SUCCESS: Optimal solution found.</pre>"
      ],
      "text/plain": [
       "SUCCESS: Optimal solution found."
      ]
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     "data": {
      "text/html": [
       "<pre></pre>"
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   ],
   "source": [
    "model1 = graphlab.linear_regression.create(poly1_data, target = 'price', features = ['power_1'], validation_set = None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\"><table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">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\">-43579.0852515</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4402.68969743</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\">280.622770886</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.93639855513</td>\n",
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       "Rows: 2\n",
       "\n",
       "Data:\n",
       "+-------------+-------+----------------+---------------+\n",
       "|     name    | index |     value      |     stderr    |\n",
       "+-------------+-------+----------------+---------------+\n",
       "| (intercept) |  None | -43579.0852515 | 4402.68969743 |\n",
       "|   power_1   |  None | 280.622770886  | 1.93639855513 |\n",
       "+-------------+-------+----------------+---------------+\n",
       "[2 rows x 4 columns]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#let's take a look at the weights before we plot\n",
    "model1.get(\"coefficients\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x333d45f8>,\n",
       " <matplotlib.lines.Line2D at 0x333d46a0>]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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0DpkehouGW+UFqEsz9ifj7/EFQTqbtItDR75yPnehzGf8\nu/Kzg12I87E3uZDnNNmUl+dCmnNzVQcOjIRPxxL56NeoUU5YwgIW3XcsR30q9sBJlbAZRmtJlujY\n4tB2MncunH22e3xlNbmfw/BFbups9FzYPsJNnVVOhp3D0m0dAHffDVdd5RbS5uXBc8+546uugpUr\nXdLOILlneC8iiGyNAC6QYM8eWL3afQ5vaxAmFXvgLFniAhaCLNjxMhjYYlEj1VhGgjaSTNFZtco9\njKL3fska8j6DQ+dD8WwY9RRsHQtVk6HqXNg1JN3WNeGgg+DDDyOf8/Jc4EBBQSRbQFWV25RNFaZO\nherqxn+fQYNckEdBgcsgDS5DAcR+qCd7D5xEhM22ujbSgYlOG0mW6NTWul/M4Z08s4Iun8CIZ9yI\nZuQzsOlIN6JZeQ7UZlzkeSNibfD2xz/Cv/1b5HM4VD0vzwVw5OZGAjlijSaC1DVr1qTnod6SsCU6\nGjKMjsT208kgNm6E3/0uiwQnvxZGPe0izg5dADUTnNA8ewd83Lfl9hnC4MHws5/BlVe6B3C3bi4P\nWpgVK5qGqou4Ec6WLU3XvNTWOsEJknRWVrr2qXyotxSlVlLibA5GQ7Zmx8hmbKTTSlatgsMOy4IE\nnV13wegn3Yim8HlY/zU/ojkLPu2TbuvaRGGh89OMHOlCoidPjmyoFhAe6QQ7kHbrBm++GXuhZ3TS\nzxEj3PqYTJu+sq2ujVRj02ttpCNFJ+On1PbbDqP97ppD/g/WlDqhWfUN+Kxnuq1rM7m5LjBg3brY\nU0zRTvbaWpdl+rLLnJgEW1HHc9AH/pLCwsY7gxrGvoxNr2UAL72UgYKz/wcw5gknNIOWwnunwPLv\nwOyZsKd7uq1rF337wi23uGm1oiI3lVZZ6RaGfvSREwyI7WSfMgXuuqtp/ehRQqKpaQzD6BhspNMC\nwa/oPn3c3H+8VDYp5cBNUPS4E5pDXoN3JrkRzerTYO8B6bauXeT4NG1B5oHwpmq1tTB7Ntxzj5vm\nHDvW7a9z2mnxR0DLlkVCqi3yyzASx0Y6aSCYennrLfc5vElYyum+IbK7Zt+3YPXX4aUfwTsToW6/\nNBrWsUR/x3V1brSybBlcfbX7WwR1KitdkEA8J3tBAey/vwujrq93o5lUBwkYhtEYE51mmDcPli9P\n48LPnmsiCTX7rILqM+H/roH3Tob6rmkyKrUE/pyPP44EBwSMHu3W2DQ3PTZ0qBsBBb6dIZm3/Mgw\n9ilsei0Oq1a5h1rK6f1ORGh6rnHrZyonw5r/F3Mb52ykZ0844ACoiZOmtWtXJy4jRrjMAevWuQCO\nTz6JZI/OzYX5853oNLdS39a4GEbbsOm1FBH4cO69N4UXPWhlZC+aAze7jACLboG1x7stAzoZO3fC\n7t2xz+Xmwt/+5vYe+uijiL+mutr5c37yk8geM0VFLa/UtzUuhpFZ2EgnRLAyPVgomDwU+q7wQjMb\nuu10o5nKMlj/VdDcZBuQsYTzoMVKEQMRkVmxIvG8ZRadZhitw9bptJFERae2Fo44ounmXx2HQv83\nIiOavD0RoamZQFt318xkevVyo5VE9hLq2xfuvx9KSxPPfZaKhJyGsa9iotNGEhGd2lq3IdiVV3b0\n1RUGvhwRGs3xmZvLYOM4smAD1Hbx4IPwve+5kUheHtx+u5s2W7cO/vQnN2UGbh3O0qVtW5RpoxjD\nSA4mOm2kJdFZtaqD199IAwxa4qbNima7cOZAaDYfTmcXmr594bzz4Ec/gkMOiT8SCdbQgAsGMMEw\njMzCRKeNNCc6Gze6RJDt/gqk3qWdKS53a2k+7R0Rmg+K6cxC07cvbPWblQ8f7oQlPGKxkYhhZCcW\nvZYE/vSndghOTh0UVjihGfOE2xagsgweeg62pSPWOnUEIc3FxW4tU1WVK481Ymkpg7JhGPsW+7To\ntHpKLfdzGPac311zjttRs7IM/vQv2HFoUmxMFWeeCevXw09/CtdfD++/7/wvF17o3s86y50HF6q8\nbl1k9GIJMg3DSJR9dnqtthaefhouuKCFDvI+g+ELndCMego+HOOEpupc2DU0OUYnmSC/2fDhzvcS\nvUWATYkZhmE+nRiIyCRgOpAD/ElVb4lRp4nohNPZDx/uknkuWRKq0OUTv41zOYycB1sOd+HNVedC\n7cCk3lNbmToVZsxwCy8POAC+9CWXoblfPxdFdt55sGOHqxs9UjEMw4jGRCcKEckBVgEnARuBl4Ep\nqroyql4T0YlOjfKrX8F1v/7ICUxxuROcjUf7Tc/Oho/6p+q2YlBBz56l9OnjRigNDU40ioogPx96\n9IBvf9uNVDJthFJRUUFpaWm6zWgzZn96MfvTiwUSNGU8sFpV1wKIyCzgLGBls62IpEZ5+91d9Dvu\nKX63bjb85B+w4StOaJ6+Cz45OKnGDxrkdsEMyM93Dvfhw+GUU2D6dCcyRUUVPPhgaUJ9ZprTPtv/\n02JHvFwAAAV7SURBVJn96cXs75xks+gMBNaHPm/ACVGLFBTAhBt+yOq3HmJQ9xPY+FAZVP4JPuvV\noQZ26wbf/a6LkFuyxL0fdhhcdx2MGuVCtv/+d5cJOXol/re+5d6nTetQkwzDMNJKNotOu7h8wr9x\n68Rfk7O3B8c9AJX1MLoELr8cnnoKDjwQnn8ePvigadtu3dxI5bDD4NRT3Yhlwwa3sn78eBg3LjGf\nyYAB8B//kbx7NAzDyDSy2adzDDBNVSf5z9cCGh1MICLZeYOGYRhpxgIJQohILlCNCyTYBCwDLlDV\nqrQaZhiGYcQla6fXVLVeRP4DWEAkZNoExzAMI4PJ2pGOYRiGkX10vk1cPCIySURWisgqEbkm3fYE\niMggEXlORN4WkbdE5Ee+vJeILBCRahGZLyI9Qm2mishqEakSkVND5UeJyHJ/j9NTeA85IvKaiMzN\nQtt7iMjfvD1vi8iELLP/xyKywl/7ryKSn8n2i8ifRGSLiCwPlXWYvf7+Z/k2S0RkSArsv9Xb94aI\nzBaR7tlkf+jc1SLSICK9U2q/qna6F05M3wGGAl2AN4Ax6bbL29YfOMIfH4jzS40BbgF+7suvAX7r\nj4uB13FToYX+voIR6kvA0f54HjAxRffwY+AvwFz/OZts/zPwXX+cB/TIFvuBAcB7QL7//ChwcSbb\nDxwLHAEsD5V1mL3AZcDd/vibwKwU2H8ykOOPfwvcnE32+/JBwLPA+0BvX1aUCvuT/p88HS/gGOCZ\n0OdrgWvSbVccW5/w/4hXAv18WX9gZSzbgWeACb5OZah8CjAjBfYOAhYCpUREJ1ts7w68G6M8W+wf\nAKwFevkHw9xs+LeD+/EXfmh3mL24B+cEf5wLfJBs+6POnQ08km32A38DDqOx6KTE/s46vRZr4WjG\nJU0TkULcr5CluP+EWwBUdTPQ11eLvpcaXzYQd18BqbrH24GfAWFnYLbYPgz4UEQe9NOD94nI/mSJ\n/aq6EbgNWOdt2aWqi8gS+0P07UB7v2ijqvXAzvB0UQr4/3C//BvZ4slI+0XkTGC9qr4VdSol9ndW\n0cl4RORAoBy4UlU/ovFDnBif046IfB3Yoqpv0PzOdBlnuycPOAq4S1WPAj7G/brL+O8eQER64lI9\nDcWNeg4QkW+TJfY3Q0fam7IdE0Xkl8BeVZ3Zkd12YF9NOxfZD/gFcH2yLtFShc4qOjVA2KE1yJdl\nBCKShxOcR1R1ji/eIiL9/Pn+gN+PkxpgcKh5cC/xypPJ14AzReQ9YCZwoog8AmzOAtvB/UJbr6qv\n+M+zcSKUDd89uKm091R1u/9V+TjwVbLH/oCOtPeLc+LW7nVX1e3JM90hIpcApwPfChVng/2H4vw1\nb4rI+96W10SkL/Gfmx1qf2cVnZeBESIyVETycXOQc9NsU5gHcHOkd4TK5gKX+OOLgTmh8ik+SmQY\nMAJY5qcldonIeBER4KJQm6Sgqr9Q1SGqOhz3nT6nqhcCT2a67d7+LcB6ERnli04C3iYLvnvPOuAY\nEenmr3sSUJkF9guNfwF3pL1zfR8A5wHPJdt+cVuq/Aw4U1X3hOplvP2qukJV+6vqcFUdhvshdqSq\nbvW2fDPp9ne00ypTXsAkXGTYauDadNsTsutrQD0uou514DVva29gkbd5AdAz1GYqLpKkCjg1VD4O\neMvf4x0pvo8TiAQSZI3twOG4HyVvAH/HRa9lk/3Xe1uWAw/hojMz1n7gf3Fbj+zBieZ3cYEQHWIv\n0BV4zJcvBQpTYP9qXEDHa/51dzbZH3X+PXwgQarst8WhhmEYRsrorNNrhmEYRgZiomMYhmGkDBMd\nwzAMI2WY6BiGYRgpw0THMAzDSBkmOoZhGEbKMNExDMMwUoaJjmEYhpEy/n+XJaIFon/P9QAAAABJ\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x33233f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(poly1_data['power_1'],poly1_data['price'],'.',\n",
    "        poly1_data['power_1'], model1.predict(poly1_data),'-')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's unpack that plt.plot() command. The first pair of SArrays we passed are the 1st power of sqft and the actual price we then ask it to print these as dots '.'. The next pair we pass is the 1st power of sqft and the predicted values from the linear model. We ask these to be plotted as a line '-'. \n",
    "\n",
    "We can see, not surprisingly, that the predicted values all fall on a line, specifically the one with slope 280 and intercept -43579. What if we wanted to plot a second degree polynomial?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre>Linear regression:</pre>"
      ],
      "text/plain": [
       "Linear regression:"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>--------------------------------------------------------</pre>"
      ],
      "text/plain": [
       "--------------------------------------------------------"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of examples          : 21613</pre>"
      ],
      "text/plain": [
       "Number of examples          : 21613"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of features          : 2</pre>"
      ],
      "text/plain": [
       "Number of features          : 2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of unpacked features : 2</pre>"
      ],
      "text/plain": [
       "Number of unpacked features : 2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of coefficients    : 3</pre>"
      ],
      "text/plain": [
       "Number of coefficients    : 3"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Starting Newton Method</pre>"
      ],
      "text/plain": [
       "Starting Newton Method"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>--------------------------------------------------------</pre>"
      ],
      "text/plain": [
       "--------------------------------------------------------"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>+-----------+----------+--------------+--------------------+---------------+</pre>"
      ],
      "text/plain": [
       "+-----------+----------+--------------+--------------------+---------------+"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>| Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |</pre>"
      ],
      "text/plain": [
       "| Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>+-----------+----------+--------------+--------------------+---------------+</pre>"
      ],
      "text/plain": [
       "+-----------+----------+--------------+--------------------+---------------+"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>| 1         | 2        | 0.092054     | 5913020.984255     | 250948.368758 |</pre>"
      ],
      "text/plain": [
       "| 1         | 2        | 0.092054     | 5913020.984255     | 250948.368758 |"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>+-----------+----------+--------------+--------------------+---------------+</pre>"
      ],
      "text/plain": [
       "+-----------+----------+--------------+--------------------+---------------+"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>SUCCESS: Optimal solution found.</pre>"
      ],
      "text/plain": [
       "SUCCESS: Optimal solution found."
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre></pre>"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "poly2_data = polynomial_sframe(sales['sqft_living'], 2)\n",
    "my_features = poly2_data.column_names() # get the name of the features\n",
    "poly2_data['price'] = sales['price'] # add price to the data since it's the target\n",
    "model2 = graphlab.linear_regression.create(poly2_data, target = 'price', features = my_features, validation_set = None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\"><table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">name</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">index</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">value</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">stderr</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">(intercept)</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">199222.496445</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">7058.00483552</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_1</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">67.9940640677</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5.28787201316</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_2</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.0385812312789</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.000898246547032</td>\n",
       "    </tr>\n",
       "</table>\n",
       "[3 rows x 4 columns]<br/>\n",
       "</div>"
      ],
      "text/plain": [
       "Columns:\n",
       "\tname\tstr\n",
       "\tindex\tstr\n",
       "\tvalue\tfloat\n",
       "\tstderr\tfloat\n",
       "\n",
       "Rows: 3\n",
       "\n",
       "Data:\n",
       "+-------------+-------+-----------------+-------------------+\n",
       "|     name    | index |      value      |       stderr      |\n",
       "+-------------+-------+-----------------+-------------------+\n",
       "| (intercept) |  None |  199222.496445  |   7058.00483552   |\n",
       "|   power_1   |  None |  67.9940640677  |   5.28787201316   |\n",
       "|   power_2   |  None | 0.0385812312789 | 0.000898246547032 |\n",
       "+-------------+-------+-----------------+-------------------+\n",
       "[3 rows x 4 columns]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model2.get(\"coefficients\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x3385a240>,\n",
       " <matplotlib.lines.Line2D at 0x3385a2e8>]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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xS9EtTP9oOs+PeJ5+bfsl2yQjjljAzxpiomP4RFu0X7zYJVsrLXV7YRYuTNwU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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xe9fdfd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(poly2_data['power_1'],poly2_data['price'],'.',\n",
    "        poly2_data['power_1'], model2.predict(poly2_data),'-')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The resulting model looks like half a parabola. Try on your own to see what the cubic looks like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre>Linear regression:</pre>"
      ],
      "text/plain": [
       "Linear regression:"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>--------------------------------------------------------</pre>"
      ],
      "text/plain": [
       "--------------------------------------------------------"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of examples          : 21613</pre>"
      ],
      "text/plain": [
       "Number of examples          : 21613"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of features          : 3</pre>"
      ],
      "text/plain": [
       "Number of features          : 3"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of unpacked features : 3</pre>"
      ],
      "text/plain": [
       "Number of unpacked features : 3"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of coefficients    : 4</pre>"
      ],
      "text/plain": [
       "Number of coefficients    : 4"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Starting Newton Method</pre>"
      ],
      "text/plain": [
       "Starting Newton Method"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>--------------------------------------------------------</pre>"
      ],
      "text/plain": [
       "--------------------------------------------------------"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>+-----------+----------+--------------+--------------------+---------------+</pre>"
      ],
      "text/plain": [
       "+-----------+----------+--------------+--------------------+---------------+"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>| Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |</pre>"
      ],
      "text/plain": [
       "| Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>+-----------+----------+--------------+--------------------+---------------+</pre>"
      ],
      "text/plain": [
       "+-----------+----------+--------------+--------------------+---------------+"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>| 1         | 2        | 0.062497     | 3261066.736007     | 249261.286346 |</pre>"
      ],
      "text/plain": [
       "| 1         | 2        | 0.062497     | 3261066.736007     | 249261.286346 |"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>+-----------+----------+--------------+--------------------+---------------+</pre>"
      ],
      "text/plain": [
       "+-----------+----------+--------------+--------------------+---------------+"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>SUCCESS: Optimal solution found.</pre>"
      ],
      "text/plain": [
       "SUCCESS: Optimal solution found."
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre></pre>"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "poly3_data = polynomial_sframe(sales['sqft_living'], 3)\n",
    "poly3_features = poly3_data.column_names() # get the name of the features\n",
    "poly3_data['price'] = sales['price'] # add price to the data since it's the target\n",
    "model3 = graphlab.linear_regression.create(poly3_data, target = 'price', features = poly3_features, validation_set = None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\"><table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">name</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">index</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">value</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">stderr</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">(intercept)</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">336788.117952</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">10661.0153713</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_1</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-90.1476236119</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">10.6222891844</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_2</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.087036715081</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.00296630623148</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_3</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-3.8398521196e-06</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.2417490959e-07</td>\n",
       "    </tr>\n",
       "</table>\n",
       "[4 rows x 4 columns]<br/>\n",
       "</div>"
      ],
      "text/plain": [
       "Columns:\n",
       "\tname\tstr\n",
       "\tindex\tstr\n",
       "\tvalue\tfloat\n",
       "\tstderr\tfloat\n",
       "\n",
       "Rows: 4\n",
       "\n",
       "Data:\n",
       "+-------------+-------+-------------------+------------------+\n",
       "|     name    | index |       value       |      stderr      |\n",
       "+-------------+-------+-------------------+------------------+\n",
       "| (intercept) |  None |   336788.117952   |  10661.0153713   |\n",
       "|   power_1   |  None |   -90.1476236119  |  10.6222891844   |\n",
       "|   power_2   |  None |   0.087036715081  | 0.00296630623148 |\n",
       "|   power_3   |  None | -3.8398521196e-06 | 2.2417490959e-07 |\n",
       "+-------------+-------+-------------------+------------------+\n",
       "[4 rows x 4 columns]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model3.get(\"coefficients\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x3575e828>,\n",
       " <matplotlib.lines.Line2D at 0x3575e8d0>]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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pF+jGHRubZphhBEiU6MQ1vaaqu7xiK09MFDgfmOzVTwYu8MrneaJRpaprvNHL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\nvEzvRVshAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x33acca90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(poly3_data['power_1'],poly3_data['price'],'.',\n",
    "        poly3_data['power_1'], model3.predict(poly3_data),'-')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now try a 15th degree polynomial:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre>Linear regression:</pre>"
      ],
      "text/plain": [
       "Linear regression:"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>--------------------------------------------------------</pre>"
      ],
      "text/plain": [
       "--------------------------------------------------------"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of examples          : 21613</pre>"
      ],
      "text/plain": [
       "Number of examples          : 21613"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of features          : 15</pre>"
      ],
      "text/plain": [
       "Number of features          : 15"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of unpacked features : 15</pre>"
      ],
      "text/plain": [
       "Number of unpacked features : 15"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of coefficients    : 16</pre>"
      ],
      "text/plain": [
       "Number of coefficients    : 16"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Starting Newton Method</pre>"
      ],
      "text/plain": [
       "Starting Newton Method"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>--------------------------------------------------------</pre>"
      ],
      "text/plain": [
       "--------------------------------------------------------"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>+-----------+----------+--------------+--------------------+---------------+</pre>"
      ],
      "text/plain": [
       "+-----------+----------+--------------+--------------------+---------------+"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>| Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |</pre>"
      ],
      "text/plain": [
       "| Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>+-----------+----------+--------------+--------------------+---------------+</pre>"
      ],
      "text/plain": [
       "+-----------+----------+--------------+--------------------+---------------+"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>| 1         | 2        | 0.078119     | 2662308.584343     | 245690.511190 |</pre>"
      ],
      "text/plain": [
       "| 1         | 2        | 0.078119     | 2662308.584343     | 245690.511190 |"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>+-----------+----------+--------------+--------------------+---------------+</pre>"
      ],
      "text/plain": [
       "+-----------+----------+--------------+--------------------+---------------+"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>SUCCESS: Optimal solution found.</pre>"
      ],
      "text/plain": [
       "SUCCESS: Optimal solution found."
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre></pre>"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "poly15_data = polynomial_sframe(sales['sqft_living'], 15)\n",
    "poly15_features = poly15_data.column_names()\n",
    "poly15_data['price'] = sales['price']\n",
    "model15 = graphlab.linear_regression.create(poly15_data, target='price', features=poly15_features, validation_set=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\"><table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">name</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">index</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">value</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">stderr</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">(intercept)</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">73619.7521173</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">nan</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_1</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">410.287462519</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">nan</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_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\">-0.23045071441</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">nan</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_3</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">7.58840542352e-05</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">nan</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_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\">-5.65701802391e-09</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">nan</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_5</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-4.57028130952e-13</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">nan</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_6</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.66360206687e-17</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">nan</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_7</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3.38584769195e-21</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">nan</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_8</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.14723104126e-25</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">nan</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_9</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-4.65293586386e-30</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">nan</td>\n",
       "    </tr>\n",
       "</table>\n",
       "[16 rows x 4 columns]<br/>Note: Only the head of the SFrame is printed.<br/>You can use print_rows(num_rows=m, num_columns=n) to print more rows and columns.\n",
       "</div>"
      ],
      "text/plain": [
       "Columns:\n",
       "\tname\tstr\n",
       "\tindex\tstr\n",
       "\tvalue\tfloat\n",
       "\tstderr\tfloat\n",
       "\n",
       "Rows: 16\n",
       "\n",
       "Data:\n",
       "+-------------+-------+--------------------+--------+\n",
       "|     name    | index |       value        | stderr |\n",
       "+-------------+-------+--------------------+--------+\n",
       "| (intercept) |  None |   73619.7521173    |  nan   |\n",
       "|   power_1   |  None |   410.287462519    |  nan   |\n",
       "|   power_2   |  None |   -0.23045071441   |  nan   |\n",
       "|   power_3   |  None | 7.58840542352e-05  |  nan   |\n",
       "|   power_4   |  None | -5.65701802391e-09 |  nan   |\n",
       "|   power_5   |  None | -4.57028130952e-13 |  nan   |\n",
       "|   power_6   |  None | 2.66360206687e-17  |  nan   |\n",
       "|   power_7   |  None | 3.38584769195e-21  |  nan   |\n",
       "|   power_8   |  None | 1.14723104126e-25  |  nan   |\n",
       "|   power_9   |  None | -4.65293586386e-30 |  nan   |\n",
       "+-------------+-------+--------------------+--------+\n",
       "[16 rows x 4 columns]\n",
       "Note: Only the head of the SFrame is printed.\n",
       "You can use print_rows(num_rows=m, num_columns=n) to print more rows and columns."
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model15.get('coefficients')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x35ac8128>,\n",
       " <matplotlib.lines.Line2D at 0x35ac81d0>]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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SRJ4RkSZAB2PMbgBjzC6gvVO/E7DD077IKesE7PSU73TKKrQxxpQBB0Wkdbi+RKQNsN+Y\n7+OC7wQyIrlhRVHig4YSUToSGpLrdCTrIClAf+A2Y8yHIvIYdmrNBNUL/lwbIvGdjNi/cuzYsd8f\n5+XlkZeXV32LFEWpMzbv28xn+z9j+EnDq67cABiWNYznPnmOu7nbNxvy8/PJz8+P+nUiEZ2dwA5j\njDv2ex0rOrtFpIMxZrczdbbHOV8EdPa0z3TKwpV72xSLSDLQ3BizT0SKgLygNu8aY/Y6zg1JzmjH\n29dxeEVHURT/eWnVS1zd+2pSk1P9NiUuOCvrLH7xn19QbspJEn+cioN/kN93331RuU6Vd+dMoe0Q\nkRyn6DxgLTAb+LlTdgMwyzmeDYxyPNK6AicDK5wpuIMiMtBxLLg+qM0NzvGVWMcEgHnABY7AtAIu\ncMoA3nXqBl9fUZQ4xhjDC6teaJBhb8LRsVlH2jZpy9o9a/02JepE6mb8W+AlEUkFtgA3AsnAKyJy\nE7AN67GGMWadiLwCrAOOAaONMe7U223AP4HGWG+4uU75FOAFEdkE7AVGOX3tF5G/Ah9ip+/ucxwK\nwI62ZjjnP3b6UBQlzlm6YykpSSmckXGG36bEFW4ctj4d+vhtSlSRgB7UT0TE1Pd7VJRE4sZZN9K7\nXW/+MOQPfpsSVzz38XMs3LKQl6942W9TABsF2xhT57GJNCKBoigx4+B3B3lj/Rtcf+r1VVduYDQU\nDzYVHUVRYsb0NdM5v9v5tG/avurKDYzurbtzpOwI2w5s89uUqKKioyhKzJi8cjK/6P8Lv82IS9yk\nbvV9tKOioyhKTPj4i4/58vCXXNDtAr9NiVsaQvBPFR1FUWLClI+ncFO/mxpUSurqMqxL/c8kqqKj\nKEqdUFICBQX2PZjDxw4zfc10bjztxtgblkD069iPbQe3se/bfX6bEjVUdBRFqTUlJTBsGJx9tn0P\nFp7X173OwE4DyWqRFboDBYCUpBQGdRpUr5O6qegoilJr1qyBtWuhtBTWrbPHXiZ/PJlb+t/ij3EJ\nxrCsYfV6XUdFR1GUWpObC717Q2oq9Oplj1027t1I4VeF/DDnh/4ZmEAMzRpar9d1NNumoii1Jj0d\nFi+2I5zeve1nl8krJ3P9qdeTlpzmn4EJxKDMQXyy6xO+PfYtJ6Se4Lc5dY6OdBRFqRPS02Hw4IqC\nc7TsKNM+naZ7c6pBs7Rm9G7Xu94mdVPRURQlary58U1OaXsKOW1yqq6sfE99nmJT0VGUekhl7sux\nZPLKyfziNB3lVJf6HJlARUdR4piaiEdV7suxYvvB7SwvWs4Vva7wx4AEZmjWUJbuWEpZeZnfptQ5\nKjqKEqfUVDyqcl+OFVM/nspPc39Kk9Qm/hiQwLRv2p4OzTqwZs8av02pc1R0FCVOqal4VOa+HCvK\nyst47pPn1IGgFtTXOGwqOooSp9RUPFz35UWL7LvXmyxWLNyykHZN2tGvY7/YX7yeMKzLMJbsUNFR\nFCVG1EY8Qrkvx5JnVz6ro5xaMjRrKIu3Laa+ZT5W0VGUOKam4uGn99qeb/awcMtCrulzTewvXo84\nqdVJlJaXsu1g/UrqFpHoiMhWEflURD4WkRVOWSsRmS8ihSIyT0RaeOqPEZFNIrJeRIZ7yvuLyCoR\n2SgiEzzlaSIyw2lTICJZnnM3OPULReR6T3m2iCxzzk0XEY2uoCj47732/KfPc3nPy2neqHlsL1zP\nEBE7xVbP1nUiHemUA3nGmNOMMQOdsruBhcaYHsA7wBgAEekFXAX0BC4CJoqIOG0mATcbY3KAHBEZ\n4ZTfDOwzxnQHJgDjnb5aAfcAA4BBwL0ecRsHPOL0dcDpQ1EaPH56rxljdG9OHTK0s51iq09EKjoS\nou6lwDTneBpwmXM8EphhjCk1xmwFNgEDRaQjkG6M+cCp97ynjbev14BzneMRwHxjzEFjzAFgPnCh\nc+5c4HXP9S+P8F4UpV7jp/faku1LSJIkhnQeEruL1mOGZg2td84EkYqOARaIyAci4v6E6WCM2Q1g\njNkFtHfKOwE7PG2LnLJOwE5P+U6nrEIbY0wZcFBEWofrS0TaAPuNMeWevjIivBdFqdf46b02+ePJ\n/KL/LwhMbii14dSOp7Lj4A72Ht7rtyl1RqTrIGcZY74QkXbAfBEpxAqRl7p0sYjkX2zE/6rHjh37\n/XFeXh55eXnVt0hREgjXASGWHPjuALM2zOLhCx6O7YXrMSlJKQzOHMz7O95nZI+RUb1Wfn4++fn5\nUb0GRCg6xpgvnPcvReTfwEBgt4h0MMbsdqbO9jjVi4DOnuaZTlm4cm+bYhFJBpobY/aJSBGQF9Tm\nXWPMXhFpISJJzmjH29dxeEVHUZTo8PLqlxl+0nDaNW3ntyn1CjcOW7RFJ/gH+X333ReV61Q5vSYi\nTUSkmXPcFBgOrAZmAz93qt0AzHKOZwOjHI+0rsDJwApnCu6giAx0HAuuD2pzg3N8JdYxAWAecIEj\nMK2AC5wygHedusHXVxQlxpSbcv6x4h/8+oxf+21KvaO+ZRKNZKTTAXhDRIxT/yVjzHwR+RB4RURu\nArZhPdYwxqwTkVeAdcAxYLQJ7G66Dfgn0BiYY4yZ65RPAV4QkU3AXmCU09d+Efkr8CF2+u4+x6EA\nrPfcDOf8x04fiqL4wL83/Jtmac34QfYP/Dal3jGw00A+3f1pvUnqJvVtt2swImLq+z0qip8YYxjw\n7AD+39n/j8tOuazqBkq1GTR5EOPPH8852efE7JoigjGmzj1CNCKBoii1YuGWhXxb+m3U1xwaMvVp\nik1FR1GUWvHAkgcYM3QMSaKPk2hRnzKJ6r8SRVFqzNIdS9l2YBujckf5bUq95qzOZ1Gws6BeJHVT\n0VEUpcY8uORB/jjkj6QkRR76MF5SaScS7Zq2IyM9g9V7VvttSq1R0VEUpUZ8uutTPir+iBtPuzHi\nNn4HI01k6kscNhUdRVFqxEPvP8TvB/+eximNI24TL6m0E5H6EodNRUdRlGqzae8mFm5ZWO3NoPGQ\nSjtRcdMcJPoWEBUdRYkC9X3dYvz74xl9xmjSG1Uvmmg8pNJOVLq27Ioxhs8PfO63KbVCRUdRakmw\nwNT3dYuiQ0W8vv51fjvotzVq73cq7URFRL6Pw5bIqOgoSi0IJTD1fd3ikYJHuLHfjbRp0sZvUxoc\n9WGTqIqOotSCUAJTn9ctvjr8Ff/85J/cfubtfpvSIKkPm0RVdBSlFoQSmPq8bvH48se5steVdGre\nqerKSp3Tt0NfikuK+fKbL/02pcZowE9FqSUlJXaE4wpOfeXQkUN0+3s3lv9iOSe1PslvcxosF754\nIbeecSuXnnJpVK+jAT8VJU5pKAvjT334FMNPGq6C4zOJPsWmoqMoSpV8e+xbHlv2GHcPvdtvUxo8\nie7BpqKjKHFOPOz5mfrJVAZkDKBvh77+GaEANqnb6j2rOXzssN+m1AgVHUWJY+Jhz8+xsmOMf388\nfxr2p9hfXDmOJqlN6NuhLyuKVvhtSo1Q0VGUOCYe9vzMWDODbq26MThzcOwvroQkkYN/qugoShzj\n956fclPOg0se1FFOnDGsy7CEDf4ZseiISJKIrBSR2c7nViIyX0QKRWSeiLTw1B0jIptEZL2IDPeU\n9xeRVSKyUUQmeMrTRGSG06ZARLI8525w6heKyPWe8mwRWeacmy4ikSf0UJQEwe89P7M2zKJZWjPO\n63pebC+sVMqQzkNYtnMZpeWlfptSbaoz0vlvYJ3n893AQmNMD+AdYAyAiPQCrgJ6AhcBE0XE9fWe\nBNxsjMkBckRkhFN+M7DPGNMdmACMd/pqBdwDDAAGAfd6xG0c8IjT1wGnD0Wpd/jlkm2M4YElD/Cn\nYX8i8F9YiQfaNmlLp/ROrNq9ym9Tqk1EoiMimcDFwGRP8aXANOd4GnCZczwSmGGMKTXGbAU2AQNF\npCOQboz5wKn3vKeNt6/XgHOd4xHAfGPMQWPMAWA+cKFz7lzgdc/1L4/kXhQlnogHz7RwLNyykMPH\nDjOyx0i/TVFCkKhx2CId6TwG/BHwbu3vYIzZDWCM2QW0d8o7ATs89Yqcsk7ATk/5TqesQhtjTBlw\nUERah+tLRNoA+40x5Z6+MiK8F0WJC+LBM60yHljyAGOGjiFJdOk3HknU/TpVroOIyCXAbmPMJyKS\nV0nVuow1E8lYPuLx/tixY78/zsvLIy8vr/oWKUodE8ozbXCcOIgt3raYrQe2Mip3lN+mKGEYmjWU\nOxfeiTGmTqY/8/Pzyc/Pr71hVRDJ4vtZwEgRuRg4AUgXkReAXSLSwRiz25k62+PULwI6e9pnOmXh\nyr1tikUkGWhujNknIkVAXlCbd40xe0WkhYgkOaMdb1/H4RUdRYkXXM+0deviKxr1t8e+5Zdv/pJx\n548jJUn9c+KV7JbZJEsyW/ZvqZPQRME/yO+7775a9xmKKsfNxpg/GWOyjDHdgFHAO8aY64D/AD93\nqt0AzHKOZwOjHI+0rsDJwApnCu6giAx0HAuuD2pzg3N8JdYxAWAecIEjMK2AC5wygHedusHXV5Rq\n4de6it+eaeG459176NO+D1f1vspvU5RKSNSkbrWZrH0IKwiFwHnOZ4wx64BXsJ5uc4DRnjDPtwFT\ngI3AJmPMXKd8CtBWRDYBv8N6xmGM2Q/8FfgQWA7c5zgU4NS5XUQ2Aq2dPhSlWvi9rhJvwUKX7ljK\ni6tf5MmLn/TbFCUCEjH4p6Y2UBoMblbP3NzAQ76gwApOaandgLloUezWVULZ4yeHjx2m31P9ePC8\nB7mi1xV+m6NEwKe7PuXq165mw39tqPO+NbWBotSCcCMav3b8+z3CCsWf/+/PnJFxhgpOApHbPpdd\nX+9KqKRuKjpKg8DrKbZmDaxwYiX6ta4SDzHVvCzatoiZa2fyxEVP+GuIUi2Sk5I5s/OZCbWuo6Kj\nNAhyc+GUU+xxWRn87neB0YUf6yp+x1Tz8s3Rb7hx1o1MumQSbZq08c8QpUYk2iZRFR0lIQjlYVYd\nr7OSEjj/fEhOtp8LC/0dXcST59rdC+/mrM5nRT39sRIdhmYNTajgn+qEr8Q97vrH2rV2RLDYcdYZ\nMgQ2bLAjmKVLwz+4i4vhpJPgu+9AJD5GFxAYYfnJu5+/yxsb3mD1rav9NUSpMQMyBrBmzxq+OfoN\nTdOa+m1OlehIR4l7Qq3HLF9uj4PXaELx5ptWcACMgTvu8H90EQ+UHCnhptk38fQPn6bVCa38Nkep\nISeknkC/jv1YXrTcb1MiQkVHiXtCrcccrkam3h/+EBo3tseNG8NvfqOCA3Dngjv5QfYPuCTnEr9N\nUWrJ0M6Js0lURUeJe9LT4bHHIMWZDC4shKZNrRglJ9v3gQPDt8/IgM8+g2efte8ZGhqWhVsW8tam\nt3h0xKN+m6LUAYm0SVQ3hyoJgbuu48Ypc9d13HUeHblEzqEjh+g7qS9P//BpRpw8ouoGStyz79t9\nZE/IZt9d++osXl60Noeq6CgJQ0lJzUQm3nb++80v//NLAJ750TM+W6LUJbkTc5l22TROzzi9TvrT\niARKvaG6rs5u3Uj20wT3HY87//1k3uZ5zP9sPg8Pf9hvU5Q6JlGm2FR0lJhSHRGormAE1y8uhunT\n42vnv58c+O4At/znFiaPnEzzRs39NkepYxJlk6iKjhJTqhP+pbqhYrz1166Fc86B0aOtA0K87M3x\nk9vn3c4Pc37I+d3O99sUJQq4aQ7ifTlBRUeJKV26QHZ2ZCJQ3VAx3vrZ2bB1q3WxLi2FiRNrvzen\nNnl3opGzp6o+veff2vgW+VvzGX/B+LozQIkrslpkkZqcyuZ9m/02pXKMMfX6ZW9RiQcOHTLm1FON\nSU425uSTjSkqiqxNQYF9j/QaBQW271NPNSY11b5H2r4q21NSqt9fbdrWtE/v+d5n7DMZD3cy737+\nbu0vrMQ1P33tp+a5lc/VSV/Os7POn8k60lFihjv9VVYG27bB9u1Vt/GGiolkpODWz8io29hmtYkK\nHY2I0lX1WeF81n9zVusfk5edV/sLK3FNImQSVdFRYoZ3+qtHD/j66+NFJFxgz5p4oNVl9Gg3KkJy\nsrW9OmtDoaYJvfdZk6m3qqYe3fPJvWeR2m0pj1/6YOSdKwlLIniwqegoMcONrPz22/bzRRdVFJFw\n4hJPuWddOnfYAAAgAElEQVSkBrsWgiNKQ+A+hwyxr5oIamUjufR0+Pf8vbT62a3MvmkqHVvHfyBI\npfbkts/ly8Nfsvvr3X6bEhYVHaXOqeyXe3o6NGlio0N7RaSkJLx7c1W/6qOxSB/MmjUBm2uSFsE7\n6vKK6Pr1x/8tatJnMMYY7l50G9edNooRPYdVz1glYUmSJIZ0HsL7O97325SwVCk6ItJIRJaLyMci\nslpE7nXKW4nIfBEpFJF5ItLC02aMiGwSkfUiMtxT3l9EVonIRhGZ4ClPE5EZTpsCEcnynLvBqV8o\nItd7yrNFZJlzbrqIaJqGOKCkxP5yHzbMvntHMa4wBItIVpatP3q0nb5KSak4hVXZr/pYbf6sy6Rr\nXboE4silpEBOTt27dN/33n1s3reZ+8+9v246VBKGoZ2HsnhbHE+xReJtADRx3pOBZcBAYBxwp1N+\nF/CQc9wL+Bibqycb2Ewg3M5yYIBzPAcY4RzfCkx0jq8GZjjHrYDPgBZAS/fYOTcTuNI5ngT8Kozt\ndeLJoUTGggXG2AQC9rVwYWhPK69X2tKl9pzbJjnZmNzcyLy8vG1TU22f0aK6nnThWLrU3iNY2xcu\nrJt+XZ758BnT7e/dzK6SXXXToZJQLN622JzxzBm17gc/vdeMMW4g+UaOmBjgUmCaUz4NuMw5HumI\nRqkxZiuwCRgoIh2BdGPMB0695z1tvH29BpzrHI8A5htjDhpjDgDzgQudc+cCr3uuf3kk96LEnlBr\nMl6vtG++CSzSg/VuW7/++Bw5oabR3AX+4NFRuPq1oTqOCZVdOzfXvlJTrb0DB9adw8N/Cv/DPfn3\nMPfauXRo1qH2HSoJxxkZZ7Duy3V8ffRrv00JSUSiIyJJIvIxsAtY4AhHB2PMbgBjzC6gvVO9E7DD\n07zIKesE7PSU73TKKrQxxpQBB0Wkdbi+RKQNsN8YU+7pSwPWxwG9ekG3blYE3JQD4aam3Kmxiy6y\nQvPAA1Y4IJA3xzs9F2razsUEbcKO1rRbJEJW1bWrk6q6OsK5eNtibpp9E7NGzaJ7m+6R3ZBS72ic\n0pjTOp7Gsp3L/DYlJBGtgzgP99NEpDnwhoj0xo52KlSrQ7si8RGK2I9o7Nix3x/n5eWRl5dXfYuU\nKikpgYsvtntwunaFefMCD9TFi4+PEL18ecUF9T//GTp1gqQkKC8PLNgPHhzIFAqBTKHnnRdY4C8r\nq1g/1OiqtqmhQ6XNDiUYkVw7klTVkV4PYMn2Jfz4lR/z8o9fZmCnSpILKQ0CNw5bdUIe5efnk5+f\nHz2jXKo7Hwf8D3AHsB472gHoCKx3ju8G7vLUnwsM8tZxykcBk7x1TGDdaI+nzlOeNk8BVzvHe4Ak\n53gw8HYYe2s9t6lUjrsus2BB5Osrhw7ZdRvv+k/wy7uuE2qtyBgbeeDkk+31cnNtPXfNKDfX2lPV\n+lBRkTFPP111hIRI14/cNazaRkOI9Hrvb3/ftBvfzszbPK9mFwqB+53W1TqTElveLHzTnDftvFr1\nQZTWdCIRmbYEFu9PABYBF2MdCe4y4R0J0oCuVHQkcJ0QBOtIcKFTPpqAI8EoQjsSuMctTcCRwBWg\nScCvw9hfqz+8UjleJ4HcXPuK5GHrfaAmJRnTrZt99wrL7NkVrxMsIq7gJCfb9r16BZwViopsvaqc\nEoqKjGnc2F6vcePKhac6YlIXTgeRXG/p9qWm3fh2Zu6muTW/UJjr1mXYHiW27Du8zzR7oJk5Wnq0\nxn34KTp9gJXAJ8Aq4M9OeWtgIVCIXeBv6WkzxhGb9cBwT/npwGqsc8HfPeWNgFec8mVAtufcz53y\njcD1nvKuWG+4jY4ApYaxv8Z/dKVqgn+NR+qJFfxALSoy5vHHQ49mvG3cvg8dsoLj9Xjz2vHMM5GN\nEp5+uuI1n322arvr0tOsKiq73oLPFph249uZORvn1Ok1Y+kRqESP3Im5ZsXOFTVu75voJPpLRSe6\n1GYqKfiB6o5m3JFLZaMOr9sx2PreUVakAT+rM9KJJ2aumWnajW9n3tv6Xp33XVfTg4q/3PrmrebR\npY/WuH20REfTVSu1JpI00pWljPaeKymxeXC2bq188dy7yJ6dDe+9Z+t57Yg0vXVxMcyZY50gMiLw\ngfQz/bUxhidWPMG498cx55o5nNrx1Khcp6apwZX44eXVL/P6+td5/arXq64cgmilq/Z9JBLtFzrS\niQnBC8/ez8HrPu5iv1vPu1ZTXWeEcFNP0VoID17vKCqK3YL70dKj5lf/+ZXJnZhrtuzbEtI2XfxX\nXLYd2GbajW9nysvLa9QenV5T0YlXQj2IvZ+9QuKuv7j5dIK90mbPrv3UTjQXwr3rHSkp9j5iseC+\n9/Bec+60c80lL11iDn538LjzuvivhCLrsSxT+FVhjdpGS3Q04KdSa4L3pbz1VsXPIk6YfU/Egc2b\n7TTa4cMV+2rSJBCJ+i9/sftzqruxM1xU6rqIUBAqO2m0o1+v/GIlA58dSL8O/Zg1ahbNGzU/rk48\nReJW4oe4zK8TDSWLpxc60qkVkUzZhPJECx6tHDpkvdG6dQuMalxvt2DX5uA9PJHGYXPx7t3xXr+u\nRgLRyk4aTHl5uXli+ROm3fh2ZuaamVXapIv/SjATV0w0P//3z2vUFp1eU9GJFa7QBE+TVWdfSrj1\nlnCCsHBhYK0n2DMtOdm6QEfyIA2XEjtabsDRcqE+8O0Bc8XMK8xpT51mNu3d5KstSuKyevdqc/Lj\nJ9eorYqOik5M8I4I3PWKyh7Uke7md/t2xcwdKYQSN3djpys6jRqFFr5QozCvuCQn2zWipUuNKSyM\nH9foqkaP8zbPM1mPZZnb3rrNfHvs29gap9QrysrLTKuHWpkvSr6odlsVHRWdmBAqUkBKin2fNavi\ng7KyPS6hvNm8wlJYGBC1UOLmjn4efzy08IWbLguemnMFyxvxoDojp7qmsmm+A98eMDfPutlkPZZV\npyFtlIbNJS9dYl5d+2q120VLdNSRQKmAmyoAbNDNlBTIzIQtW+DSSytGeH7zTfjuO3v83Xd2rwuE\njrLsXehevRp+8APrTFBaCp9/Dh07VoxCnZ5uI1R36WKTvAVHqA63cJ6eDo89FnBaOHLE1tmyxd4P\n2HsaPbpuok+7zgnFxZU7Kbj1vEFOvXa/velt+kzqQ2pSKqtvXc3wk4aH7khRqokb/DNuiIaSxdML\nHelUG6+Lc3JyxfWVlJTAaCPcSCfU+klVAT6D12CC6wdHKKhslOU9J1LR/qSkwOfaru14148aNw6/\n9lVZfLqNxcXm2tevNdkTss3CzxaGvlA17NF9OkowS7YtMac/fXq126EjHaWuCedCPGhQwC04Jwc6\ndw6cO+UUe6642I503n8fnn0WPv3UpjQIl456+XK47rrACCSYsjLbfvt228f06Tbdgcv27YFzBQV2\nlHDsmD1XWmrPuWzbZsvAXm/CBGuHm+itZ8/Q6aGr41Lt2rh2rbX9u+/Cuyt7R2WFhdaed/KPcfWE\nxzjzhT50bt6Z1beu5rxu51V94UrsiUXabiXxOCPjDDZ8tYGSI3HyjyIaShZPL3SkE5LK1kTcxX2v\nO3O3bsbMmGFHQcGL8oWF4dNRh3IKSE01pmdPY7Kz7cjDLfO6Wycn23Kv27TX4SA3NxBVOtilOpQL\nt3sfPXvatSk3jXZVf4/K/nbeEU7jxuHdlb329D213Lz00b9MzhM5ZvgLw82GLzfUyfepQTqVyhj2\n3DAzf/P8arVBHQlUdOqScFNg4SIJeBf8O3UyFabG7r47/AMvlPvzs88GhCAlxZicHGPGjbNiEHzN\nJ54ICERwNADXOSBUcFCv+7C3nds2WGiffjryh3awHe79VOaufOiQMc++XWAGP3OW6TOxT52mInD7\n1306SjjGLBxj7nnnnmq1UdFR0alTQj2kgt2NZ8wI7KnxepglJxuTlmaOG+kE771ZsMCY554zpn37\nwAO/Z09bHhwax3s+XE4er81uHh233cknh3en9o5MvBtTvULrjloizZVTnQf8mt1rzE9e+Ynp9Egn\n89zK50xpWWntvrxK7NJ9Okoo3tr4ljl7yg+qteanoqOiU+d4p8DcKbXgqbCkJGMyMoyZOrWiGBQW\nBn7hB/e1YIEVj2BB6dw5MCXWs2fF6TPvKCQ4J493ym/BAnve3WTqbff44/Z8qE2trgt2sKCFGrVE\nugm1qgf82j1rzdWvXm3a/629GbdknPnm6DcRfy/qEKDUJdv37DdJf25mktOORjwSVtFR0YkKwVNq\ns2aFHoG4HmTjxxszfXrFSNHuBlF3xOMdUXhfIhX3yoSq16tXxZHSrFmB9ZhgDzFXeFJSKgqYu7co\n1FRZqMgJrs2dOtl7cMtr+uBfu2etGfXaKNP+b+3NQ4sfMiVHSmr8fajwKHXB0qXGyI9+ZWhWHPGa\nn4qOik5UCJX5033opaaGFg/v4r7XqSAtLbxguefd4+7dA2LiXe9x128qc68O3iT6zDPHu0UHh9qp\njMLC0NOF1X3wf1T8kbn61atNu/HtzIOLH6yW2IT7PtQhQKkLarLmFy3RUZfpBk6XLjZasutCPHCg\njfI8dy507Vp52w0b4LnnAhtEjx6FZs1sXz172n5F7MbPv/414MYMNjrztGl2I2evXrZNbq69vuti\nHEyjRqFdnTt0gBNPDHxOTbWRrhctCp8Ezkt+vrUd7L1MnRp5xGZjDPM/m8/5z5/PyOkjOSPjDD77\n7WfcPfRumqU1q/zCIQh2N/fep6LUlPR0+38h0v8T0UQzhzZg3L0da9ZYgXnrrYr7XS66qKJQBJOb\nC6+/DqeeGhAegLQ0G3XgxBMD2SfBClFRUaBeZibs2mX3/kyYYAUnPd3uAcrODuzDAbvf5o03oF27\niplBhwyx9ntJTbX/uXr3tvuDwO49CvcfrbgYTjrJ3kPjxnbP0VVXWcHp1Sv0f9JjZcd4Ze0r/G3p\n3ygtL+XOs+5kVO4o0pLTwv/BIkSzdirxgG+ZQ4FM4B1gLbAa+K1T3gqYDxQC84AWnjZjgE3AemC4\np7w/sArYCEzwlKcBM5w2BUCW59wNTv1C4HpPeTawzDk3HUgJY381B6INh1AuyKG8yLp0CazFuGsz\nXjfloiJjrruu4hTYs88efz3vNFZqamBKzBvlwLUreL0nVHqDUPVcT7Zgp4iq0iMUFYV2jAhuU3Kk\nxEwomGCyHssyef/MM29tfKvGmRkVJZ7BrzUdoCPQzzlu5jz8TwHGAXc65XcBDznHvYCPgRRHGDYT\nGFEtBwY4x3OAEc7xrcBE5/hqYIYJCNtnQAugpXvsnJsJXOkcTwJ+Fcb+qHwh9YHKXJC9XmTeDZve\n816hCF4XCRX8s6jIipmIXbR3F/9D1Xevl5FhzMyZoQUj1NqPK4bBghRsb3XZVbLL/Pn//mzajm9r\nfvLKT8zynctr3pmiJAC+ic5xDeDfwPnABqCDCQjTBuf4buAuT/23gUFOnXWe8lHAJOd4LjDIOU4G\n9gTXMQFxudo5/hJIco4HA3PD2Fu330QCEM7zyvUIC/Y8e+YZKxqVjQyKiqznWiihcB/+SUl2T85f\n/lLxnDdVQqiRievA4AqTm4ogklTQriv07NkBV+pQ7t+hohZE4p1W+FWh+eXsX5pWD7Uyt755a9jc\nNurmrNQ34kJ0nJHLVmfEsz/o3D7n/QngGk/5ZODHwOnAfE/5UGC2c7wayPCc2wS0Bu4A/uQp/3/A\n7UAbYKOnPBNYFcbmOv0i4hlXVNyd/pWF/PeGlXGDbRYW2ge39+HtdU0OtbnSGHvNUJ5qH31kzN//\nHmiXlGRMx44V67kRBTp2DITEcaf6vIE5XVGKZNOmNy+Pez/VDXlTsKPA/Hjmj0278e3MPe/cY/Z8\nvadSMY+Wm7OKmeIX0RKdFCJERJoBrwH/bYz5WkSCV+frcrU+ksWriBe4xo4d+/1xXl4eeXl51bco\nzvE6BZSV2TLX82rwYFvuDaC5YYN1HFi92ob837zZOg588ok9P2yYbXvKKXD4sE0N4JKcHEg5EI6j\nR61jgGsL2OsEB/wsL6/Y95Ej9t1b1q0b/OY3sHGjdUZYujT0AntwuoPt2+G8EDE0Q6VFGDwYyk05\nb296m3Hvj2PHoR3cceYdPH/Z8zRNa/r939dd4Pc6F4Trr7q4KSBycwOOEuGuGa6NotSU/Px88vPz\no3+hSJQJuz4zFys4btl6Kk6vrTehp9fmEpheW+8pj3R67SlPm6cITK/toeL02tthbK9b+Y9TguOL\nBcckO3SoYpSA3FxjFi2q6CAAdppq1qzwmzizswObL3v2tCMZd2pO5PgRT01ewVNwwaOjhZ4MAMHR\nCsKF0PESvGfhq/1HzFPLppmuf+tt+j7Zz7y86mVzrOxY2L9vqA2n3inEmmQlDTVaqmrPjm4kVaIJ\nfk6vAc8DjwaVjXPFhdCOBGlAVyo6EiwDBmJHKXOAC53y0QQcCUYR2pHAPW7pnJvpEaBJwK/D2B6F\nryP+8D6AvJsw3bWMoiIrFiL2IT5xYuiNnJmZFdv36BHYxJmZaeOxBbdLS7Mx1h5/3JhHH62d4GRk\n2Gt4PemCRcgVnVDRnnv2tHaEe/BXiKK9+JB54N1HTeYjnU2z0eeZpJx5pu+p5WGdFirbXOeNjlAT\nAagsAGu4a+pGUiWa+CY6wFlAGfCJIyYrgQuxay4Lsd5s810xcNqMccQm2GX6dOz6zSbg757yRsAr\nTvkyINtz7udO+UYqukx3xXrDbXQEKDWM/VH5QuKRULvzXS80b5yyyl7BI5+//a3iA9VNQhZcz311\n7lw70UlKCkQ6cKMKuGkM3BQLoZLFeV9VJVNLbrHLtB/1Z9NmXFtz1atXmSlvfxA2JXZwyu1QMeFC\njUoiWYMKZVuwwFQW400jSyvRxNeRTiK/GpLoGBN6Gm3BgvDx0IJf7oPe/XzKKRUjQrsP1PHjq+4r\nLS28OIUTOe9oxvvA9TozuFNY3tFd48bHh8KZPTvwN1mwwJh7Ht1i5Ee/NtzVyiT96FbzysJN358P\nFSW7sqkr1zHDFWLXKcMVyVDOHJF8d9WNEq2RpZVoES3RidiRQIk/wi0iJydDUpLd1T9vni1LTa24\nqA+QkQE33gi7d8PQodC6NfzpTxUjAWzYAHv32j5LS+0j/auv4NprYfJku7gfjqNHbQSBL78MX6e8\nPHT54cMV723NGvj8c3sPmzfDOefAypV2cX3tWuvUsH49jB5tbSovhyuvhFWr4Ic3bGJThwegx2yS\nj/wKeWoDvbPbc+HAwPUefhi+/RZOOMF+9joHrFkDK1ZUdEpYvjwQCcF10nBt+frrQDSH6jgWpKdX\n3wGhJm0UxVeioWTx9KKejnRCuQcvWFDRRdkNoLl0aegRRUZGYP2mUaPQ6zVg990El3XrZtMdVMd5\n4Ior7MipqjYZGfYVHFHau9aUlGTXboJdoX/3O09f7daaXv9zjeGPbQ3njDU03vd9ErlQUaYbNbLv\n7silsn0+wW7iwc4NOu2lJDro9JqKjpfKQth4X716VYwEXdmrQ4fQ5T/9aejyqqJQh1pryckxpmXL\n8HVEjt8PtHChzSwa7v68029JScbQ8RPDlT8x/LG9uf1fD5ie/Q5+X99NIucKQbh1oYULj59WDPZY\ncx0sQoXYiea0l+7dUWKBik5Nb7Ceik5lIWy8r+RkO1JxRzpVrbHE26tjR5sGobI6s2c7jhIZHxhG\njTTccaJhyMOmR+7X36/PuFEL3CRyXq++UILsrilVNmLxYz1F3aSVWBEt0dHUBglKejrMmQNPPmk3\nefbsGTiX5gl0XFYG99wTWDvp2NGu7yQKIrBpU+V1Cj5bx+YzfgyjLoUt58PfP4Old7ClsClr19q/\n1cCBdk1o3bqK6zTbth0fzdpNsZCeDq+8Arffbt+DN1+66ylueUkJFBTY92gRaiOqoiQU0VCyeHpR\nj0Y63mmVUN5TbsiXwkJjfv/7xBvVJCVVngTO+0pNNSapzRbT8ufXm9YPtjMpZ//NkHLYpKQYk5UV\n8CLzpq8O/nvMmFFx5NCtmx0NeePSubHmGjWqfNNnrEYgul6kxAp0eq1hi07wQ23WrIoPUHdR3RWj\nuooOUJevVq0qP3/LLaGn0pKTA5taJ00y5i+PFZtrXhptmv9va3P33HvNv98+eJy7dEaGdVpwowSE\nEjNXSAoL7cZXbwy6BQuMGT36+L9xOGK5UVPdpJVYoKJT0xtMQNEJtVAc/FB7/PGKD8SkJLteESxG\nEB8C1LixjYJQ0/aZmcYsX7XXtLvmTsNdrUy7a283qzbvMQsWVNyXFOrlCk9q6vEhdZ544viNs+Ec\nJGbMqPw7q8yxINz3qijxSrRER9d04gw3yOPZZ9v34mK7TtCliw36mJJij0eMsGsPLuXldo7///7v\n+D67dIE2bWJ3D6F44IHAHphIad/eOUj7mqKT7ufcN3L46usDMGkVX738CCOGtWPEiIqBTINJSbF/\nt/feg7ffhubNA+caNbL7ez7/vGIb7xqPl7Ztq7ZZwoShDf5eo7nuoyhxTTSULJ5eJNhIx+um650a\nOvVUmyogI6PiXpLbbqv4azzUOk6bNjUfYbjTUH6Mjlq2/daknz/B8IcOhh9fY04asNHk5ISuG8p7\nr1u3imkNvKNFN2KBd59OWpo9773ftLTKRy8uVU2vaZw0JdEgSiMdNxBnvUVETKLcY3Gx/RXshvXv\n0gV27rQeaCkp9pd/cXGg/uzZ8Ic/VB4VICFJKoVTp0HefbCrH7xzP+zuS3IytGgB+/Yd3+Qvf4Hn\nnoOtW+3nbt1shICMjEAdd7Sxbh306mW9/9ats9EPmja1HoDbtweiG0CgrHfvylMHBPcdnIagqvOK\nEm+ICMaYiFPIRNxvojyQa0qiiE5JCfTvb0O8gA1jk5lpH3gAHTrAnj3297fLbbdZl+l6g5Qjua9h\n8v4HDmXA/z0AO8+0pyQQiieYrCw7bbZ+PXTubEPhXHpp4G/Xq5d1je7SxT70RayYjBgRCGWTmxvI\n01PTHDUlJYHcN6HaVXVeUeIJFZ0akiiiU1Bgfwm78dHatLExzxoGBrq/Def+GUyKFZvPzsebp0+k\nouC6ZGbaBG9//nNAkJKT7cjQTQjXqJE9l5pq33v3trHWLrww8PdOSbGjj969j0+cBuFFSJOoKfWV\naImOOhL4iHczYW6ufSUn282d+/f7bV2MyFoMN54NF/wR3ruHnPdW0M1cQHBi2FCCI2IdKP70Jysa\nblbSsrKA4IA9LiuD774LbKoUgZycQJ3kZBvwdPr0ipsvV6ywIjRsmB2Jeqc3QzkHxGKDqKIkMio6\nPlFSAkOG2AfWkCH281/+Yn+1l5eHj74cCUmJ8K2euBKuvQguvx5W3gKTVsGGyznnbGHixPDNUlNt\nCu2kJPsqLraCcvQo3HuvXctJSbGjG5dGjWxd17MsOdlOrz3+eECojh2zkaFHj7btU1PttJwxgRTg\nbnRrV1CCowNUJlCKojhEwzshnl7Emfeam9slOIBldnZFj6nUVGPatq2+x1fcRyFou94G47zjRMOA\nJw3JR46rU9m+opQUG0sulLdao0aBNN2FhdZzbepUuzfH+3dJSQlsrgy1xyclJRCJ+tChivt4gpO8\neaMDBOctOvlk3ZOjJC6o91rNiKc1HXd04y5eewles+jY0f66riwXTULRciuccx/kvAlL/wArfgPH\nmkTcPCUl8H7kSOjpNi8LF9rRTNeudhTk7ce7VtOvX8BbMPi8u0ZTXGxHONu2Bbzetm0L7JNy13+g\nojNIaiosWqT5bpTERNd06gFr1thpGC9JSXYNJ/ghumtXPRGc9GK4+Db45elwqDM8sQnev6taggN2\nuvEPfwgkkvOSlXX8lOJXX8Gdd1YUnIwMmDs3IChr1ljxcMnOhkcfta7X06dbV/SCAlt35UorIHPm\nwMUXB9ZxIBD0Mz3dbkI9+eTA9JwrRi6Rrvno2pBSb6lqKARMAXYDqzxlrYD5QCEwD2jhOTcG2ASs\nB4Z7yvsDq4CNwARPeRoww2lTAGR5zt3g1C8ErveUZwPLnHPTgZRK7K/bMWctOHTImC5dKk7ltG5d\n8XO7dnEwBVYXryZfGi74g+HO1obhdxia7Kl1nx99FIg/56bCzsmxoX9mz7ZTZcnJtix4Q2tamp1y\nc7+HpUsDgUDdYJ+9etk+3ek9keMDeEayyTNcbLRIg4J6N6y6qbkVJdYQpem1SERnKNAvSHTGAXc6\nx3cBDznHvYCPgRRHGDYTcMteDgxwjucAI5zjW4GJzvHVwAznuBXwGdACaOkeO+dmAlc6x5OAX1Vi\nfxS+jppx6JA5bkd98BrMj34UB4JRm1ejA4a8e6zYXHKrIX1nnfU9apQxzz1ns6O6azZupO1TT7Vl\nzzxz/HrZddcFHtyhMq4WFFSMBBH8qmwdpzprNpFGJVi6VNeGFP/xTXTstekSJDobgA7OcUdgg3N8\nN3CXp97bwCCnzjpP+ShgknM8FxjkHCcDe4LrOJ8nAVc7x18CSc7xYGBuJbbX7TdRDby/qJcuDR2M\nMzvbmB49rPh40zEn3Cv1a8NZDxn+2M5w2Q2Glluiej03A2iokEE5ORVHK+4Ix5jwD37v6MLbNpS4\n1DTKc6SCVZnzgqLEimiJjrM8W23aG2N2O0/0XSLihmbshJ0icylyykqBnZ7ynU6522aH01eZiBwU\nkdbecm9fItIG2G+MKff05Ql2Eh+4ezjWrLHz+8eOQbt2x9fbutWuJfzwhzasTcKRVgIDJsGZj8K2\ns2Hqe/BVz6rbRUCLFnDwYOhz69fbzbMpKXadJynJ/i1LS+Gzz+zjGuz7jh2BPTm5udblev166NEj\nsOaSnm7Xetautft1Fi2y6zb79h0fQcBN3lZdvNeoLCqBuzbkdV4IXhtSlESlpqITjKmjfiB4V2DN\n6/jK8uX24VJWFtj1vmtX6LpbtwZihiUMjQ7CwH/A4L/DlvPg+YWwJ7fqdtUgnOC4bN8eiAhdVmY9\n1SyKlvgAAA53SURBVLZts6FwvB5pEIgc0KWL/WyMFZQvvgg8/L1i4t04WpdEKlgZGdZ5QcPmKPWN\nmorObhHpYIzZLSIdgT1OeRHQ2VMv0ykLV+5tUywiyUBzY8w+ESkC8oLavGuM2SsiLUQkyRntePsK\nydixY78/zsvLIy8vL2zd2lJcDK+9Bv/4RyAsizvSqRc03m+FZsCTsPkimLoIvjolJpdOSgpsmu3R\nA6ZODQh6ly4wcya8/z40awa33mpdqxs1siLkjjo7drRCU15uv6tevaxHYTiR8TPMTU1HVIpSE/Lz\n88nPz4/+hSKZg8M6Baz2fB6Hs3ZDaEeCNKArFR0JlgEDsaOUOcCFTvloAo4EowjtSOAet3TOzSSw\nvjMJ+HUlttfdJGcY3A2fTz4ZetNiPCRRq/Wr2ReG88YY7mxjGHmTofWmmF5fJPC3TU62Sey8C/9J\nSaFTMLh1gzOLeutkZIRPuharFNSa3E2JN4jSmk4kgvMyUAwcAbYDNzoisBDryjzfFQOn/hhHbIJd\npk8HVmNdo//uKW8EvOKULwOyPed+7pRvpKLLdFesN9xGR4BSK7E/Gt/H97gZI30XhWi92q4zjLzZ\ncFcrw8Wjo+4gEO6VkmJdmpOTjenUKeA+HUrkg185OVZYvAIW3HeohfpY5MCJlbApSnWJluhoRIJa\nMns2XHaZfXzVHwx0WQRDHoZOH8CK2+CD0fCtv+lHJ06E3/3ObvhMSYF33rHHv/sdbNhg46i5gT69\nuYggkBoBrCPBkSOwaZP97E1r4CUWOXAKCqzDghsFO1wEA41mrcQaTW1QQ6IpOhs32oeR+2BLeFK+\ng94zrYNAo0NQcAd8eh2UVjPPdJRo29ZGGnBJSbGOA+npdsHdTb52+LD9ETBmDBQWVvx+MjOtk0d6\nug3QCTBwoH0P9VCPdg6cSITNreNNt6DCo0QbFZ0aEi3RKSmxv5jrRSThlp9bt+d+U6H4DDuq2XQJ\nmPiKkuRNXeDy7LPwi18EPntd1VNSrANHcnLAkSPUaMKNrbZ1qz8P9aqELdLRkKLUJRp7LY4oLoZ7\n7klwwUkqhe5vwTWXwC8HgJTDlAJ46W3Y+KO4ExywXmiPPx4I/tm4sY2D5sVNN+Dm1HHTRGRmho6H\nVlJiBWfz5kCKgrVrY3dPEPBSCyd0ubnW5nDx3BQlkdCRTjXZuBH69KkYSDKhaLcW+k2Dvi/Cwc7w\n4a9h7dXVDsDpB9nZdp2me3frEn3FFXY/ixfvSKe83E6zNW4Mn34aeqNncMbWk0+2+2PibfpKU10r\nsUan12pIXYpOwk6pNfnKrtX0+6eN+vzp9fDpDTHbX1NbkpOtY8D27aGnmIIX2UtKYMYMK0xlZYFU\n1OEW6N31kuxsGwkgWMgUpSESLdGpq4gEDYLlyxNIcJp8CT3fgF6vQqcVsOlieOd+2HI+mGS/rYuI\n9u1h3Dg7rdazp51KW7fObgz9+utA2P9Qi+yjRsGTTx5fP3iUEGloGkVR6gYd6VSB+yu6TRs79x8u\nlE1c0HwH5LwFvV6DjA9h84Ww7iew6SI41tRv6yLCzYvjRh7wJlUrKYHXX4ennrLTnL17w8MP2zTT\n4UZAK1YEXKrV80tRIkdHOj7gTr2sXm0/uw/CuCGpFDILrNB0n2OnzjaPsN5nmy9MiHWaYIL/xu7i\n/ooVcMcd9rtw66xbZ/ff9O4dcDn2LrKnp0OTJtaNuqzMjmbWrlXPL0XxExWdSpgzB1atiqONn1IO\n7ddAl/cgOx+6vgv7u9qps/88DUUDE2bqLFLc9Zxvvgk4B7j06GH32FQ2Pdalix0BuWs7WVmxtV9R\nlIro9FoYNm60DzVfST4CHVZB1vtWaLosslEBtp4DW/Pg83Ph6xN9NrL6tGwJTZtCUZgwrY0aWXE5\n+WTr9rx9u3XgOHw4ED06ORnmzbOiU9lOfd3joig1Q6fXYoS7hvP00zG+sJRDm0K76N/pA/vefg3s\n7Q47B8Paq2DOk1CS+K5VBw7AoUOhzyUnw6uv2txDX38dWK8pLLTrObffHsgx07Nn1Tv13T0uoabf\nFEWJPTrS8eDuTN+8OcpGNfnSCkr7NdBhdeD4m3Z2iqx4gH3/4rSEcQCoK7xx0EKFiIGAyKxZE3nc\nMvVOU5Tqoft0akikolNSAv36HZ/8q1akfW03YwaLS/IRm/BsTx/n3Xl927oOL+4/rVrZ0UokuYTa\nt4fJkyEvL/LYZ7EIyKkoDRUVnRoSieiUlNiEYP/93zW8SPIRaLshICrtHaFputtuwPSKy+4+zhRZ\n3Cc/rTVTp8Itt9iRSEoKPPaYnTbbvh2mTLFTZmD34SxbVrNNmTqKUZTooKJTQ6oSnY0bq7P/xkDz\nIrsHpuMnVljarYWWW2F/t4qjli97w76T6p03WVW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      "text/plain": [
       "<matplotlib.figure.Figure at 0x33ac2b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(poly15_data['power_1'], poly15_data['price'], '.',\n",
    "        poly15_data['power_1'], model15.predict(poly15_data), '-')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What do you think of the 15th degree polynomial? Do you think this is appropriate? If we were to change the data do you think you'd get pretty much the same curve? Let's take a look."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Changing the data and re-learning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We're going to split the sales data into four subsets of roughly equal size. Then you will estimate a 15th degree polynomial model on all four subsets of the data. Print the coefficients (you should use .print_rows(num_rows = 16) to view all of them) and plot the resulting fit (as we did above). The quiz will ask you some questions about these results.\n",
    "\n",
    "To split the sales data into four subsets, we perform the following steps:\n",
    "* First split sales into 2 subsets with `.random_split(0.5, seed=0)`. \n",
    "* Next split the resulting subsets into 2 more subsets each. Use `.random_split(0.5, seed=0)`.\n",
    "\n",
    "We set `seed=0` in these steps so that different users get consistent results.\n",
    "You should end up with 4 subsets (`set_1`, `set_2`, `set_3`, `set_4`) of approximately equal size. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "bigset_1 , bigset_2 = sales.random_split(0.5, seed=0)\n",
    "set_1, set_2 = bigset_1.random_split(0.5, seed=0)\n",
    "set_3, set_4 = bigset_2.random_split(0.5, seed=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit a 15th degree polynomial on set_1, set_2, set_3, and set_4 using sqft_living to predict prices. Print the coefficients and make a plot of the resulting model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def get_poly_model(set_data):\n",
    "    poly15_data = polynomial_sframe(set_data['sqft_living'], 15)\n",
    "    poly15_features = poly15_data.column_names()\n",
    "    poly15_data['price'] = set_data['price']\n",
    "    model15 = graphlab.linear_regression.create(poly15_data, target='price', features=poly15_features, validation_set=None)\n",
    "    return poly15_data, model15\n",
    "\n",
    "def get_Coefficient(set_data):\n",
    "    poly15_data, model15 = get_poly_model(set_data)\n",
    "    return model15.get('coefficients')\n",
    "\n",
    "def plot_fitted_line(set_data):\n",
    "    poly15_data, model15 = get_poly_model(set_data)\n",
    "    return plt.plot(poly15_data['power_1'], poly15_data['price'], '.',\n",
    "        poly15_data['power_1'], model15.predict(poly15_data), '-')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre>Linear regression:</pre>"
      ],
      "text/plain": [
       "Linear regression:"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>--------------------------------------------------------</pre>"
      ],
      "text/plain": [
       "--------------------------------------------------------"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of examples          : 5404</pre>"
      ],
      "text/plain": [
       "Number of examples          : 5404"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of features          : 15</pre>"
      ],
      "text/plain": [
       "Number of features          : 15"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of unpacked features : 15</pre>"
      ],
      "text/plain": [
       "Number of unpacked features : 15"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of coefficients    : 16</pre>"
      ],
      "text/plain": [
       "Number of coefficients    : 16"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Starting Newton Method</pre>"
      ],
      "text/plain": [
       "Starting Newton Method"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>--------------------------------------------------------</pre>"
      ],
      "text/plain": [
       "--------------------------------------------------------"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>+-----------+----------+--------------+--------------------+---------------+</pre>"
      ],
      "text/plain": [
       "+-----------+----------+--------------+--------------------+---------------+"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>| Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |</pre>"
      ],
      "text/plain": [
       "| Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>+-----------+----------+--------------+--------------------+---------------+</pre>"
      ],
      "text/plain": [
       "+-----------+----------+--------------+--------------------+---------------+"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>| 1         | 2        | 0.058978     | 2195218.932304     | 248858.822200 |</pre>"
      ],
      "text/plain": [
       "| 1         | 2        | 0.058978     | 2195218.932304     | 248858.822200 |"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>+-----------+----------+--------------+--------------------+---------------+</pre>"
      ],
      "text/plain": [
       "+-----------+----------+--------------+--------------------+---------------+"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>SUCCESS: Optimal solution found.</pre>"
      ],
      "text/plain": [
       "SUCCESS: Optimal solution found."
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre></pre>"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+----------+-------+-------------------+-------------------+\n",
      "|   name   | index |       value       |       stderr      |\n",
      "+----------+-------+-------------------+-------------------+\n",
      "| power_15 |  None | 5.01975232689e-55 | 2.48426782389e-50 |\n",
      "+----------+-------+-------------------+-------------------+\n",
      "[? rows x 4 columns]\n",
      "Note: Only the head of the SFrame is printed. This SFrame is lazily evaluated.\n",
      "You can use sf.materialize() to force materialization.\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<pre>Linear regression:</pre>"
      ],
      "text/plain": [
       "Linear regression:"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>--------------------------------------------------------</pre>"
      ],
      "text/plain": [
       "--------------------------------------------------------"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of examples          : 5404</pre>"
      ],
      "text/plain": [
       "Number of examples          : 5404"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of features          : 15</pre>"
      ],
      "text/plain": [
       "Number of features          : 15"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of unpacked features : 15</pre>"
      ],
      "text/plain": [
       "Number of unpacked features : 15"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of coefficients    : 16</pre>"
      ],
      "text/plain": [
       "Number of coefficients    : 16"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Starting Newton Method</pre>"
      ],
      "text/plain": [
       "Starting Newton Method"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>--------------------------------------------------------</pre>"
      ],
      "text/plain": [
       "--------------------------------------------------------"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>+-----------+----------+--------------+--------------------+---------------+</pre>"
      ],
      "text/plain": [
       "+-----------+----------+--------------+--------------------+---------------+"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>| Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |</pre>"
      ],
      "text/plain": [
       "| Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>+-----------+----------+--------------+--------------------+---------------+</pre>"
      ],
      "text/plain": [
       "+-----------+----------+--------------+--------------------+---------------+"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>| 1         | 2        | 0.072386     | 2195218.932304     | 248858.822200 |</pre>"
      ],
      "text/plain": [
       "| 1         | 2        | 0.072386     | 2195218.932304     | 248858.822200 |"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>+-----------+----------+--------------+--------------------+---------------+</pre>"
      ],
      "text/plain": [
       "+-----------+----------+--------------+--------------------+---------------+"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>SUCCESS: Optimal solution found.</pre>"
      ],
      "text/plain": [
       "SUCCESS: Optimal solution found."
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre></pre>"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x35df5e10>,\n",
       " <matplotlib.lines.Line2D at 0x35df5eb8>]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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IBDYUbeD0Z09n1MmjGHnsyIobGAnHoMzkcbGZ6BhGHWbbj9s447kzuPrYq/lV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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x359ac588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "set_1_coefficient = get_Coefficient(set_1)\n",
    "print set_1_coefficient[set_1_coefficient['name'] == 'power_15']\n",
    "plot_fitted_line(set_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre>Linear regression:</pre>"
      ],
      "text/plain": [
       "Linear regression:"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>--------------------------------------------------------</pre>"
      ],
      "text/plain": [
       "--------------------------------------------------------"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of examples          : 5398</pre>"
      ],
      "text/plain": [
       "Number of examples          : 5398"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of features          : 15</pre>"
      ],
      "text/plain": [
       "Number of features          : 15"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of unpacked features : 15</pre>"
      ],
      "text/plain": [
       "Number of unpacked features : 15"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of coefficients    : 16</pre>"
      ],
      "text/plain": [
       "Number of coefficients    : 16"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Starting Newton Method</pre>"
      ],
      "text/plain": [
       "Starting Newton Method"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>--------------------------------------------------------</pre>"
      ],
      "text/plain": [
       "--------------------------------------------------------"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>+-----------+----------+--------------+--------------------+---------------+</pre>"
      ],
      "text/plain": [
       "+-----------+----------+--------------+--------------------+---------------+"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>| Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |</pre>"
      ],
      "text/plain": [
       "| Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>+-----------+----------+--------------+--------------------+---------------+</pre>"
      ],
      "text/plain": [
       "+-----------+----------+--------------+--------------------+---------------+"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>| 1         | 2        | 0.055977     | 2069212.978547     | 234840.067186 |</pre>"
      ],
      "text/plain": [
       "| 1         | 2        | 0.055977     | 2069212.978547     | 234840.067186 |"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>+-----------+----------+--------------+--------------------+---------------+</pre>"
      ],
      "text/plain": [
       "+-----------+----------+--------------+--------------------+---------------+"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>SUCCESS: Optimal solution found.</pre>"
      ],
      "text/plain": [
       "SUCCESS: Optimal solution found."
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre></pre>"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+----------+-------+-------------------+-------------------+\n",
      "|   name   | index |       value       |       stderr      |\n",
      "+----------+-------+-------------------+-------------------+\n",
      "| power_15 |  None | 1.68636658309e-52 | 4.84361695187e-48 |\n",
      "+----------+-------+-------------------+-------------------+\n",
      "[? rows x 4 columns]\n",
      "Note: Only the head of the SFrame is printed. This SFrame is lazily evaluated.\n",
      "You can use sf.materialize() to force materialization.\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<pre>Linear regression:</pre>"
      ],
      "text/plain": [
       "Linear regression:"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>--------------------------------------------------------</pre>"
      ],
      "text/plain": [
       "--------------------------------------------------------"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of examples          : 5398</pre>"
      ],
      "text/plain": [
       "Number of examples          : 5398"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of features          : 15</pre>"
      ],
      "text/plain": [
       "Number of features          : 15"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of unpacked features : 15</pre>"
      ],
      "text/plain": [
       "Number of unpacked features : 15"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of coefficients    : 16</pre>"
      ],
      "text/plain": [
       "Number of coefficients    : 16"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Starting Newton Method</pre>"
      ],
      "text/plain": [
       "Starting Newton Method"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>--------------------------------------------------------</pre>"
      ],
      "text/plain": [
       "--------------------------------------------------------"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>+-----------+----------+--------------+--------------------+---------------+</pre>"
      ],
      "text/plain": [
       "+-----------+----------+--------------+--------------------+---------------+"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>| Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |</pre>"
      ],
      "text/plain": [
       "| Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>+-----------+----------+--------------+--------------------+---------------+</pre>"
      ],
      "text/plain": [
       "+-----------+----------+--------------+--------------------+---------------+"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>| 1         | 2        | 0.051993     | 2069212.978547     | 234840.067186 |</pre>"
      ],
      "text/plain": [
       "| 1         | 2        | 0.051993     | 2069212.978547     | 234840.067186 |"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>+-----------+----------+--------------+--------------------+---------------+</pre>"
      ],
      "text/plain": [
       "+-----------+----------+--------------+--------------------+---------------+"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>SUCCESS: Optimal solution found.</pre>"
      ],
      "text/plain": [
       "SUCCESS: Optimal solution found."
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre></pre>"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x360ac470>,\n",
       " <matplotlib.lines.Line2D at 0x360ac518>]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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GCuzev5uJSyeydHQOramQB5ilYxiGkQJPvvskZ/Q7gx5tbF56QzDRMQzDaCB+njVbqK3h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\nw0THMAzDyBomOoZhGEbW+P8BhGrt1xPKUWAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x35db4320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "set_2_coefficient = get_Coefficient(set_2)\n",
    "print set_2_coefficient[set_2_coefficient['name'] == 'power_15']\n",
    "plot_fitted_line(set_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre>Linear regression:</pre>"
      ],
      "text/plain": [
       "Linear regression:"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>--------------------------------------------------------</pre>"
      ],
      "text/plain": [
       "--------------------------------------------------------"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of examples          : 5409</pre>"
      ],
      "text/plain": [
       "Number of examples          : 5409"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of features          : 15</pre>"
      ],
      "text/plain": [
       "Number of features          : 15"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of unpacked features : 15</pre>"
      ],
      "text/plain": [
       "Number of unpacked features : 15"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of coefficients    : 16</pre>"
      ],
      "text/plain": [
       "Number of coefficients    : 16"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Starting Newton Method</pre>"
      ],
      "text/plain": [
       "Starting Newton Method"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>--------------------------------------------------------</pre>"
      ],
      "text/plain": [
       "--------------------------------------------------------"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>+-----------+----------+--------------+--------------------+---------------+</pre>"
      ],
      "text/plain": [
       "+-----------+----------+--------------+--------------------+---------------+"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>| Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |</pre>"
      ],
      "text/plain": [
       "| Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>+-----------+----------+--------------+--------------------+---------------+</pre>"
      ],
      "text/plain": [
       "+-----------+----------+--------------+--------------------+---------------+"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>| 1         | 2        | 0.062432     | 2269769.506524     | 251460.072754 |</pre>"
      ],
      "text/plain": [
       "| 1         | 2        | 0.062432     | 2269769.506524     | 251460.072754 |"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>+-----------+----------+--------------+--------------------+---------------+</pre>"
      ],
      "text/plain": [
       "+-----------+----------+--------------+--------------------+---------------+"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>SUCCESS: Optimal solution found.</pre>"
      ],
      "text/plain": [
       "SUCCESS: Optimal solution found."
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre></pre>"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+----------+-------+-------------------+-------------------+\n",
      "|   name   | index |       value       |       stderr      |\n",
      "+----------+-------+-------------------+-------------------+\n",
      "| power_15 |  None | 6.39045886172e-53 | 6.42695506473e-49 |\n",
      "+----------+-------+-------------------+-------------------+\n",
      "[? rows x 4 columns]\n",
      "Note: Only the head of the SFrame is printed. This SFrame is lazily evaluated.\n",
      "You can use sf.materialize() to force materialization.\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<pre>Linear regression:</pre>"
      ],
      "text/plain": [
       "Linear regression:"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>--------------------------------------------------------</pre>"
      ],
      "text/plain": [
       "--------------------------------------------------------"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of examples          : 5409</pre>"
      ],
      "text/plain": [
       "Number of examples          : 5409"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of features          : 15</pre>"
      ],
      "text/plain": [
       "Number of features          : 15"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of unpacked features : 15</pre>"
      ],
      "text/plain": [
       "Number of unpacked features : 15"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of coefficients    : 16</pre>"
      ],
      "text/plain": [
       "Number of coefficients    : 16"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Starting Newton Method</pre>"
      ],
      "text/plain": [
       "Starting Newton Method"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>--------------------------------------------------------</pre>"
      ],
      "text/plain": [
       "--------------------------------------------------------"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>+-----------+----------+--------------+--------------------+---------------+</pre>"
      ],
      "text/plain": [
       "+-----------+----------+--------------+--------------------+---------------+"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>| Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |</pre>"
      ],
      "text/plain": [
       "| Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>+-----------+----------+--------------+--------------------+---------------+</pre>"
      ],
      "text/plain": [
       "+-----------+----------+--------------+--------------------+---------------+"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>| 1         | 2        | 0.078098     | 2269769.506524     | 251460.072754 |</pre>"
      ],
      "text/plain": [
       "| 1         | 2        | 0.078098     | 2269769.506524     | 251460.072754 |"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>+-----------+----------+--------------+--------------------+---------------+</pre>"
      ],
      "text/plain": [
       "+-----------+----------+--------------+--------------------+---------------+"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>SUCCESS: Optimal solution found.</pre>"
      ],
      "text/plain": [
       "SUCCESS: Optimal solution found."
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre></pre>"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x362fc6d8>,\n",
       " <matplotlib.lines.Line2D at 0x362fc780>]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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qqGoVsE9EDovXloh0AvaoanWorR4JjsUwDKMGW8q3MHLGSCZ+eyIn9T4p091p0SQ6D/It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\nesCJJ7p0OPgwWjzOOsudmRNYOkcfHXt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      "text/plain": [
       "<matplotlib.figure.Figure at 0x35f92c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "set_3_coefficient = get_Coefficient(set_3)\n",
    "print set_3_coefficient[set_3_coefficient['name'] == 'power_15']\n",
    "plot_fitted_line(set_3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre>Linear regression:</pre>"
      ],
      "text/plain": [
       "Linear regression:"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>--------------------------------------------------------</pre>"
      ],
      "text/plain": [
       "--------------------------------------------------------"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of examples          : 5402</pre>"
      ],
      "text/plain": [
       "Number of examples          : 5402"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of features          : 15</pre>"
      ],
      "text/plain": [
       "Number of features          : 15"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of unpacked features : 15</pre>"
      ],
      "text/plain": [
       "Number of unpacked features : 15"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of coefficients    : 16</pre>"
      ],
      "text/plain": [
       "Number of coefficients    : 16"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Starting Newton Method</pre>"
      ],
      "text/plain": [
       "Starting Newton Method"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>--------------------------------------------------------</pre>"
      ],
      "text/plain": [
       "--------------------------------------------------------"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>+-----------+----------+--------------+--------------------+---------------+</pre>"
      ],
      "text/plain": [
       "+-----------+----------+--------------+--------------------+---------------+"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>| Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |</pre>"
      ],
      "text/plain": [
       "| Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>+-----------+----------+--------------+--------------------+---------------+</pre>"
      ],
      "text/plain": [
       "+-----------+----------+--------------+--------------------+---------------+"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>| 1         | 2        | 0.056010     | 2314893.173823     | 244563.136754 |</pre>"
      ],
      "text/plain": [
       "| 1         | 2        | 0.056010     | 2314893.173823     | 244563.136754 |"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>+-----------+----------+--------------+--------------------+---------------+</pre>"
      ],
      "text/plain": [
       "+-----------+----------+--------------+--------------------+---------------+"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>SUCCESS: Optimal solution found.</pre>"
      ],
      "text/plain": [
       "SUCCESS: Optimal solution found."
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre></pre>"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+----------+-------+--------------------+--------+\n",
      "|   name   | index |       value        | stderr |\n",
      "+----------+-------+--------------------+--------+\n",
      "| power_15 |  None | -4.74535333046e-51 |  nan   |\n",
      "+----------+-------+--------------------+--------+\n",
      "[? rows x 4 columns]\n",
      "Note: Only the head of the SFrame is printed. This SFrame is lazily evaluated.\n",
      "You can use sf.materialize() to force materialization.\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<pre>Linear regression:</pre>"
      ],
      "text/plain": [
       "Linear regression:"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>--------------------------------------------------------</pre>"
      ],
      "text/plain": [
       "--------------------------------------------------------"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of examples          : 5402</pre>"
      ],
      "text/plain": [
       "Number of examples          : 5402"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of features          : 15</pre>"
      ],
      "text/plain": [
       "Number of features          : 15"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of unpacked features : 15</pre>"
      ],
      "text/plain": [
       "Number of unpacked features : 15"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of coefficients    : 16</pre>"
      ],
      "text/plain": [
       "Number of coefficients    : 16"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Starting Newton Method</pre>"
      ],
      "text/plain": [
       "Starting Newton Method"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>--------------------------------------------------------</pre>"
      ],
      "text/plain": [
       "--------------------------------------------------------"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>+-----------+----------+--------------+--------------------+---------------+</pre>"
      ],
      "text/plain": [
       "+-----------+----------+--------------+--------------------+---------------+"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>| Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |</pre>"
      ],
      "text/plain": [
       "| Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>+-----------+----------+--------------+--------------------+---------------+</pre>"
      ],
      "text/plain": [
       "+-----------+----------+--------------+--------------------+---------------+"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>| 1         | 2        | 0.123982     | 2314893.173823     | 244563.136754 |</pre>"
      ],
      "text/plain": [
       "| 1         | 2        | 0.123982     | 2314893.173823     | 244563.136754 |"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>+-----------+----------+--------------+--------------------+---------------+</pre>"
      ],
      "text/plain": [
       "+-----------+----------+--------------+--------------------+---------------+"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>SUCCESS: Optimal solution found.</pre>"
      ],
      "text/plain": [
       "SUCCESS: Optimal solution found."
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre></pre>"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x36551da0>,\n",
       " <matplotlib.lines.Line2D at 0x36551e48>]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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hNYd1Oizb5mQNC50ZRgfC3hXTujyz6hkuHHZhhxaZdGNCYxjNkO2wVWvM3GxEKV9ezhVj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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x363414a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "set_4_coefficient = get_Coefficient(set_4)\n",
    "print set_4_coefficient[set_4_coefficient['name'] == 'power_15']\n",
    "plot_fitted_line(set_4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some questions you will be asked on your quiz:\n",
    "\n",
    "**Quiz Question: Is the sign (positive or negative) for power_15 the same in all four models?**\n",
    "* Set-1 power_15 |  None | 5.01975232689e-55 \n",
    "* Set-2 power_15 |  None | 1.68636658309e-52 | 4.84361695187e-48\n",
    "* Set-3 power_15 |  None | 6.39045886172e-53 | 6.42695506473e-49\n",
    "* Set-4  power_15 |  None | -4.74535333046e-51 |  nan\n",
    "\n",
    "* (No) -> Set 4 - value sign is negative, for the rest -> positive.\n",
    "\n",
    "**Quiz Question: (True/False) the plotted fitted lines look the same in all four plots**\n",
    "* No"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Selecting a Polynomial Degree"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Whenever we have a \"magic\" parameter like the degree of the polynomial there is one well-known way to select these parameters: validation set. (We will explore another approach in week 4).\n",
    "\n",
    "We split the sales dataset 3-way into training set, test set, and validation set as follows:\n",
    "\n",
    "* Split our sales data into 2 sets: `training_and_validation` and `testing`. Use `random_split(0.9, seed=1)`.\n",
    "* Further split our training data into two sets: `training` and `validation`. Use `random_split(0.5, seed=1)`.\n",
    "\n",
    "Again, we set `seed=1` to obtain consistent results for different users."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "training_and_validation, testing = sales.random_split(0.9, seed=1)\n",
    "training, validation = training_and_validation.random_split(0.5, seed=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next you should write a loop that does the following:\n",
    "* For degree in [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15] (to get this in python type range(1, 15+1))\n",
    "    * Build an SFrame of polynomial data of train_data['sqft_living'] at the current degree\n",
    "    * hint: my_features = poly_data.column_names() gives you a list e.g. ['power_1', 'power_2', 'power_3'] which you might find useful for graphlab.linear_regression.create( features = my_features)\n",
    "    * Add train_data['price'] to the polynomial SFrame\n",
    "    * Learn a polynomial regression model to sqft vs price with that degree on TRAIN data\n",
    "    * Compute the RSS on VALIDATION data (here you will want to use .predict()) for that degree and you will need to make a polynmial SFrame using validation data.\n",
    "* Report which degree had the lowest RSS on validation data (remember python indexes from 0)\n",
    "\n",
    "(Note you can turn off the print out of linear_regression.create() with verbose = False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5 5.8918247781e+14 15\n"
     ]
    }
   ],
   "source": [
    "arr = []\n",
    "for degree in range(1, 16):\n",
    "    poly_data = polynomial_sframe(training['sqft_living'], degree)\n",
    "    poly_features = poly_data.column_names()\n",
    "    poly_data['price'] = training['price']\n",
    "    poly_model = graphlab.linear_regression.create(poly_data, target='price', features=poly_features, \n",
    "                                                   validation_set= None, verbose = False)\n",
    "    poly_validation = polynomial_sframe(validation['sqft_living'], degree)\n",
    "    predictions = poly_model.predict(poly_validation)\n",
    "    residuals = validation['price'] - predictions\n",
    "    RSS = (residuals * residuals).sum()\n",
    "    arr.append(RSS)\n",
    "    #print arr, degree   \n",
    "\n",
    "print arr.index(min(arr)), min(arr)   \n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Quiz Question: Which degree (1, 2, …, 15) had the lowest RSS on Validation data?**\n",
    "* Model 6 -> array(5) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that you have chosen the degree of your polynomial using validation data, compute the RSS of this model on TEST data. Report the RSS on your quiz."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.25264322989e+14\n"
     ]
    }
   ],
   "source": [
    "# arrtest = []\n",
    "# for degree in range(1, 16):\n",
    "#     poly_data = polynomial_sframe(training['sqft_living'], degree)\n",
    "#     poly_features = poly_data.column_names()\n",
    "#     poly_data['price'] = training['price']\n",
    "#     poly_model = graphlab.linear_regression.create(poly_data, target='price', features=poly_features,\n",
    "#                                                   validation_set = None, varbose = False)\n",
    "    \n",
    "poly_val_data = polynomial_sframe(validation['sqft_living'], 6)\n",
    "poly_val_features = poly_val_data.column_names()\n",
    "poly_val_data['price'] = validation['price']\n",
    "poly_val_model = graphlab.linear_regression.create(poly_val_data, target='price', features=poly_val_features,\n",
    "                                                  validation_set = None, verbose = False)\n",
    "poly_test = polynomial_sframe(testing['sqft_living'], 6)\n",
    "predictions = poly_val_model.predict(poly_test)\n",
    "residuals = testing['price'] - predictions\n",
    "RSS = (residuals * residuals).sum()\n",
    "print RSS"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Quiz Question: what is the RSS on TEST data for the model with the degree selected from Validation data?**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "125264322989000.0"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1.25264322989e+14"
   ]
  },
  {
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    "### Quiz\n",
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