Course_2/Week_3_Assessing_fit.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 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": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import graphlab\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sales = graphlab.SFrame('kc_house_data.gl/')\n",
    "sales = sales.sort(['sqft_living','price'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def polynomial_sframe(feature, degree):\n",
    "    poly_sframe = graphlab.SFrame()\n",
    "    poly_sframe['power_1'] = feature\n",
    "    if degree > 1:\n",
    "        for power in range(2, degree+1):\n",
    "            name = 'power_' + str(power)\n",
    "            tmp = feature.apply(lambda x: x**power)\n",
    "            poly_sframe[name] = tmp\n",
    "    return poly_sframe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "poly1_data = polynomial_sframe(sales['sqft_living'], 1)\n",
    "poly1_data['price'] = sales['price']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create different models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Linear model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PROGRESS: Linear regression:\n",
      "PROGRESS: --------------------------------------------------------\n",
      "PROGRESS: Number of examples          : 21613\n",
      "PROGRESS: Number of features          : 1\n",
      "PROGRESS: Number of unpacked features : 1\n",
      "PROGRESS: Number of coefficients    : 2\n",
      "PROGRESS: Starting Newton Method\n",
      "PROGRESS: --------------------------------------------------------\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: | Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: | 1         | 2        | 0.013398     | 4362074.696077     | 261440.790724 |\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: SUCCESS: Optimal solution found.\n",
      "PROGRESS:\n"
     ]
    }
   ],
   "source": [
    "model1 = graphlab.linear_regression.create(poly1_data, target = 'price', features = ['power_1'], validation_set = None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x116c20690>,\n",
       " <matplotlib.lines.Line2D at 0x116c20450>]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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wrrglS6JTwSQzcb5ihROb3r2jsyVk8h2ku0z4t8aHuz/kkbWPULmmkpc/fJkL\nh17IN8d8k0eufIQj84/MtHlGpknF8CmbPph7rV2E3VBFRapnnul+FhdHu6tUE6/mb8tlFri/ktk9\ns70JPWNdeOF9esLXy5QbKpdW+7eH93e9r3esuEPP/t3ZWnhboX7t4a/po7WP6qf7Ps20aUYHwXYO\nNdLBvHmRiLKdO2HDBvcT3GgkmcSTbSWqfO65SI41cOWSEjcxH4yCgoWir7zi8rCdemp0HrPwyCVc\nLi11AQlB4tHwNcDleYs3cuoIwailsRFE3Igq3uilo/npsp13d75LVW0VVbVVrN++notPupibz7qZ\n84acx2F5h2XaPCNLMdExoigtdfMnsSHO8ViyJHFIdCxhMQsLDkBDg/sZzkwdzlgdewyiXWSx7rJw\nXsfiYujZMxLaXFDQdelzYueegrpYIQu3mzAh8jvrymSg6XLbbdi+garaKirXVPJ+w/tMGzaNOeVz\nmDBoAr169krNRY1uhYnOIUprD6lgMr+xEfbuhaYm9yAPRhuxczkDBkT3Fc6rNmeOm7gP5mcCwpml\n49kV3vYgns1hYQkWaAb07h0pn3GGsyGw97774M47I7Ym8/toj41t0Z78dO0hldsg1G6rpXJNJVW1\nVdTvqefSYZfy8/N/zj98/h/I62GPEKOdpMJnl00fbE4nLvHmFmLnYhJlkA5vtBbMjyQzJxNuv3ix\nKwfzRvGuWVQUHfocPjZ+vDtWUqK6alX0NVu7j0TzOe2Za4m3+dzEiYnnidIRztyVc0XNzc362pbX\n9EfLfqRld5Zp6e2l+t0l39W/bvyrbeN8CIHN6RipJvZtOcwbb0Tvf9NRTjvNvYWHs0TX1kJeHkyf\nHt12/PjEb+xvvRWdDWD16tY3jQuInc/pzKglfD+tkY5s0Z3dw0dVWb1l9cFNz/Yd2EdFWQX3XnQv\n40rH0UNsHbnRNdg6nUOUeO6k8BqXoiIYPtwFEgQr74Ow5vHj3UMf4rvXwAUBvPQS7N7t3r/z8uCU\nU9ycSu/esGsX/P3vLe1qLZ9ZojVEEL0mJ1F49qpVLdPWxKa1SWY9UHcJe1ZVXqh74eAcTQ/pweVl\nl3NZ2WWMGTDGNj3rRnTk36zlXusgJjqtE/7HGMx9xE605+e7NTi9eyeO0Ar3FX64hwnnKisqikTF\nhYldhJooQgyi87YVFTlhixXI1sQoVmizIWdZqgWtWZtZsWnFwTmaI/OPpGJ4BRVlFZx8zMkmNN2U\njvw7T5XHdzaVAAAeBUlEQVToZHzOJdUfbE6nVWLnAmLnYMKfPn1artlZtSoyt3LmmYnPjbdWJvZ4\ncXEkjU6wlic8f5RoDiq2r9bW/cSyebObH8rPd9datSqzKWVSsY6n6UCTLn93ud6w+AYd8IsBOvKu\nkTqnZo7trnkI0ZF/V9icjpEOgrmBnTtdlNr+/ZFju3dHysGanfCoJgh9BjfqaGpyZRHnVtu1K/L9\nF7+ABx+MPv+MMyKjj9h1NvEI5krCb3EAJ5zg3GTB/bTVx1tvuUi6HTvcW2A4ZLyrI8HSRVNzEzUb\na6hcU8kjax+htE8pFWUVLJ+xnJM+d1KmzTPSTGfn/LoSE51DmLo657YKL8wMP8jDgpMM+/ZFXHG/\n+lX0Tp7hIAVV+J//080NjRjR0m3W2Niy76Ii504LtwsWkL70UnTbVIUlp4POPBz2HdjHs+88S1Vt\nFY+te4whRUOoGF7BiutWMKRoSNcba+QMWbX1eSqGT9n0wdxrCYkNiQ5nZ544MXJMJNp91auXc6WF\n3WvhNuGUOAGbN0e718Ll2OF++NqtuQQSuQIDt1i8bNPxCLsIM+1eay+N+xt10dpFOv2R6Vp0W5Ge\nde9Z+su//1I37tyYadOMHIcUudeSeWgPBJYBbwKvA9/19UVANbAOWAoUhM6ZBWwAaoELQvWjgdeA\n9cAdofp8YKE/ZwVwfOjYDN9+HTA9VD8IWOmPPQDkJbA/FX+PbkHsepPwgzu8LicZEUiUhy3M4sVO\nbPLzVUeOjL5WIrvy8xOLRjzRKSlpuTanu+U527Nvj1atqdKrK6/WwtsK9Zzfn6O/ef43urkhyxXS\nyCkyKTr9gVN9+Sj/8B8GzAV+4OtvAm7z5TJgNc51Nwh4i0iU3PPAab68BJjky98G7vLlK4GFGhG2\nt4ECoDAo+2MPApf78t3ANxPYn5I/SHcg/EYfKyyxSTSnTHFBBPGEIt5kfFvXyMuLlCdObGlXMqOU\noF28hKTdTXR2792tD77xoF7+0OXa96d99bwF5+lvV/1Wt+zekmnTjG5KxkSnxQnwKHAesBY4RiPC\ntNaXbwZuCrV/Ejjdt1kTqr8KuNuXnwJO9+WewNbYNhoRlyt9eRvQw5fPAJ5KYG/X/iWynNY2UIt9\nkIfbrlqV+EEftAtHkoWFIiwmvXpFZwlobTQVO6oKr+wP95msYLT3frrKfZYqd9yuxl36h1f/oNMW\nTtM+P+mjk/8wWe956R7dtmdb113EMBKQFaLjRy4b/YhnZ8yxHf7nb4CvhurvAS4FxgDVofqzgUW+\n/DpwbOjYBqAY+B7ww1D9/wH+BTgaWB+qHwi8lsDmLv1DZCvxwocTbQUQLzw6cEuF+woe3vHEItx3\nvON5eW7eJzx3U1TkRCncrkcP92ktvDrs6mvtoZ5sWGhHwkdbE5auDHPe/ul2/f3q3+uX//RlPerf\n+2i/G7+iJ0+/T994e0fnOjaMdpIq0Uk6ek1EjgIqgRtV9RMR0Zgmsd87QzILkpJetDR79uyD5fLy\ncsrLy9tvUZYTL+NxW4SjxLZtc2lonn02uq/YhZ7BIszPPnPRY4m2EmhqaplxYOdO6BGTTaW5Ob5t\n4a0IPv440v8110RnIkgXqUyo+dGnH/H7FY/ysycq2XXUCs77wrlcM+Zq9v7pjzz9RF+2Aj/4qOU1\nu0tmBCM7qKmpoaamJvUXSkaZcPMzT+EEJ6irJdq9VuvLse61p4i412pD9cm6134bOue3RNxrW4l2\nrz2ZwPaulf8sJfy2nZfnRgpBhJmqG7EUFUXqFy9W7dkzenTRq1dksj+eSyxwVYVHIyUl7pwpU9y8\nTjz3WXs+xcUtR06x9gQEo4/ALddW4s3Y84J2ybjHWhvNtCdSLuDD3R/qXS/cpRPnT9SCnxbogO9c\noZQ9pOTvPth/WyOo7rohnJEdkEn3GrAA+GVM3dxAXIgfSJAPDCY6kGAlMA43SlkCTPb11xMJJLiK\n+IEEQbnQH3swJEB3A99KYHsK/hzZR6LV+cGDNFyfn9/SzRXvAZ+f33JuJF4kW8+ekeOFhR0XnLw8\n10esSy/RXFKi6LX2ZntO5uHdljAl1UfDZv31yl/rl37/JS28rVC/WvVVfXjNw7pn356ksn535JqG\n0VEyJjrAWcAB4BUvJi8Dk3FzLs/gotmqAzHw58zyYhMbMj0GN3+zAfhVqP4w4CFfvxIYFDp2ra9f\nT3TI9GBcNNx6L0C9Etifkj9IttLW3E1bn1jRSbTFQezanbBwJHutRH2EtzJoLSigtftqz8igIw/8\nZLeBWFm7UW//++06/p7xWjy3WGc8MkMfX/e4Nu5vbLW/ZMil9URG7pHRkU4ufw410Yl1o23eHH90\nEghEXp7LqVZc7NqPGdNSAMLnByONZFxpI0e2T4TCo5VY4gU9xLrXYkdzwULPeHnc4oWEhx/ebY0i\nYn8n4T7OmPKWctZc5Z9O0/xbPqffeOwb+uSGJ3Vv096u/4MbRoow0THRiaI9rqIJE+I/3OfPj16J\nH2/kEIhRWy6wZEY1iVx6sZ/x41veW2vriMK/k9j5n9h7inW/xQpXvJFLOLIvIHaua+22tfrjv/xY\nT/3tqZp/Sz9l6reUwc/o5Cn7u/6PbxhpwETHRCeKWHdO8DZfUBAtGMGbfryHeziQoG/f+CJSUBA/\n03OwIDNZ0Skudna0lYn6iCOixSmRcMZmKgiEoi3RiRWreEIb9NtaturyCc1Kv9eV8lv1yP89Qo+9\n/Vj9zpLv6F82/kXfe7/J3F5GzpMq0bGEn92A8K6eYXbscCG14S1SRNxjFODAgUj9xx/H73v37vhh\nzfH2wmmNHTtc2HNbu45++mn098ZGOPNMWLEiun7fPhc6PX06LFgQvbeOCPTqBffd5zaOu+Ya9zsa\nOtSFek+dGgkx/uyzlja8/ro7Fs42De4F7dX6V6lcU8mmiyrpfUYj/Xdexh1X/xdfGXVG1O6aqUqu\naGHSRq5jm7jlKK3tohmmb1/34A4yRhcWRrYYyAbCIhiPsWPdFguJCHb7jLdGKXazqnPPjfyeJk50\na5ImTmy5xmjCBNeurg7+aabScOSLnHJ1JdWbqlD04KZnY48dm/ZNz7Jt0zmj+5KqTdxspNMNmDsX\nfvCDyNs8uAf1vn0tRzDBostsoa33gVdfbf34iBHRo5VevVpuyRAI9N/+Fql7/XX3M9gaGyIC9tv/\nambFpuf5z+WVLB1WhRw4jJP2VPDny//Mqf1PjSs0NgIxjOSwkU6OEPtQmz695Vt7uN2KFe13gaWS\ntkY0+fkwZkzLjeNiKSyEsrLorbOvuSYyWikocH0NHRppE28k2KuXy5gwYIA7//U3D3DcWc9x6tWV\nVG96mMLehbz9RAWfvVQBW79IcbGwfXtiu9I1AjFxM9KFjXQOcWLTsARv6uDe4IN5irAYZROFhW7U\nFZ5HCqMK69bFF5z8fDj7bDeiC28MV1rqHsJvvBFpG+xe2tAQGdWVlESOB+K3fz9cOLWJO5/4KyuK\nK/ls+sN8tHsAtfdUMKz5GepeHcZnoXmy8K6pmSSrNuMyjA5gI50sI9GbbOybdGNjy7mIM8+EtWvd\npH2YoqLkRz1tjUg6QmEhPP00XHBB8naEt7sGd88Q+R1MmOBcY7G54eIRtG1shP/39/00DVwGZZVI\n2aP0PTCIhhUVUHsZ7DghYR/h7bbj8eKL0TaOHRt93EYoRq6RqpFOxkOaU/0hx0KmE61sj12VH6yr\niV3VH5tPraBAdcSI1sOU0/EZMaKlba19evSIDsmOzfuWzCcImX77vc/08XWPa+kN1yo/KFauG689\nz/6FPvaXd5PO1hC70VxrfzfLk2Z0B7CQ6e5PXZ17cw8Ih0I3NrpJ9R07nPvspptcqPCgQdEjglj3\nVUNDxOWUScIusGRobnbuuCAwYNs29zuIHQGBc78VFESPeD7Xv5GfVi5leX0lYx5YzMh+Iyn4tIK6\n+/8NPh7IpClw0ZdgzBfcCKSxMTLK27sXNmyInheaN6/zvwPDMMy9ljXU1UWvNSkqcg/BwFVWUhL9\nUC0pgZEjs3P+JlXk58ePvhs/3gnD6jf20DR4CUeMreSzgUsZWzqGiuEVXDL8Evof1T/KxTVnTiTi\nb+RIJ+CdcXm15T4z95qRa6TKvWaikyWE52wAiouj52Zi3/ALC2HPntYjvXKRgoL4I7N4odAARf0/\nZsA5i1mjlTDkGXptPYMhjRX0/WAaG9eUHBytqDoRD0YtsfsPBRFnJg6G4bDotUOI/PyW0VKxLqVs\nWuDZlSTKWBAlOL13wUmLyDu5ko8/X8OezV+CVyrg8f9mf2Mx60JN4wUZBKISJljrExslGAgUtBQh\nEyjDaD820skQsQ8scN+TicbqrvTsCStXwnnnxRntHL4dhj2GfLESHfgcvDuRnusv48Car8DegoNh\n0cn87iZOdO60kSMj0XTjxzuXZvj3HxsxV1ICq1cnjihsTaAMI9ewkU43I7ye5oor4LDD3PxConUs\nydKnT/asKWkvBw64eZY9e3zFkfUw7FEoq4TSF+DtCxi6ZwaFf3uQVc/14UDoXaKpCYYPd+UgK8OG\nDXD88fDuuy4oIRgtqjpBGD8+IhovvRS9rue006JFBJwYtbZVdXiUNGpUtEAZhuFJRUhcNn3IopDp\n8N4u4UzK4czIwfe2sjG3Fmqc6fDoTn361CnjfqPMKFduLlAuu1oZXqX02nMwDLqtLRKCPX9WrWr5\nuw2HLLd1PPibJco23dpGbhYabeQ6pChk2txraSQ2WCAg3iR5okitbknB+zD8YTeiKVkD678Mayrg\n7QugqTdAu9xnJSWwdSv069cy4i8YwZSWtvx7xB4PiI16i82KEG4XjkC0hJxGLmPutW6ISPRK93A2\ngG4vOEXvwPAqJzTFb8Pai+Gvt8C758KBltEEQ4e6iL1Y0R49Gvr3j841d9xxTnA++ijSLj+/dXdX\nUVFkjufkk93fYfhwd8158yLiERaqWFdbaam7RuxcXUCygQcWoGB0a9oaCgH3AvXAa6G6IqAaWAcs\nBQpCx2YBG4Ba4IJQ/WjgNWA9cEeoPh9Y6M9ZARwfOjbDt18HTA/VDwJW+mMPAHmt2N+1Y85OsGpV\ny+2bw+6dYJvpjLu4UvU5ep1y9k+UmaOV/91P+fI3lSHVSo99bZ4bbEgX3uUzvNtnkKFhypToTAYi\nkZ1RVaNdYuFzWst2EHaTdSazQLLntrVrqWGkA1LkXktGdM4GTo0RnbnAD3z5JuA2Xy4DVuNGUIOA\nt4hEyD0PnObLS4BJvvxt4C5fvhJY6MtFwNtAAVAYlP2xB4HLfflu4Jut2J+CP0fHiPdgKyqKlAsK\nWqa1yflPyZvKOXOUb49UvjdAmXKDMmi5Ik3t7isvT7WwMLKzZ6KUQYWFkfri4ui/QaIHf2vpcFqb\nx2kPHRGdjoibYXQFqRKdNt1rqvo3Efl8TPXFwDm+PB+oAW4GLvKi0QRsFJENwDgReQ/oo6pBkpcF\nwDTcKOli4FZfXwn8xpcnAdWq2gAgItXAZC84E4GrQ9efDfxXW/eSTgIXSZBepXdveOWV6Db5+c6F\n07u3yxrdPUKlFY553bnNyiohf7ebn1l8F2w6E7RH2114gm0JApqanCty2TK3HUF4W5sgRRC4CL6A\nwYOTu1YQqbZzp8t2rRrtXgvoTJbn2JDq1tqF54YMozvR0TmdfqpaD6CqW0Skn68vxbnIAup8XROw\nOVS/2dcH52zyfR0QkQYRKQ7Xh/sSkaOBnaraHOrr2A7eR8qIXfEej3373J4uuY/CgJcjQtOjyQnN\no7+HD05rl9CEibeVdMAbb7gN3OKxd2+k/P770cfmzInkt5szJ1Kfji0Dkr1GW3NDhpHLdFUggXZR\nPwDJREukd4/gdhKbuLNbIs1u7UwQDNCcB2suh8qF8OFoUv0nGjo0OonoKadEdgGtr3frbgBOOKHl\n1t7BCOKss+C551puQ5AN2L45Rnelo6JTLyLHqGq9iPQHtvr6OuC4ULuBvi5RfficD0SkJ9BXVXeI\nSB1QHnPOclXdLiIFItLDj3bCfcVl9uzZB8vl5eWUl5cnbNsZgj1Vdu6MLEQUcSvtY9PY5CTSDMf9\n3YnM8CrY18eNaBY+BvUjSaXQhMPKS0qc6y0Qj/x8N7oJskOHw88PPzx61BlOs7Nvn1sgunFj/Agx\niyIzDiVqamqoqalJ/YWSmfjBBQW8Hvo+F7jJl+MFEuQDg4kOJFgJjMM9mZYAk3399UQCCa4ifiBB\nUC70xx4ErvTlu4FvtWJ718yqJSBY8Nm3bxZM2qfi02O/MmiZMuV6FwjwrZOVL/2rCxBIox3hiLRg\nIj+Z85LZhyfRRH069sDpTGCCYaQSUhRI0HYD+BPwAbAXeB/4uheBZ3ChzNWBGPj2s7zYxIZMjwFe\nx4VG/ypUfxjwkK9fCQwKHbvW168nOmR6MC4abr0XoF6t2J+Kv8dBkn345dSnxz4Xyvzlmcr3S1yI\n89k/cSHPGbJpzBjV8eNdSHlxserixe53H84WEP60Fooejm7LtOjY5m5GtpIq0bGMBJ3gxRfhjDM6\nny8tK+i5D4Y841xnJy1yWzevqYA1l8GuJEPAUkh+Phx1VCRCTQReeAEGDIhECQbutZEjXZvYvYby\n8+Hss2Hu3OT20kmHey02aWi8eRxz8xmZwPbT6SCpEp26OhgyJMczB+R9Bl9YCmVVcOITsPWLUHsZ\n1F4KDcdn2roWxKYGCtLdhAke0EHo8yefRJ8T78GeyYd6MtdORpgMo6uxNDhZxvTpOSo4vT6FE550\nI5qhT8KHo9yI5pnbYHfWRZ5HMWaM2/qgtXeIeKHqreWxi82X1loW6VRgUWrGoYaJTjsJItRyauFe\n/m44cbGLOPtCNdSd7oTmqV/Bnn5tn58F5OW5SLQzznAjmJ49214HFTB2rFvkCS3XvMycmf1/y2QX\nlRpGLmDutXZQV+dWuOfEFtGHNcBJj7sRzaDlsOksJzRrL4bGozNtXbsJb9/dmospcFeFE4BOmNBy\nficg7LqK3aTNMA5lzL2WBcycmeWCc/gOOOkxJzTH/w02lvvMAPfBZ4WZtq7d9OnjJvoLC92iznjC\nEW9OZPHiaDEJFo3Gw3b7NIz0YiOdJKmrg7IytwNlVnHEtsjumgNXwjvnu4izDVNhb99MW9du8vIi\nC2nD+9tAy1x2gWDEm2SPl/vORMUwksdGOhkg/OB66aUsEpyjPoThjzihGfAyvDUZXv4nePBh2H9k\npq3rFOH3g23bnKDMnBkRnjfeiJ70T0S8EU+6gwQMw2iJiU4rJJO0M2303RzZXbPf624k8/x34a1J\n0NSK/yjHSLTmKdHfoq1J9sbG+GXDMDKDiU4ClizJAsEp3BhJqHn0elh3EfztJnjnPDhwWIaN6ziF\nhZHdUlujqMi52+Jlmy4piZ7DSUR4+wPJ6jSxhnFoYKKTgEsuydCFi9+KCE3hRlh7CdTMho0T4m7j\nnIscOABHHAGfftryWFGRWzcT7KWzbJn7TJjghCZwrZ12mvs5dar7mWi+pnfv+GXDMDKDiU6IYA5n\ny5Y0L/z83NrIXjRHbXEZAZ6ZC+99yW0Z0M3YvTvxsfHjIyOXQFDARaDF7jETdrklmq+xNS6GkV10\nvydaB4ldmZ5aFPq94YWmCnrvchFnS37jd9fsmQ4jUs6RR8KePcm1DfKihYUhXjhzewMBbMW/YWQX\nFjLtOffcxAsIuwaF/q9ERjR5e53QrKlwGQI6uLtmNnPmmZGdUQsKXGRaMJkfXu9UWOii0tobzmyJ\nMA0jdVjCzw7SlugED67q6lRstKZQuioiNNrDZ26ugA/GkOUboHaYXr3g0UfhzjsTr6G55pq2szwb\nhpE5THQ6SGui8+KLcPrp0NzclRdshoErnNtseJULZw6EZsspdFehgZZpZGwkYhi5i4lOB2lNdPr0\ncanvO3+RAy7tTFmlW0vTWBwRmm1ldFehmTDB/bQRi2F0P0x0OkhrotOpdRs9mmBQjROaYY+6bQGC\nTc+2n9SJjjNLvFDmPn3gxBPh/fdh6FAXemxpZQyje2Oi00FaE51evdo5j9NzHwxe5nfXfMztqBkI\nzc4vdI3BaSQvz62LWbLEpf8Hc4kZhuEw0ekg8UQnvB7n1Vfb2G467zMY8rQTmhOfgI+GOaGpvRQa\nPp9a4zvJN77hXF7NzTB8uLtfG6kYhpEMJjpxEJHJwB1AD+BeVZ0bp00L0Ynd/vfpp2O2LOj1qd/G\nuRKGLoH6U9xopvZS2J1dT+nCQmf/gAE2QjEMo+tIlejk7OIQEekB/CcwCfgicLWIDGtvP42Nbh6D\n/E/giw/B5VfA9wbAuDvh/X+AO2vhvhp44TsZEZwbbqhBlYSfnTudayxYBLl4cfYITk1NTaZN6BRm\nf2Yx+7snOSs6wDhgg6q+p6r7gYXAxcmcOG+eG+Gc/5UG6o/5Iw2TL4V/KYVRv4O3L4BfvwULnoEX\nvwWf9O9So3v0cMKwapWbT8nPd4soN2+OLyqf+1xNl14/neT6fzqzP7OY/d2TXE6DUwpsCn3fjBOi\ntk8shSE3fIf5r87n8PpzoKYCHruX3hTFzWicLHl5cMopbvV9MnMmwfbLhmEYhwq5LDqd4hujv8GP\nJ/6YT7YXMHMDUBotEsGq+VdecaHVw4bZBLxhGEZnydlAAhE5A5itqpP995sBjQ0mEJHcvEHDMIwM\nY9FrIUSkJ7AOOBf4EHgBuFpVazNqmGEYhpGQnHWvqeoBEflnoJpIyLQJjmEYRhaTsyMdwzAMI/fI\n5ZDpVhGRySKyVkTWi8hNmbYnQEQGisgyEXlTRF4Xke/6+iIRqRaRdSKyVEQKQufMEpENIlIrIheE\n6keLyGv+Hu9I4z30EJGXRWRRDtpeICJ/9va8KSKn55j9s7zdr4nIH0UkP5vtF5F7RaReRF4L1XWZ\nvf7+F/pzVojI8Wmw/2fevldEpEpE+uaS/aFj3xORZhEpTqv9qtrtPjgxfQv4PNALeAUYlmm7vG39\ngVN9+SjcvNQwYC7wA19/E3CbL5cBq3Gu0EH+voIR6vPAab68BJiUpnv4X8AfgEX+ey7Zfh/wdV/O\nAwpyxX7/7/kdIN9/fxCYkc32A2cDpwKvheq6zF7g28BdvnwlsDAN9p8H9PDl24Cf5pL9vn4g8BTw\nLlDs64anw/6U/yfPxAc4A3gy9P1m4KZM25XA1kf9P+K1wDG+rj+wNp7twJPA6b7NmlD9VcDdabB3\nIPA0UE5EdHLF9r7A23Hqc8X+Im9rkX8wLMqFfzs4sQw/tLvMXtyD83Rf7glsS7X9McemAffnmv3A\nn4GRRItOWuzvru61eAtHs25ljYgMwr2FrMT9J6wHUNUtQD/fLPZe6nxdKe6+AtJ1j/8BfB8ITwbm\niu2DgY9E5PfePThPRI4gR+xX1Z3A7cD73pYGVX2GHLE/RL8utPfgOap6ANgVdhelgX/EvflH2eLJ\nSvtF5CJgk6q+HnMoLfZ3V9HJekTkKKASuFFVPyH6IU6c7xlHRKYC9ar6Cq3vTJd1tnvygNHAnao6\nGtiDe7vL+t89gIgMwbk2Pw8cCxwpIv+DHLG/FbrS3rTtmCgitwD7VfWBruy2C/tq2bnI4cAPgVtT\ndYm2GnRX0akDwhNaA31dViAieTjBuV9VH/PV9SJyjD/eH9jq6+uA40KnB/eSqD6VnAVcJCLvAA8A\nE0XkfmBLDtgO7g1tk6q+6L9X4UQoF373AGOB51R1h3+rfAQ4k9yxP6Ar7T14TNzavb6qmvIEUyJy\nLTAF+GqoOhfs/wJuvuZVEXnX2/KyiPQj8XOzS+3vrqKzCjhBRD4vIvk4H+SiDNsU5nc4H+mvQnWL\ngGt9eQbwWKj+Kh8lMhg4AXjBuyUaRGSciAgwPXROSlDVH6rq8ao6BPc7Xaaq1wCPZ7vt3v56YJOI\nnOirzgXeJAd+9551wBki0ttf91xgTQ7YL0S/AXelvYt8HwCXA8tSbb+4LVW+D1ykqntD7bLeflV9\nQ1X7q+oQVR2MexEbpapbvS1Xptz+rp60ypYPMBn3n3QDcHOm7QnZdRZwABdRtxp42dtaDDzjba4G\nCkPnzMJFktQCF4TqxwCv+3v8VZrv4xwigQQ5YztwCu6l5BXgYVz0Wi7Z/32cUL4GzMdFZ2at/cCf\ngA+Avbi5qK/jAiG6xF7gMOAhX78SGJQG+zcA7/n/uy/jo7dyxf6Y4+/gAwnSZb8tDjUMwzDSRnd1\nrxmGYRhZiImOYRiGkTZMdAzDMIy0YaJjGIZhpA0THcMwDCNtmOgYhmEYacNExzAMw0gbJjqGYRhG\n2vj/yt/Zrsj2F4YAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116c20810>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.plot(poly1_data['power_1'], poly1_data['price'],'.',\n",
    "         poly1_data['power_1'], model1.predict(poly1_data),'-')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "poly2_data = polynomial_sframe(sales['sqft_living'], 2)\n",
    "poly2_data['price'] = sales['price']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PROGRESS: Linear regression:\n",
      "PROGRESS: --------------------------------------------------------\n",
      "PROGRESS: Number of examples          : 21613\n",
      "PROGRESS: Number of features          : 2\n",
      "PROGRESS: Number of unpacked features : 2\n",
      "PROGRESS: Number of coefficients    : 3\n",
      "PROGRESS: Starting Newton Method\n",
      "PROGRESS: --------------------------------------------------------\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: | Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: | 1         | 2        | 0.015301     | 5913020.984255     | 250948.368758 |\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: SUCCESS: Optimal solution found.\n",
      "PROGRESS:\n"
     ]
    }
   ],
   "source": [
    "model2 = graphlab.linear_regression.create(poly2_data, \n",
    "                                           target = 'price', \n",
    "                                           features = ['power_1', 'power_2'], \n",
    "                                           validation_set = None)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Ploynomial model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x11726aed0>,\n",
       " <matplotlib.lines.Line2D at 0x11726afd0>]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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l6Q+W0qZ5m3SrZDQgLJ+OkfGEDMzcudCrlzNCe/aEzwfL0XjnnXA5Nzd7Ns9M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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117062990>"
      ]
     },
     "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": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PROGRESS: Linear regression:\n",
      "PROGRESS: --------------------------------------------------------\n",
      "PROGRESS: Number of examples          : 21613\n",
      "PROGRESS: Number of features          : 3\n",
      "PROGRESS: Number of unpacked features : 3\n",
      "PROGRESS: Number of coefficients    : 4\n",
      "PROGRESS: Starting Newton Method\n",
      "PROGRESS: --------------------------------------------------------\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: | Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: | 1         | 2        | 0.022190     | 3261066.736007     | 249261.286346 |\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: SUCCESS: Optimal solution found.\n",
      "PROGRESS:\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x11755fe10>,\n",
       " <matplotlib.lines.Line2D at 0x11755ff10>]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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TJ0c2VuvYMTKpH2/NTHV1dODApk2ub2GCBMfLl8cvZ5Km5oJL9fXue+gTpjw5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\nhJMGAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1170fb290>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "poly3_data = polynomial_sframe(sales['sqft_living'], 3)\n",
    "poly3_data['price'] = sales['price']\n",
    "\n",
    "model3 = graphlab.linear_regression.create(poly3_data, \n",
    "                                           target = 'price', \n",
    "                                           features = ['power_1', 'power_2', 'power_3'], \n",
    "                                           validation_set = None)\n",
    "\n",
    "plt.plot(poly3_data['power_1'], poly3_data['price'],'.',\n",
    "         poly3_data['power_1'], model3.predict(poly3_data),'-')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PROGRESS: Linear regression:\n",
      "PROGRESS: --------------------------------------------------------\n",
      "PROGRESS: Number of examples          : 21613\n",
      "PROGRESS: Number of features          : 15\n",
      "PROGRESS: Number of unpacked features : 15\n",
      "PROGRESS: Number of coefficients    : 16\n",
      "PROGRESS: Starting Newton Method\n",
      "PROGRESS: --------------------------------------------------------\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: | Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: | 1         | 2        | 0.029435     | 2662308.584336     | 245690.511190 |\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: SUCCESS: Optimal solution found.\n",
      "PROGRESS:\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x11784cf10>,\n",
       " <matplotlib.lines.Line2D at 0x1173e1410>]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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5+fLYl1w/53qmjZ1Gu5btghXGqDXptkjUlI6R8kSKMKtN1NmqVdC3Lxw6lHhZ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\nzrUiWW61ZeOejTruxXHa4bc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pvb/hFog/h5uIY32sXOn8BtGslupy1vktlvpkFoi1b6St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\nmNIxDMMwkoYpHcMwDCNp/P97jYzfKXZcrAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1173e1050>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "poly15_data = polynomial_sframe(sales['sqft_living'], 15)\n",
    "poly15_data['price'] = sales['price']\n",
    "\n",
    "model15 = graphlab.linear_regression.create(poly15_data, \n",
    "                                           target = 'price', \n",
    "                                           features = ['power_1', 'power_2', 'power_3', 'power_4', 'power_5','power_6','power_7','power_8','power_9','power_10','power_11','power_12','power_13','power_14','power_15'], \n",
    "                                           validation_set = None)\n",
    "\n",
    "plt.plot(poly15_data['power_1'], poly15_data['price'],'.',\n",
    "         poly15_data['power_1'], model15.predict(poly15_data),'-')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "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\">73619.7521124</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">932386.401678</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\">410.287462538</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4736.29673944</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\">-0.230450714433</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">9.8605324062</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\">7.58840542482e-05</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.0111697430756</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\">-5.65701802745e-09</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">7.69719587967e-06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_5</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-4.57028130487e-13</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3.4042245283e-09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_6</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.66360206432e-17</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">9.86624536049e-13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_7</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3.38584769256e-21</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.85621317895e-16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_8</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.14723104066e-25</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.13709629311e-20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_9</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-4.65293586333e-30</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.22655023693e-24</td>\n",
       "    </tr>\n",
       "</table>\n",
       "[16 rows x 4 columns]<br/>Note: Only the head of the SFrame is printed.<br/>You can use print_rows(num_rows=m, num_columns=n) to print more rows and columns.\n",
       "</div>"
      ],
      "text/plain": [
       "Columns:\n",
       "\tname\tstr\n",
       "\tindex\tstr\n",
       "\tvalue\tfloat\n",
       "\tstderr\tfloat\n",
       "\n",
       "Rows: 16\n",
       "\n",
       "Data:\n",
       "+-------------+-------+--------------------+-------------------+\n",
       "|     name    | index |       value        |       stderr      |\n",
       "+-------------+-------+--------------------+-------------------+\n",
       "| (intercept) |  None |   73619.7521124    |   932386.401678   |\n",
       "|   power_1   |  None |   410.287462538    |   4736.29673944   |\n",
       "|   power_2   |  None |  -0.230450714433   |    9.8605324062   |\n",
       "|   power_3   |  None | 7.58840542482e-05  |  0.0111697430756  |\n",
       "|   power_4   |  None | -5.65701802745e-09 | 7.69719587967e-06 |\n",
       "|   power_5   |  None | -4.57028130487e-13 |  3.4042245283e-09 |\n",
       "|   power_6   |  None | 2.66360206432e-17  | 9.86624536049e-13 |\n",
       "|   power_7   |  None | 3.38584769256e-21  | 1.85621317895e-16 |\n",
       "|   power_8   |  None | 1.14723104066e-25  | 2.13709629311e-20 |\n",
       "|   power_9   |  None | -4.65293586333e-30 | 1.22655023693e-24 |\n",
       "+-------------+-------+--------------------+-------------------+\n",
       "[16 rows x 4 columns]\n",
       "Note: Only the head of the SFrame is printed.\n",
       "You can use print_rows(num_rows=m, num_columns=n) to print more rows and columns."
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model15.get('coefficients')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "split1, split2 = sales.random_split(0.5, seed=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "set_1, set_2 = split1.random_split(0.5, seed=0)\n",
    "set_3, set_4 = split2.random_split(0.5, seed=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PROGRESS: Linear regression:\n",
      "PROGRESS: --------------------------------------------------------\n",
      "PROGRESS: Number of examples          : 5404\n",
      "PROGRESS: Number of features          : 15\n",
      "PROGRESS: Number of unpacked features : 15\n",
      "PROGRESS: Number of coefficients    : 16\n",
      "PROGRESS: Starting Newton Method\n",
      "PROGRESS: --------------------------------------------------------\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: | Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: | 1         | 2        | 0.021105     | 2195218.932304     | 248858.822200 |\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: SUCCESS: Optimal solution found.\n",
      "PROGRESS:\n",
      "+-------------+-------+--------------------+-------------------+\n",
      "|     name    | index |       value        |       stderr      |\n",
      "+-------------+-------+--------------------+-------------------+\n",
      "| (intercept) |  None |   223312.750249    |   1256782.60077   |\n",
      "|   power_1   |  None |   118.086127587    |   6007.14384425   |\n",
      "|   power_2   |  None |  -0.0473482011344  |    11.969007003   |\n",
      "|   power_3   |  None | 3.25310342469e-05  |  0.0131429551736  |\n",
      "|   power_4   |  None | -3.32372152561e-09 | 8.85414511316e-06 |\n",
      "|   power_5   |  None | -9.75830457761e-14 | 3.83982596813e-09 |\n",
      "|   power_6   |  None | 1.15440303426e-17  |  1.0847728091e-12 |\n",
      "|   power_7   |  None | 1.05145869404e-21  | 1.93625236102e-16 |\n",
      "|   power_8   |  None | 3.46049616546e-26  |  1.8950619488e-20 |\n",
      "|   power_9   |  None | -1.09654454168e-30 |        nan        |\n",
      "|   power_10  |  None | -2.42031812009e-34 |  3.4981969864e-29 |\n",
      "|   power_11  |  None | -1.99601206824e-38 | 2.50800893225e-33 |\n",
      "|   power_12  |  None | -1.07709903827e-42 | 1.15429777633e-36 |\n",
      "|   power_13  |  None | -2.72862818141e-47 | 1.56910289863e-40 |\n",
      "|   power_14  |  None | 2.44782693088e-51  | 7.93831963225e-45 |\n",
      "|   power_15  |  None | 5.01975232933e-55  | 1.49249715723e-49 |\n",
      "+-------------+-------+--------------------+-------------------+\n",
      "[16 rows x 4 columns]\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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dw6iFHDxykAtnXEi3E7ox6bxJllMtzmneoDnpyel8uuPTaJtSLiY6Ro3BNn+G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\ncvbUnD0N2n4IGy6B1WNga7+wz2oC11y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      "text/plain": [
       "<matplotlib.figure.Figure at 0x117bbd4d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# set_1\n",
    "poly15_data = polynomial_sframe(set_1['sqft_living'], 15)\n",
    "poly15_data['price'] = set_1['price']\n",
    "\n",
    "model15 = graphlab.linear_regression.create(poly15_data, \n",
    "                                           target = 'price', \n",
    "                                           features = ['power_1', 'power_2', 'power_3', 'power_4', 'power_5','power_6','power_7','power_8','power_9','power_10','power_11','power_12','power_13','power_14','power_15'], \n",
    "                                           validation_set = None)\n",
    "\n",
    "plt.plot(poly15_data['power_1'], poly15_data['price'],'.',\n",
    "         poly15_data['power_1'], model15.predict(poly15_data),'-')\n",
    "\n",
    "model15.get('coefficients').print_rows(num_rows=16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PROGRESS: Linear regression:\n",
      "PROGRESS: --------------------------------------------------------\n",
      "PROGRESS: Number of examples          : 5398\n",
      "PROGRESS: Number of features          : 15\n",
      "PROGRESS: Number of unpacked features : 15\n",
      "PROGRESS: Number of coefficients    : 16\n",
      "PROGRESS: Starting Newton Method\n",
      "PROGRESS: --------------------------------------------------------\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: | Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: | 1         | 2        | 0.019175     | 2069212.978547     | 234840.067186 |\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: SUCCESS: Optimal solution found.\n",
      "PROGRESS:\n",
      "+-------------+-------+--------------------+-------------------+\n",
      "|     name    | index |       value        |       stderr      |\n",
      "+-------------+-------+--------------------+-------------------+\n",
      "| (intercept) |  None |   89836.5077327    |   1575072.52605   |\n",
      "|   power_1   |  None |   319.806946764    |   9306.12882948   |\n",
      "|   power_2   |  None |  -0.103315397042   |   23.4277359048   |\n",
      "|   power_3   |  None | 1.06682476069e-05  |  0.0331642866136  |\n",
      "|   power_4   |  None | 5.75577097718e-09  |  2.9410878859e-05 |\n",
      "|   power_5   |  None | -2.5466346476e-13  | 1.72262411743e-08 |\n",
      "|   power_6   |  None | -1.09641345061e-16 |  6.8337583788e-12 |\n",
      "|   power_7   |  None | -6.36458441713e-21 | 1.84750094523e-15 |\n",
      "|   power_8   |  None | 5.52560416991e-25  | 3.35734055021e-19 |\n",
      "|   power_9   |  None | 1.35082038963e-28  | 3.79203635463e-23 |\n",
      "|   power_10  |  None |  1.1840818825e-32  |        nan        |\n",
      "|   power_11  |  None | 1.98348000558e-37  |        nan        |\n",
      "|   power_12  |  None | -9.9253359041e-41  |        nan        |\n",
      "|   power_13  |  None | -1.60834847047e-44 |        nan        |\n",
      "|   power_14  |  None | -9.12006024287e-49 | 2.33825680386e-43 |\n",
      "|   power_15  |  None | 1.68636658328e-52  |  6.7296077272e-48 |\n",
      "+-------------+-------+--------------------+-------------------+\n",
      "[16 rows x 4 columns]\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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KYPfuum2++EUnNH4fwfDngwfd8FxrYt/hfWz+ZHM9Eak9UEvtp3XF5fCxw/Q6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\nx654b34AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117cee210>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# set_2\n",
    "poly15_data = polynomial_sframe(set_2['sqft_living'], 15)\n",
    "poly15_data['price'] = set_2['price']\n",
    "\n",
    "model15 = graphlab.linear_regression.create(poly15_data, \n",
    "                                           target = 'price', \n",
    "                                           features = ['power_1', 'power_2', 'power_3', 'power_4', 'power_5','power_6','power_7','power_8','power_9','power_10','power_11','power_12','power_13','power_14','power_15'], \n",
    "                                           validation_set = None)\n",
    "\n",
    "plt.plot(poly15_data['power_1'], poly15_data['price'],'.',\n",
    "         poly15_data['power_1'], model15.predict(poly15_data),'-')\n",
    "\n",
    "model15.get('coefficients').print_rows(num_rows=16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PROGRESS: Linear regression:\n",
      "PROGRESS: --------------------------------------------------------\n",
      "PROGRESS: Number of examples          : 5409\n",
      "PROGRESS: Number of features          : 15\n",
      "PROGRESS: Number of unpacked features : 15\n",
      "PROGRESS: Number of coefficients    : 16\n",
      "PROGRESS: Starting Newton Method\n",
      "PROGRESS: --------------------------------------------------------\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: | Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: | 1         | 2        | 0.022118     | 2269769.506521     | 251460.072754 |\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: SUCCESS: Optimal solution found.\n",
      "PROGRESS:\n",
      "+-------------+-------+--------------------+-------------------+\n",
      "|     name    | index |       value        |       stderr      |\n",
      "+-------------+-------+--------------------+-------------------+\n",
      "| (intercept) |  None |   87317.9795547    |        nan        |\n",
      "|   power_1   |  None |   356.304911045    |        nan        |\n",
      "|   power_2   |  None |  -0.164817442809   |        nan        |\n",
      "|   power_3   |  None | 4.40424992697e-05  |        nan        |\n",
      "|   power_4   |  None | 6.48234876179e-10  |        nan        |\n",
      "|   power_5   |  None | -6.75253226587e-13 |        nan        |\n",
      "|   power_6   |  None | -3.36842592661e-17 |        nan        |\n",
      "|   power_7   |  None | 3.60999704242e-21  |        nan        |\n",
      "|   power_8   |  None | 6.46999725625e-25  |        nan        |\n",
      "|   power_9   |  None | 4.23639388865e-29  |        nan        |\n",
      "|   power_10  |  None | -3.62149427043e-34 |        nan        |\n",
      "|   power_11  |  None | -4.27119527274e-37 |        nan        |\n",
      "|   power_12  |  None | -5.61445971705e-41 | 3.22504679661e-36 |\n",
      "|   power_13  |  None | -3.87452772861e-45 | 3.81940189807e-40 |\n",
      "|   power_14  |  None | 4.69430359483e-50  | 1.00042633659e-44 |\n",
      "|   power_15  |  None | 6.39045885992e-53  |        nan        |\n",
      "+-------------+-------+--------------------+-------------------+\n",
      "[16 rows x 4 columns]\n",
      "\n"
     ]
    },
    {
     "data": {
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2gX5n9Ut3c7KaoPMgl6rqpyJSABSLyAY8IfIT+bkmBHGoBna6Tpw48ct0UVERRUVF1W+R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\ntYaJjmEYhlFr/H+G+unPahU6PAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117ea7610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# set_3\n",
    "poly15_data = polynomial_sframe(set_3['sqft_living'], 15)\n",
    "poly15_data['price'] = set_3['price']\n",
    "\n",
    "model15 = graphlab.linear_regression.create(poly15_data, \n",
    "                                           target = 'price', \n",
    "                                           features = ['power_1', 'power_2', 'power_3', 'power_4', 'power_5','power_6','power_7','power_8','power_9','power_10','power_11','power_12','power_13','power_14','power_15'], \n",
    "                                           validation_set = None)\n",
    "\n",
    "plt.plot(poly15_data['power_1'], poly15_data['price'],'.',\n",
    "         poly15_data['power_1'], model15.predict(poly15_data),'-')\n",
    "\n",
    "model15.get('coefficients').print_rows(num_rows=16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PROGRESS: Linear regression:\n",
      "PROGRESS: --------------------------------------------------------\n",
      "PROGRESS: Number of examples          : 5402\n",
      "PROGRESS: Number of features          : 15\n",
      "PROGRESS: Number of unpacked features : 15\n",
      "PROGRESS: Number of coefficients    : 16\n",
      "PROGRESS: Starting Newton Method\n",
      "PROGRESS: --------------------------------------------------------\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: | Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: | 1         | 2        | 0.017527     | 2314893.173827     | 244563.136754 |\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: SUCCESS: Optimal solution found.\n",
      "PROGRESS:\n",
      "+-------------+-------+--------------------+-------------------+\n",
      "|     name    | index |       value        |       stderr      |\n",
      "+-------------+-------+--------------------+-------------------+\n",
      "| (intercept) |  None |   259020.879454    |   1545198.28029   |\n",
      "|   power_1   |  None |   -31.7277162076   |    9987.4875763   |\n",
      "|   power_2   |  None |   0.109702769619   |    26.738101963   |\n",
      "|   power_3   |  None | -1.58383847337e-05 |  0.0392428614089  |\n",
      "|   power_4   |  None | -4.47660623786e-09 |  3.515833293e-05  |\n",
      "|   power_5   |  None | 1.13976573482e-12  | 2.00754862175e-08 |\n",
      "|   power_6   |  None | 1.97669120547e-16  | 7.24105980967e-12 |\n",
      "|   power_7   |  None | -6.15783678661e-21 | 1.43187601549e-15 |\n",
      "|   power_8   |  None | -4.88012304074e-24 |        nan        |\n",
      "|   power_9   |  None | -6.62186781351e-28 |        nan        |\n",
      "|   power_10  |  None | -2.70631583161e-32 | 5.65043690743e-27 |\n",
      "|   power_11  |  None | 6.72370411466e-36  | 9.67662635909e-31 |\n",
      "|   power_12  |  None | 1.74115646268e-39  |        nan        |\n",
      "|   power_13  |  None | 2.09188375728e-43  |        nan        |\n",
      "|   power_14  |  None | 4.78015566061e-48  | 2.37859778541e-43 |\n",
      "|   power_15  |  None | -4.74535333101e-51 | 1.16454261473e-47 |\n",
      "+-------------+-------+--------------------+-------------------+\n",
      "[16 rows x 4 columns]\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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unatjFqxlluoEw4aOG29dou0b2zY8YbShcwtaZGVl6a3VVltbq8s2LdPr51+v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\nRvn/J/UE6hbohdAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117de0310>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# set_4\n",
    "poly15_data = polynomial_sframe(set_4['sqft_living'], 15)\n",
    "poly15_data['price'] = set_4['price']\n",
    "\n",
    "model15 = graphlab.linear_regression.create(poly15_data, \n",
    "                                           target = 'price', \n",
    "                                           features = ['power_1', 'power_2', 'power_3', 'power_4', 'power_5','power_6','power_7','power_8','power_9','power_10','power_11','power_12','power_13','power_14','power_15'], \n",
    "                                           validation_set = None)\n",
    "\n",
    "plt.plot(poly15_data['power_1'], poly15_data['price'],'.',\n",
    "         poly15_data['power_1'], model15.predict(poly15_data),'-')\n",
    "\n",
    "model15.get('coefficients').print_rows(num_rows=16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "training_and_validation, testing = sales.random_split(0.9, seed=1)\n",
    "training, validation = training_and_validation.random_split(0.5, seed=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def model_run(degree):\n",
    "    poly_data = polynomial_sframe(training['sqft_living'], degree)\n",
    "    poly_data['price'] = training['price']\n",
    "    \n",
    "    features = []\n",
    "    for i in range(1, degree+1):\n",
    "        features.append('power_' + str(i))\n",
    "    \n",
    "    model = graphlab.linear_regression.create(poly_data, \n",
    "                                               target = 'price', \n",
    "                                               features = features,\n",
    "                                               validation_set = None,\n",
    "                                             verbose = False )\n",
    "    \n",
    "    validation_poly_data = polynomial_sframe(validation['sqft_living'], degree)\n",
    "    \n",
    "    errors_squared = (validation['price'] - model.predict(validation_poly_data))**2\n",
    "    rss_validation = errors_squared.sum()\n",
    "    return rss_validation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "degree: 1 rss: 6.76709775198e+14\n",
      "degree: 2 rss: 6.07090530698e+14\n",
      "degree: 3 rss: 6.16714574533e+14\n",
      "degree: 4 rss: 6.09129230654e+14\n",
      "degree: 5 rss: 5.99177138584e+14\n",
      "degree: 6 rss: 5.89182477809e+14\n",
      "degree: 7 rss: 5.91717038418e+14\n",
      "degree: 8 rss: 6.01558237777e+14\n",
      "degree: 9 rss: 6.12563853988e+14\n",
      "degree: 10 rss: 6.21744288936e+14\n",
      "degree: 11 rss: 6.27012012704e+14\n",
      "degree: 12 rss: 6.27757914772e+14\n",
      "degree: 13 rss: 6.24738503262e+14\n",
      "degree: 14 rss: 6.19369705905e+14\n",
      "degree: 15 rss: 6.13089202414e+14\n"
     ]
    }
   ],
   "source": [
    "for i in range(1, 16):\n",
    "    rss_validation = model_run(i)\n",
    "    print 'degree:', i, 'rss:', rss_validation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.25529337848e+14\n"
     ]
    }
   ],
   "source": [
    "# on testing data with the best model\n",
    "degree = 6\n",
    "poly_data = polynomial_sframe(training['sqft_living'], degree)\n",
    "poly_data['price'] = training['price']\n",
    "\n",
    "features = []\n",
    "for i in range(1, degree+1):\n",
    "    features.append('power_' + str(i))\n",
    "\n",
    "model = graphlab.linear_regression.create(poly_data, \n",
    "                                           target = 'price', \n",
    "                                           features = features,\n",
    "                                           validation_set = None,\n",
    "                                         verbose = False )\n",
    "\n",
    "testing_poly_data = polynomial_sframe(testing['sqft_living'], degree)\n",
    "\n",
    "errors_squared = (testing['price'] - model.predict(testing_poly_data))**2\n",
    "rss_testing = errors_squared.sum()\n",
    "\n",
    "print rss_testing"
   ]
  }
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