1.0 PhillyCrime.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#Fire up graphlab create"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "import graphlab"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#Load some house value vs. crime rate data\n",
    "\n",
    "Dataset is from Philadelphia, PA and includes average house sales price in a number of neighborhoods.  The attributes of each neighborhood we have include the crime rate ('CrimeRate'), miles from Center City ('MilesPhila'), town name ('Name'), and county name ('County')."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PROGRESS: Finished parsing file C:\\Users\\coursera\\Course2Regression\\notebooks\\course2-for-students\\Philadelphia_Crime_Rate_noNA.csv\n",
      "PROGRESS: Parsing completed. Parsed 99 lines in 0.019001 secs.\n",
      "------------------------------------------------------\n",
      "Inferred types from first line of file as \n",
      "column_type_hints=[long,float,float,float,float,str,str]\n",
      "If parsing fails due to incorrect types, you can correct\n",
      "the inferred type list above and pass it to read_csv in\n",
      "the column_type_hints argument\n",
      "------------------------------------------------------\n",
      "PROGRESS: Finished parsing file C:\\Users\\coursera\\Course2Regression\\notebooks\\course2-for-students\\Philadelphia_Crime_Rate_noNA.csv\n",
      "PROGRESS: Parsing completed. Parsed 99 lines in 0.018001 secs.\n"
     ]
    }
   ],
   "source": [
    "sales = graphlab.SFrame.read_csv('Philadelphia_Crime_Rate_noNA.csv/')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "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\">HousePrice</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">HsPrc ($10,000)</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">CrimeRate</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">MilesPhila</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">PopChg</th>\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\">County</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">140463</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">14.0463</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">29.7</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">10.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-1.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Abington</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Montgome</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">113033</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">11.3033</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">24.1</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">18.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Ambler</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Montgome</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">124186</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">12.4186</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">19.5</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">25.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">8.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Aston</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Delaware</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">110490</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">11.049</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">49.4</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">25.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.7</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Bensalem</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Bucks</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">79124</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">7.9124</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">54.1</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">19.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3.9</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Bristol B.</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Bucks</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">92634</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">9.2634</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">48.6</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">20.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.6</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Bristol T.</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Bucks</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">89246</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">8.9246</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">30.8</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">15.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-2.6</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Brookhaven</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Delaware</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">195145</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">19.5145</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">10.8</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">20.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-3.5</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Bryn Athyn</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Montgome</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">297342</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">29.7342</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">20.2</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">14.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.6</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Bryn Mawr</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Montgome</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">264298</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">26.4298</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">20.4</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">26.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">6.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Buckingham</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Bucks</td>\n",
       "    </tr>\n",
       "</table>\n",
       "[99 rows x 7 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",
       "\tHousePrice\tint\n",
       "\tHsPrc ($10,000)\tfloat\n",
       "\tCrimeRate\tfloat\n",
       "\tMilesPhila\tfloat\n",
       "\tPopChg\tfloat\n",
       "\tName\tstr\n",
       "\tCounty\tstr\n",
       "\n",
       "Rows: 99\n",
       "\n",
       "Data:\n",
       "+------------+-----------------+-----------+------------+--------+------------+\n",
       "| HousePrice | HsPrc ($10,000) | CrimeRate | MilesPhila | PopChg |    Name    |\n",
       "+------------+-----------------+-----------+------------+--------+------------+\n",
       "|   140463   |     14.0463     |    29.7   |    10.0    |  -1.0  |  Abington  |\n",
       "|   113033   |     11.3033     |    24.1   |    18.0    |  4.0   |   Ambler   |\n",
       "|   124186   |     12.4186     |    19.5   |    25.0    |  8.0   |   Aston    |\n",
       "|   110490   |      11.049     |    49.4   |    25.0    |  2.7   |  Bensalem  |\n",
       "|   79124    |      7.9124     |    54.1   |    19.0    |  3.9   | Bristol B. |\n",
       "|   92634    |      9.2634     |    48.6   |    20.0    |  0.6   | Bristol T. |\n",
       "|   89246    |      8.9246     |    30.8   |    15.0    |  -2.6  | Brookhaven |\n",
       "|   195145   |     19.5145     |    10.8   |    20.0    |  -3.5  | Bryn Athyn |\n",
       "|   297342   |     29.7342     |    20.2   |    14.0    |  0.6   | Bryn Mawr  |\n",
       "|   264298   |     26.4298     |    20.4   |    26.0    |  6.0   | Buckingham |\n",
       "+------------+-----------------+-----------+------------+--------+------------+\n",
       "+----------+\n",
       "|  County  |\n",
       "+----------+\n",
       "| Montgome |\n",
       "| Montgome |\n",
       "| Delaware |\n",
       "|  Bucks   |\n",
       "|  Bucks   |\n",
       "|  Bucks   |\n",
       "| Delaware |\n",
       "| Montgome |\n",
       "| Montgome |\n",
       "|  Bucks   |\n",
       "+----------+\n",
       "[99 rows x 7 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": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sales"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#Exploring the data "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The house price in a town is correlated with the crime rate of that town. Low crime towns tend to be associated with higher house prices and vice versa."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "$(\"head\").append($(\"<link/>\").attr({\n",
       "  rel:  \"stylesheet\",\n",
       "  type: \"text/css\",\n",
       "  href: \"//cdnjs.cloudflare.com/ajax/libs/font-awesome/4.1.0/css/font-awesome.min.css\"\n",
       "}));\n",
       "$(\"head\").append($(\"<link/>\").attr({\n",
       "  rel:  \"stylesheet\",\n",
       "  type: \"text/css\",\n",
       "  href: \"//dato.com/files/canvas/1.7.1/css/canvas.css\"\n",
       "}));\n",
       "\n",
       "            (function(){\n",
       "\n",
       "                var e = null;\n",
       "                if (typeof element == 'undefined') {\n",
       "                    var scripts = document.getElementsByTagName('script');\n",
       "                    var thisScriptTag = scripts[scripts.length-1];\n",
       "                    var parentDiv = thisScriptTag.parentNode;\n",
       "                    e = document.createElement('div');\n",
       "                    parentDiv.appendChild(e);\n",
       "                } else {\n",
       "                    e = element[0];\n",
       "                }\n",
       "\n",
       "                if (typeof requirejs !== 'undefined') {\n",
       "                    // disable load timeout; ipython_app.js is large and can take a while to load.\n",
       "                    requirejs.config({waitSeconds: 0});\n",
       "                }\n",
       "\n",
       "                require(['//dato.com/files/canvas/1.7.1/js/ipython_app.js'], function(IPythonApp){\n",
       "                    var app = new IPythonApp();\n",
       "                    app.attachView('sframe','Plots', {\"selected_variable\": {\"name\": [\"sales\"], \"descriptives\": {\"rows\": 99, \"columns\": 7}, \"view_component\": \"Plots\", \"view_file\": \"sframe\", \"view_params\": {\"y\": \"HousePrice\", \"x\": \"CrimeRate\", \"columns\": [\"HousePrice\", \"HsPrc ($10,000)\", \"CrimeRate\", \"MilesPhila\", \"PopChg\", \"Name\", \"County\"], \"view\": \"Scatter Plot\"}, \"view_components\": [\"Summary\", \"Table\", \"Bar Chart\", \"BoxWhisker Plot\", \"Line Chart\", \"Scatter Plot\", \"Heat Map\", \"Plots\"], \"type\": \"SFrame\", \"columns\": [{\"dtype\": \"int\", \"name\": \"HousePrice\"}, {\"dtype\": \"float\", \"name\": \"HsPrc ($10,000)\"}, {\"dtype\": \"float\", \"name\": \"CrimeRate\"}, {\"dtype\": \"float\", \"name\": \"MilesPhila\"}, {\"dtype\": \"float\", \"name\": \"PopChg\"}, {\"dtype\": \"str\", \"name\": \"Name\"}, {\"dtype\": \"str\", \"name\": \"County\"}], \"column_identifiers\": [\"Name\", \"PopChg\", \"County\", \"HousePrice\", \"MilesPhila\", \"HsPrc ($10,000)\", \"CrimeRate\"]}, \"complete\": 1, \"ipython\": true, \"progress\": 1.0, \"data\": [[29.7, 140463], [24.1, 113033], [19.5, 124186], [49.4, 110490], [54.1, 79124], [48.6, 92634], [30.8, 89246], [10.8, 195145], [20.2, 297342], [20.4, 264298], [17.3, 134342], [50.3, 147600], [34.2, 77370], [33.7, 170822], [45.7, 40642], [22.3, 71359], [48.1, 104923], [19.4, 190317], [71.9, 215512], [45.1, 178105], [31.3, 131025], [24.9, 149844], [27.2, 170556], [17.7, 280969], [29.0, 114233], [21.4, 74502], [28.6, 475112], [29.3, 97167], [17.5, 114572], [16.5, 436348], [17.8, 389302], [17.3, 122392], [31.2, 130436], [14.5, 272790], [15.7, 194435], [28.6, 299621], [20.8, 210884], [29.3, 112471], [19.3, 93738], [39.5, 121024], [13.0, 156035], [24.1, 185404], [38.0, 126160], [40.1, 143072], [36.1, 96769], [26.6, 94014], [25.1, 118214], [14.6, 157446], [18.2, 150283], [15.3, 153842], [15.2, 197214], [17.4, 206127], [73.3, 71981], [7.1, 169401], [12.5, 99843], [45.8, 60000], [44.9, 28000], [65.0, 60000], [49.9, 61800], [54.8, 38000], [53.5, 38000], [69.9, 42000], [366.1, 96200], [24.6, 103087], [58.6, 147720], [53.2, 78175], [17.4, 92215], [15.5, 271804], [14.5, 119566], [24.1, 100231], [21.2, 95831], [9.8, 229711], [29.9, 74308], [7.2, 259506], [19.4, 159573], [41.1, 147176], [11.2, 205732], [21.2, 215783], [42.8, 116710], [9.4, 359112], [61.7, 189959], [19.4, 133198], [6.6, 242821], [15.9, 142811], [18.8, 200498], [13.2, 199065], [34.5, 93648], [22.1, 163001], [22.1, 436348], [71.9, 124478], [31.9, 168276], [44.6, 114157], [28.6, 130088], [24.0, 152624], [13.8, 174232], [29.9, 196515], [9.9, 232714], [22.6, 245920], [13.0, 130953]], \"columns\": [{\"dtype\": \"int\", \"name\": \"HousePrice\"}, {\"dtype\": \"float\", \"name\": \"HsPrc ($10,000)\"}, {\"dtype\": \"float\", \"name\": \"CrimeRate\"}, {\"dtype\": \"float\", \"name\": \"MilesPhila\"}, {\"dtype\": \"float\", \"name\": \"PopChg\"}, {\"dtype\": \"str\", \"name\": \"Name\"}, {\"dtype\": \"str\", \"name\": \"County\"}]}, e);\n",
       "                });\n",
       "            })();\n",
       "        "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "graphlab.canvas.set_target('ipynb')\n",
    "sales.show(view=\"Scatter Plot\", x=\"CrimeRate\", y=\"HousePrice\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#Fit the regression model using crime as the feature"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "crime_model = graphlab.linear_regression.create(sales, target='HousePrice', features=['CrimeRate'],validation_set=None,verbose=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#Let's see what our fit looks like"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Matplotlib is a Python plotting library that is also useful for plotting.  You can install it with:\n",
    "\n",
    "'pip install matplotlib'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2024c898>,\n",
       " <matplotlib.lines.Line2D at 0x2024ca90>]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZYAAAEACAYAAACQx1DIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngOPlAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1f8c77b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sales['CrimeRate'],sales['HousePrice'],'.',\n",
    "        sales['CrimeRate'],crime_model.predict(sales),'-')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above: blue dots are original data, green line is the fit from the simple regression."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Remove Center City and redo the analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Center City is the one observation with an extremely high crime rate, yet house prices are not very low.  This point does not follow the trend of the rest of the data very well.  A question is how much including Center City is influencing our fit on the other datapoints.  Let's remove this datapoint and see what happens."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sales_noCC = sales[sales['MilesPhila'] != 0.0] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "$(\"head\").append($(\"<link/>\").attr({\n",
       "  rel:  \"stylesheet\",\n",
       "  type: \"text/css\",\n",
       "  href: \"//cdnjs.cloudflare.com/ajax/libs/font-awesome/4.1.0/css/font-awesome.min.css\"\n",
       "}));\n",
       "$(\"head\").append($(\"<link/>\").attr({\n",
       "  rel:  \"stylesheet\",\n",
       "  type: \"text/css\",\n",
       "  href: \"//dato.com/files/canvas/1.7.1/css/canvas.css\"\n",
       "}));\n",
       "\n",
       "            (function(){\n",
       "\n",
       "                var e = null;\n",
       "                if (typeof element == 'undefined') {\n",
       "                    var scripts = document.getElementsByTagName('script');\n",
       "                    var thisScriptTag = scripts[scripts.length-1];\n",
       "                    var parentDiv = thisScriptTag.parentNode;\n",
       "                    e = document.createElement('div');\n",
       "                    parentDiv.appendChild(e);\n",
       "                } else {\n",
       "                    e = element[0];\n",
       "                }\n",
       "\n",
       "                if (typeof requirejs !== 'undefined') {\n",
       "                    // disable load timeout; ipython_app.js is large and can take a while to load.\n",
       "                    requirejs.config({waitSeconds: 0});\n",
       "                }\n",
       "\n",
       "                require(['//dato.com/files/canvas/1.7.1/js/ipython_app.js'], function(IPythonApp){\n",
       "                    var app = new IPythonApp();\n",
       "                    app.attachView('sframe','Plots', {\"selected_variable\": {\"name\": [\"sales_noCC\"], \"descriptives\": {\"rows\": 98, \"columns\": 7}, \"view_component\": \"Plots\", \"view_file\": \"sframe\", \"view_params\": {\"y\": \"HousePrice\", \"x\": \"CrimeRate\", \"columns\": [\"HousePrice\", \"HsPrc ($10,000)\", \"CrimeRate\", \"MilesPhila\", \"PopChg\", \"Name\", \"County\"], \"view\": \"Scatter Plot\"}, \"view_components\": [\"Summary\", \"Table\", \"Bar Chart\", \"BoxWhisker Plot\", \"Line Chart\", \"Scatter Plot\", \"Heat Map\", \"Plots\"], \"type\": \"SFrame\", \"columns\": [{\"dtype\": \"int\", \"name\": \"HousePrice\"}, {\"dtype\": \"float\", \"name\": \"HsPrc ($10,000)\"}, {\"dtype\": \"float\", \"name\": \"CrimeRate\"}, {\"dtype\": \"float\", \"name\": \"MilesPhila\"}, {\"dtype\": \"float\", \"name\": \"PopChg\"}, {\"dtype\": \"str\", \"name\": \"Name\"}, {\"dtype\": \"str\", \"name\": \"County\"}], \"column_identifiers\": [\"Name\", \"PopChg\", \"County\", \"HousePrice\", \"MilesPhila\", \"HsPrc ($10,000)\", \"CrimeRate\"]}, \"complete\": 1, \"ipython\": true, \"progress\": 1.0, \"data\": [[29.7, 140463], [24.1, 113033], [19.5, 124186], [49.4, 110490], [54.1, 79124], [48.6, 92634], [30.8, 89246], [10.8, 195145], [20.2, 297342], [20.4, 264298], [17.3, 134342], [50.3, 147600], [34.2, 77370], [33.7, 170822], [45.7, 40642], [22.3, 71359], [48.1, 104923], [19.4, 190317], [71.9, 215512], [45.1, 178105], [31.3, 131025], [24.9, 149844], [27.2, 170556], [17.7, 280969], [29.0, 114233], [21.4, 74502], [28.6, 475112], [29.3, 97167], [17.5, 114572], [16.5, 436348], [17.8, 389302], [17.3, 122392], [31.2, 130436], [14.5, 272790], [15.7, 194435], [28.6, 299621], [20.8, 210884], [29.3, 112471], [19.3, 93738], [39.5, 121024], [13.0, 156035], [24.1, 185404], [38.0, 126160], [40.1, 143072], [36.1, 96769], [26.6, 94014], [25.1, 118214], [14.6, 157446], [18.2, 150283], [15.3, 153842], [15.2, 197214], [17.4, 206127], [73.3, 71981], [7.1, 169401], [12.5, 99843], [45.8, 60000], [44.9, 28000], [65.0, 60000], [49.9, 61800], [54.8, 38000], [53.5, 38000], [69.9, 42000], [24.6, 103087], [58.6, 147720], [53.2, 78175], [17.4, 92215], [15.5, 271804], [14.5, 119566], [24.1, 100231], [21.2, 95831], [9.8, 229711], [29.9, 74308], [7.2, 259506], [19.4, 159573], [41.1, 147176], [11.2, 205732], [21.2, 215783], [42.8, 116710], [9.4, 359112], [61.7, 189959], [19.4, 133198], [6.6, 242821], [15.9, 142811], [18.8, 200498], [13.2, 199065], [34.5, 93648], [22.1, 163001], [22.1, 436348], [71.9, 124478], [31.9, 168276], [44.6, 114157], [28.6, 130088], [24.0, 152624], [13.8, 174232], [29.9, 196515], [9.9, 232714], [22.6, 245920], [13.0, 130953]], \"columns\": [{\"dtype\": \"int\", \"name\": \"HousePrice\"}, {\"dtype\": \"float\", \"name\": \"HsPrc ($10,000)\"}, {\"dtype\": \"float\", \"name\": \"CrimeRate\"}, {\"dtype\": \"float\", \"name\": \"MilesPhila\"}, {\"dtype\": \"float\", \"name\": \"PopChg\"}, {\"dtype\": \"str\", \"name\": \"Name\"}, {\"dtype\": \"str\", \"name\": \"County\"}]}, e);\n",
       "                });\n",
       "            })();\n",
       "        "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sales_noCC.show(view=\"Scatter Plot\", x=\"CrimeRate\", y=\"HousePrice\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Refit our simple regression model on this modified dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "crime_model_noCC = graphlab.linear_regression.create(sales_noCC, target='HousePrice', features=['CrimeRate'],validation_set=None, verbose=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Look at the fit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x20317160>,\n",
       " <matplotlib.lines.Line2D at 0x20317358>]"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYsAAAEACAYAAABCl1qQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2014f898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sales_noCC['CrimeRate'],sales_noCC['HousePrice'],'.',\n",
    "        sales_noCC['CrimeRate'],crime_model.predict(sales_noCC),'-')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Compare coefficients for full-data fit versus no-Center-City fit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visually, the fit seems different, but let's quantify this by examining the estimated coefficients of our original fit and that of the modified dataset with Center City removed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "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",
       "    </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\">176626.046881</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">CrimeRate</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\">-576.804949058</td>\n",
       "    </tr>\n",
       "</table>\n",
       "[2 rows x 3 columns]<br/>\n",
       "</div>"
      ],
      "text/plain": [
       "Columns:\n",
       "\tname\tstr\n",
       "\tindex\tstr\n",
       "\tvalue\tfloat\n",
       "\n",
       "Rows: 2\n",
       "\n",
       "Data:\n",
       "+-------------+-------+----------------+\n",
       "|     name    | index |     value      |\n",
       "+-------------+-------+----------------+\n",
       "| (intercept) |  None | 176626.046881  |\n",
       "|  CrimeRate  |  None | -576.804949058 |\n",
       "+-------------+-------+----------------+\n",
       "[2 rows x 3 columns]"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "crime_model.get('coefficients')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "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",
       "    </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\">225204.604303</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">CrimeRate</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\">-2287.69717443</td>\n",
       "    </tr>\n",
       "</table>\n",
       "[2 rows x 3 columns]<br/>\n",
       "</div>"
      ],
      "text/plain": [
       "Columns:\n",
       "\tname\tstr\n",
       "\tindex\tstr\n",
       "\tvalue\tfloat\n",
       "\n",
       "Rows: 2\n",
       "\n",
       "Data:\n",
       "+-------------+-------+----------------+\n",
       "|     name    | index |     value      |\n",
       "+-------------+-------+----------------+\n",
       "| (intercept) |  None | 225204.604303  |\n",
       "|  CrimeRate  |  None | -2287.69717443 |\n",
       "+-------------+-------+----------------+\n",
       "[2 rows x 3 columns]"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "crime_model_noCC.get('coefficients')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above: We see that for the \"no Center City\" version, per unit increase in crime, the predicted decrease in house prices is 2,287.  In contrast, for the original dataset, the drop is only 576 per unit increase in crime.  This is significantly different!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###High leverage points: \n",
    "Center City is said to be a \"high leverage\" point because it is at an extreme x value where there are not other observations.  As a result, recalling the closed-form solution for simple regression, this point has the *potential* to dramatically change the least squares line since the center of x mass is heavily influenced by this one point and the least squares line will try to fit close to that outlying (in x) point.  If a high leverage point follows the trend of the other data, this might not have much effect.  On the other hand, if this point somehow differs, it can be strongly influential in the resulting fit.\n",
    "\n",
    "###Influential observations:  \n",
    "An influential observation is one where the removal of the point significantly changes the fit.  As discussed above, high leverage points are good candidates for being influential observations, but need not be.  Other observations that are *not* leverage points can also be influential observations (e.g., strongly outlying in y even if x is a typical value)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Remove high-value outlier neighborhoods and redo analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Based on the discussion above, a question is whether the outlying high-value towns are strongly influencing the fit.  Let's remove them and see what happens."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "sales_nohighend = sales_noCC[sales_noCC['HousePrice'] < 350000] \n",
    "crime_model_nohighend = graphlab.linear_regression.create(sales_nohighend, target='HousePrice', features=['CrimeRate'],validation_set=None, verbose=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Do the coefficients change much?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "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",
       "    </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\">225204.604303</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">CrimeRate</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\">-2287.69717443</td>\n",
       "    </tr>\n",
       "</table>\n",
       "[2 rows x 3 columns]<br/>\n",
       "</div>"
      ],
      "text/plain": [
       "Columns:\n",
       "\tname\tstr\n",
       "\tindex\tstr\n",
       "\tvalue\tfloat\n",
       "\n",
       "Rows: 2\n",
       "\n",
       "Data:\n",
       "+-------------+-------+----------------+\n",
       "|     name    | index |     value      |\n",
       "+-------------+-------+----------------+\n",
       "| (intercept) |  None | 225204.604303  |\n",
       "|  CrimeRate  |  None | -2287.69717443 |\n",
       "+-------------+-------+----------------+\n",
       "[2 rows x 3 columns]"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "crime_model_noCC.get('coefficients')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "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",
       "    </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\">199073.589615</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">CrimeRate</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\">-1837.71280989</td>\n",
       "    </tr>\n",
       "</table>\n",
       "[2 rows x 3 columns]<br/>\n",
       "</div>"
      ],
      "text/plain": [
       "Columns:\n",
       "\tname\tstr\n",
       "\tindex\tstr\n",
       "\tvalue\tfloat\n",
       "\n",
       "Rows: 2\n",
       "\n",
       "Data:\n",
       "+-------------+-------+----------------+\n",
       "|     name    | index |     value      |\n",
       "+-------------+-------+----------------+\n",
       "| (intercept) |  None | 199073.589615  |\n",
       "|  CrimeRate  |  None | -1837.71280989 |\n",
       "+-------------+-------+----------------+\n",
       "[2 rows x 3 columns]"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "crime_model_nohighend.get('coefficients')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above: We see that removing the outlying high-value neighborhoods has *some* effect on the fit, but not nearly as much as our high-leverage Center City datapoint."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}