PhillyCrime.ipynb

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   "source": [
    "# Fire up graphlab create"
   ]
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  {
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   "source": [
    "import graphlab"
   ]
  },
  {
   "cell_type": "markdown",
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   "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')."
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     "text": [
      "[INFO] graphlab.cython.cy_server: GraphLab Create v2.1 started. Logging: /tmp/graphlab_server_1492229188.log\n"
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "This non-commercial license of GraphLab Create for academic use is assigned to luv.aggarwal@nsitonline.in and will expire on March 07, 2018.\n"
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       "<pre>Finished parsing file /Users/luv/Documents/Python/University of Washington - Course Materials/Philadelphia_Crime_Rate_noNA.csv</pre>"
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      "text/plain": [
       "Finished parsing file /Users/luv/Documents/Python/University of Washington - Course Materials/Philadelphia_Crime_Rate_noNA.csv"
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      "text/html": [
       "<pre>Parsing completed. Parsed 99 lines in 0.121255 secs.</pre>"
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      "text/plain": [
       "Parsing completed. Parsed 99 lines in 0.121255 secs."
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     "text": [
      "------------------------------------------------------\n",
      "Inferred types from first 100 line(s) of file as \n",
      "column_type_hints=[int,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"
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     "data": {
      "text/html": [
       "<pre>Finished parsing file /Users/luv/Documents/Python/University of Washington - Course Materials/Philadelphia_Crime_Rate_noNA.csv</pre>"
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      "text/plain": [
       "Finished parsing file /Users/luv/Documents/Python/University of Washington - Course Materials/Philadelphia_Crime_Rate_noNA.csv"
      ]
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     "output_type": "display_data"
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       "<pre>Parsing completed. Parsed 99 lines in 0.010303 secs.</pre>"
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      "text/plain": [
       "Parsing completed. Parsed 99 lines in 0.010303 secs."
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   "source": [
    "sales = graphlab.SFrame.read_csv('Philadelphia_Crime_Rate_noNA.csv/')"
   ]
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  {
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       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\"><table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">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",
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       "        <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",
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       "    <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",
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       "    <tr>\n",
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       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">19.5</td>\n",
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       "        <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",
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       "        <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."
      ]
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   "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": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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       "        "
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     "metadata": {},
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   ],
   "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": 5,
   "metadata": {
    "collapsed": false
   },
   "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": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'module' object has no attribute 'cbook'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-6-eff513f636fd>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0;32mimport\u001b[0m \u001b[0mmatplotlib\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpyplot\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m/Users/luv/anaconda/envs/gl-env/lib/python2.7/site-packages/matplotlib/pyplot.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     27\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mcycler\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mcycler\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     28\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mmatplotlib\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 29\u001b[0;31m \u001b[0;32mimport\u001b[0m \u001b[0mmatplotlib\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcolorbar\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     30\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mmatplotlib\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mstyle\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     31\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mmatplotlib\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0m_pylab_helpers\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minteractive\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/luv/anaconda/envs/gl-env/lib/python2.7/site-packages/matplotlib/colorbar.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     30\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     31\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mmatplotlib\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mmpl\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 32\u001b[0;31m \u001b[0;32mimport\u001b[0m \u001b[0mmatplotlib\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0martist\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mmartist\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     33\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mmatplotlib\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcbook\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mcbook\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     34\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mmatplotlib\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcollections\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mcollections\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/luv/anaconda/envs/gl-env/lib/python2.7/site-packages/matplotlib/artist.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      9\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mnumpy\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     10\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mmatplotlib\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 11\u001b[0;31m \u001b[0;32mimport\u001b[0m \u001b[0mmatplotlib\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcbook\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mcbook\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     12\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mmatplotlib\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcbook\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mmplDeprecation\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     13\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mmatplotlib\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mdocstring\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrcParams\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mAttributeError\u001b[0m: 'module' object has no attribute 'cbook'"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'matplotlib' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-9-ed2d8e754638>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m matplotlib.pyplot.plot(sales['CrimeRate'],sales['HousePrice'],'.',\n\u001b[0m\u001b[1;32m      2\u001b[0m         sales['CrimeRate'],crime_model.predict(sales),'-')\n",
      "\u001b[0;31mNameError\u001b[0m: name 'matplotlib' is not defined"
     ]
    }
   ],
   "source": [
    "matplotlib.pyplot.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": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sales_noCC = sales[sales['MilesPhila'] != 0.0] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "                    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": 9,
   "metadata": {
    "collapsed": false
   },
   "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": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'plt' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-10-36fd3ca8e966>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m plt.plot(sales_noCC['CrimeRate'],sales_noCC['HousePrice'],'.',\n\u001b[0m\u001b[1;32m      2\u001b[0m         sales_noCC['CrimeRate'],crime_model.predict(sales_noCC),'-')\n",
      "\u001b[0;31mNameError\u001b[0m: name 'plt' is not defined"
     ]
    }
   ],
   "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": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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   ]
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  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
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   "outputs": [
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   "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": 13,
   "metadata": {
    "collapsed": false
   },
   "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": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">stderr</th>\n",
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       "    <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",
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       "        <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",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">491.537478123</td>\n",
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       "[2 rows x 4 columns]<br/>\n",
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       "\n",
       "Data:\n",
       "+-------------+-------+----------------+---------------+\n",
       "|     name    | index |     value      |     stderr    |\n",
       "+-------------+-------+----------------+---------------+\n",
       "| (intercept) |  None | 225204.604303  | 16404.0247514 |\n",
       "|  CrimeRate  |  None | -2287.69717443 | 491.537478123 |\n",
       "+-------------+-------+----------------+---------------+\n",
       "[2 rows x 4 columns]"
      ]
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     "execution_count": 14,
     "metadata": {},
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   ],
   "source": [
    "crime_model_noCC.get('coefficients')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\"><table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
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       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">index</th>\n",
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       "        <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",
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       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">199073.589615</td>\n",
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       "    </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",
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       "\n",
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       "\n",
       "Data:\n",
       "+-------------+-------+----------------+---------------+\n",
       "|     name    | index |     value      |     stderr    |\n",
       "+-------------+-------+----------------+---------------+\n",
       "| (intercept) |  None | 199073.589615  | 11932.5101105 |\n",
       "|  CrimeRate  |  None | -1837.71280989 | 351.519609333 |\n",
       "+-------------+-------+----------------+---------------+\n",
       "[2 rows x 4 columns]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "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": []
  }
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