REG05-NB01.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regression Week 5: Feature Selection and LASSO (Interpretation)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook, you will use LASSO to select features, building on a pre-implemented solver for LASSO (using Turi Create, though you can use other solvers). You will:\n",
    "* Run LASSO with different L1 penalties.\n",
    "* Choose best L1 penalty using a validation set.\n",
    "* Choose best L1 penalty using a validation set, with additional constraint on the size of subset.\n",
    "\n",
    "In the second notebook, you will implement your own LASSO solver, using coordinate descent. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fire up Turi Create"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import turicreate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Load in house sales data\n",
    "\n",
    "Dataset is from house sales in King County, the region where the city of Seattle, WA is located."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "sales = turicreate.SFrame('home_data.sframe/')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.7/site-packages/turicreate/visualization/_plot.py:461: UserWarning: Displaying only the first 100 rows.\n",
      "  warnings.warn(\"Displaying only the first {} rows.\".format(maximum_rows))\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<html lang=\"en\">                                                     <head>                                                               <style>                                                              .sframe {                                                            font-size: 12px;                                                   font-family: HelveticaNeue;                                        border: 1px solid silver;                                        }                                                                  .sframe thead th {                                                   background: #F7F7F7;                                               font-family: HelveticaNeue-Medium;                                 font-size: 14px;                                                   line-height: 16.8px;                                               padding-top: 16px;                                                 padding-bottom: 16px;                                              padding-left: 10px;                                                padding-right: 38px;                                               border-top: 1px solid #E9E9E9;                                     border-bottom: 1px solid #E9E9E9;                                  white-space: nowrap;                                               overflow: hidden;                                                  text-overflow:ellipsis;                                            text-align:center;                                                 font-weight:normal;                                              }                                                                  .sframe tbody th {                                                   background: #FFFFFF;                                               text-align:left;                                                   font-weight:normal;                                                border-right: 1px solid #E9E9E9;                                 }                                                                  .sframe td {                                                         background: #FFFFFF;                                               padding-left: 10px;                                                padding-right: 38px;                                               padding-top: 14px;                                                 padding-bottom: 14px;                                              border-bottom: 1px solid #E9E9E9;                                  max-height: 0px;                                                   transition: max-height 5s ease-out;                                vertical-align: middle;                                            font-family: HelveticaNeue;                                        font-size: 12px;                                                   line-height: 16.8px;                                               background: #FFFFFF;                                             }                                                                  .sframe tr {                                                         padding-left: 10px;                                                padding-right: 38px;                                               padding-top: 14px;                                                 padding-bottom: 14px;                                              border-bottom: 1px solid #E9E9E9;                                  max-height: 0px;                                                   transition: max-height 5s ease-out;                                vertical-align: middle;                                            font-family: HelveticaNeue;                                        font-size: 12px;                                                   line-height: 16.8px;                                               background: #FFFFFF;                                             }                                                                  .sframe tr:hover {                                                   background: silver;                                              },                                                               </style>                                                         </head>                                                            <body>                                                               <h1>  </h1>                                             <table border=\"1\" class=\"dataframe sframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>id</th>\n",
       "      <th>date</th>\n",
       "      <th>price</th>\n",
       "      <th>bedrooms</th>\n",
       "      <th>bathrooms</th>\n",
       "      <th>sqft_living</th>\n",
       "      <th>sqft_lot</th>\n",
       "      <th>floors</th>\n",
       "      <th>waterfront</th>\n",
       "      <th>view</th>\n",
       "      <th>condition</th>\n",
       "      <th>grade</th>\n",
       "      <th>sqft_above</th>\n",
       "      <th>sqft_basement</th>\n",
       "      <th>yr_built</th>\n",
       "      <th>yr_renovated</th>\n",
       "      <th>zipcode</th>\n",
       "      <th>lat</th>\n",
       "      <th>long</th>\n",
       "      <th>sqft_living15</th>\n",
       "      <th>sqft_lot15</th>\n",
       "      <th>sqft_living_sqrt</th>\n",
       "      <th>sqft_lot_sqrt</th>\n",
       "      <th>bedrooms_square</th>\n",
       "      <th>floors_square</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3980300371</td>\n",
       "      <td>2014-09-26 00:00:00+00:00</td>\n",
       "      <td>142000.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>290.0</td>\n",
       "      <td>20875.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1.0</td>\n",
       "      <td>290.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1963.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98024</td>\n",
       "      <td>47.530772</td>\n",
       "      <td>-121.888423</td>\n",
       "      <td>1620.0</td>\n",
       "      <td>22850.0</td>\n",
       "      <td>17.029386</td>\n",
       "      <td>144.481833</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5702500050</td>\n",
       "      <td>2014-11-04 00:00:00+00:00</td>\n",
       "      <td>280000.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>600.0</td>\n",
       "      <td>24501.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>3.0</td>\n",
       "      <td>600.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1950.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98045</td>\n",
       "      <td>47.531643</td>\n",
       "      <td>-121.748836</td>\n",
       "      <td>990.0</td>\n",
       "      <td>22549.0</td>\n",
       "      <td>24.494897</td>\n",
       "      <td>156.527953</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3421079032</td>\n",
       "      <td>2015-02-17 00:00:00+00:00</td>\n",
       "      <td>75000.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>670.0</td>\n",
       "      <td>43377.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>3.0</td>\n",
       "      <td>670.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1966.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98022</td>\n",
       "      <td>47.263814</td>\n",
       "      <td>-121.906416</td>\n",
       "      <td>1160.0</td>\n",
       "      <td>42882.0</td>\n",
       "      <td>25.884358</td>\n",
       "      <td>208.271457</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2420069251</td>\n",
       "      <td>2015-02-25 00:00:00+00:00</td>\n",
       "      <td>262000.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.75</td>\n",
       "      <td>520.0</td>\n",
       "      <td>12981.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>3.0</td>\n",
       "      <td>520.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1920.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98022</td>\n",
       "      <td>47.208201</td>\n",
       "      <td>-121.994538</td>\n",
       "      <td>1340.0</td>\n",
       "      <td>12233.0</td>\n",
       "      <td>22.803509</td>\n",
       "      <td>113.934192</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>8658300340</td>\n",
       "      <td>2014-05-23 00:00:00+00:00</td>\n",
       "      <td>80000.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.75</td>\n",
       "      <td>430.0</td>\n",
       "      <td>5050.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>4.0</td>\n",
       "      <td>430.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1912.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98014</td>\n",
       "      <td>47.649943</td>\n",
       "      <td>-121.908684</td>\n",
       "      <td>1200.0</td>\n",
       "      <td>7500.0</td>\n",
       "      <td>20.736441</td>\n",
       "      <td>71.063352</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>3089000005</td>\n",
       "      <td>2014-07-24 00:00:00+00:00</td>\n",
       "      <td>150000.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>850.0</td>\n",
       "      <td>54000.0</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>4.0</td>\n",
       "      <td>850.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1950.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98023</td>\n",
       "      <td>47.295873</td>\n",
       "      <td>-122.377304</td>\n",
       "      <td>1550.0</td>\n",
       "      <td>14440.0</td>\n",
       "      <td>29.154759</td>\n",
       "      <td>232.379001</td>\n",
       "      <td>4.0</td>\n",
       "      <td>2.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>3623059027</td>\n",
       "      <td>2014-10-22 00:00:00+00:00</td>\n",
       "      <td>200000.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.75</td>\n",
       "      <td>780.0</td>\n",
       "      <td>55764.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>4.0</td>\n",
       "      <td>780.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1945.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98058</td>\n",
       "      <td>47.441997</td>\n",
       "      <td>-122.105084</td>\n",
       "      <td>1620.0</td>\n",
       "      <td>30847.0</td>\n",
       "      <td>27.928480</td>\n",
       "      <td>236.144024</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>6146600170</td>\n",
       "      <td>2014-07-03 00:00:00+00:00</td>\n",
       "      <td>100000.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.75</td>\n",
       "      <td>660.0</td>\n",
       "      <td>5240.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>4.0</td>\n",
       "      <td>660.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1912.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98032</td>\n",
       "      <td>47.388098</td>\n",
       "      <td>-122.233657</td>\n",
       "      <td>850.0</td>\n",
       "      <td>5080.0</td>\n",
       "      <td>25.690465</td>\n",
       "      <td>72.387844</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>6929602721</td>\n",
       "      <td>2015-04-08 00:00:00+00:00</td>\n",
       "      <td>95000.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>960.0</td>\n",
       "      <td>7000.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>4.0</td>\n",
       "      <td>960.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1918.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98198</td>\n",
       "      <td>47.386386</td>\n",
       "      <td>-122.307210</td>\n",
       "      <td>1850.0</td>\n",
       "      <td>8120.0</td>\n",
       "      <td>30.983867</td>\n",
       "      <td>83.666003</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1352300580</td>\n",
       "      <td>2014-11-14 00:00:00+00:00</td>\n",
       "      <td>247000.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>460.0</td>\n",
       "      <td>4120.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>4.0</td>\n",
       "      <td>460.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1937.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98055</td>\n",
       "      <td>47.486804</td>\n",
       "      <td>-122.198990</td>\n",
       "      <td>990.0</td>\n",
       "      <td>4120.0</td>\n",
       "      <td>21.447611</td>\n",
       "      <td>64.187226</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1822059057</td>\n",
       "      <td>2014-07-25 00:00:00+00:00</td>\n",
       "      <td>152000.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>700.0</td>\n",
       "      <td>13500.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>4.0</td>\n",
       "      <td>700.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1920.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98031</td>\n",
       "      <td>47.388248</td>\n",
       "      <td>-122.207790</td>\n",
       "      <td>1600.0</td>\n",
       "      <td>10124.0</td>\n",
       "      <td>26.457513</td>\n",
       "      <td>116.189500</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>2354300456</td>\n",
       "      <td>2015-03-11 00:00:00+00:00</td>\n",
       "      <td>130000.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>600.0</td>\n",
       "      <td>1500.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>4.0</td>\n",
       "      <td>600.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1900.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98027</td>\n",
       "      <td>47.528873</td>\n",
       "      <td>-122.033091</td>\n",
       "      <td>1130.0</td>\n",
       "      <td>6000.0</td>\n",
       "      <td>24.494897</td>\n",
       "      <td>38.729833</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>3664500300</td>\n",
       "      <td>2014-11-06 00:00:00+00:00</td>\n",
       "      <td>230000.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>1470.0</td>\n",
       "      <td>25661.0</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1470.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1932.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98059</td>\n",
       "      <td>47.487846</td>\n",
       "      <td>-122.130195</td>\n",
       "      <td>1670.0</td>\n",
       "      <td>43301.0</td>\n",
       "      <td>38.340579</td>\n",
       "      <td>160.190512</td>\n",
       "      <td>4.0</td>\n",
       "      <td>2.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>1222029077</td>\n",
       "      <td>2014-10-29 00:00:00+00:00</td>\n",
       "      <td>265000.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.75</td>\n",
       "      <td>384.0</td>\n",
       "      <td>213444.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>4.0</td>\n",
       "      <td>384.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2003.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98070</td>\n",
       "      <td>47.417727</td>\n",
       "      <td>-122.491217</td>\n",
       "      <td>1920.0</td>\n",
       "      <td>224341.0</td>\n",
       "      <td>19.595918</td>\n",
       "      <td>462.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>8655900162</td>\n",
       "      <td>2015-02-19 00:00:00+00:00</td>\n",
       "      <td>156000.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.75</td>\n",
       "      <td>470.0</td>\n",
       "      <td>15000.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>4.0</td>\n",
       "      <td>470.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1947.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98014</td>\n",
       "      <td>47.655361</td>\n",
       "      <td>-121.908064</td>\n",
       "      <td>1730.0</td>\n",
       "      <td>22500.0</td>\n",
       "      <td>21.679483</td>\n",
       "      <td>122.474487</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1925069006</td>\n",
       "      <td>2014-12-03 00:00:00+00:00</td>\n",
       "      <td>355000.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.75</td>\n",
       "      <td>530.0</td>\n",
       "      <td>33278.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>4.0</td>\n",
       "      <td>530.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1950.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98074</td>\n",
       "      <td>47.641204</td>\n",
       "      <td>-122.079447</td>\n",
       "      <td>2830.0</td>\n",
       "      <td>14311.0</td>\n",
       "      <td>23.021729</td>\n",
       "      <td>182.422586</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>3340401535</td>\n",
       "      <td>2014-11-05 00:00:00+00:00</td>\n",
       "      <td>140000.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>730.0</td>\n",
       "      <td>6890.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>4.0</td>\n",
       "      <td>730.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1926.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98055</td>\n",
       "      <td>47.466980</td>\n",
       "      <td>-122.215007</td>\n",
       "      <td>1790.0</td>\n",
       "      <td>7969.0</td>\n",
       "      <td>27.018512</td>\n",
       "      <td>83.006024</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>6453300055</td>\n",
       "      <td>2014-10-07 00:00:00+00:00</td>\n",
       "      <td>188000.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>550.0</td>\n",
       "      <td>16345.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>4.0</td>\n",
       "      <td>550.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1945.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98106</td>\n",
       "      <td>47.518134</td>\n",
       "      <td>-122.339324</td>\n",
       "      <td>1100.0</td>\n",
       "      <td>9240.0</td>\n",
       "      <td>23.452079</td>\n",
       "      <td>127.847565</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>4322200105</td>\n",
       "      <td>2015-03-31 00:00:00+00:00</td>\n",
       "      <td>229050.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>420.0</td>\n",
       "      <td>3298.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>4.0</td>\n",
       "      <td>420.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1949.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98136</td>\n",
       "      <td>47.537476</td>\n",
       "      <td>-122.391385</td>\n",
       "      <td>1460.0</td>\n",
       "      <td>4975.0</td>\n",
       "      <td>20.493902</td>\n",
       "      <td>57.428216</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>2114700500</td>\n",
       "      <td>2015-04-18 00:00:00+00:00</td>\n",
       "      <td>90000.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>560.0</td>\n",
       "      <td>4120.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>4.0</td>\n",
       "      <td>560.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1947.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98106</td>\n",
       "      <td>47.533484</td>\n",
       "      <td>-122.347815</td>\n",
       "      <td>980.0</td>\n",
       "      <td>4120.0</td>\n",
       "      <td>23.664319</td>\n",
       "      <td>64.187226</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>3760500240</td>\n",
       "      <td>2015-05-12 00:00:00+00:00</td>\n",
       "      <td>435000.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.75</td>\n",
       "      <td>750.0</td>\n",
       "      <td>16321.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>4.0</td>\n",
       "      <td>750.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1936.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98034</td>\n",
       "      <td>47.698525</td>\n",
       "      <td>-122.228770</td>\n",
       "      <td>3020.0</td>\n",
       "      <td>10625.0</td>\n",
       "      <td>27.386128</td>\n",
       "      <td>127.753669</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>4391600065</td>\n",
       "      <td>2014-08-14 00:00:00+00:00</td>\n",
       "      <td>330000.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.75</td>\n",
       "      <td>520.0</td>\n",
       "      <td>6862.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>4.0</td>\n",
       "      <td>520.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1924.0</td>\n",
       "      <td>1980.0</td>\n",
       "      <td>98010</td>\n",
       "      <td>47.326012</td>\n",
       "      <td>-122.037328</td>\n",
       "      <td>1170.0</td>\n",
       "      <td>8756.0</td>\n",
       "      <td>22.803509</td>\n",
       "      <td>82.837190</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>6303400395</td>\n",
       "      <td>2015-01-30 00:00:00+00:00</td>\n",
       "      <td>325000.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.75</td>\n",
       "      <td>410.0</td>\n",
       "      <td>8636.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>4.0</td>\n",
       "      <td>410.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1953.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98146</td>\n",
       "      <td>47.507672</td>\n",
       "      <td>-122.356722</td>\n",
       "      <td>1190.0</td>\n",
       "      <td>8636.0</td>\n",
       "      <td>20.248457</td>\n",
       "      <td>92.930081</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>5279100625</td>\n",
       "      <td>2015-04-29 00:00:00+00:00</td>\n",
       "      <td>248000.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>770.0</td>\n",
       "      <td>8600.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>4.0</td>\n",
       "      <td>770.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1914.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98027</td>\n",
       "      <td>47.532470</td>\n",
       "      <td>-122.030615</td>\n",
       "      <td>1420.0</td>\n",
       "      <td>6960.0</td>\n",
       "      <td>27.748874</td>\n",
       "      <td>92.736185</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>1823069059</td>\n",
       "      <td>2014-06-11 00:00:00+00:00</td>\n",
       "      <td>355000.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.75</td>\n",
       "      <td>750.0</td>\n",
       "      <td>20339.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>4.0</td>\n",
       "      <td>550.0</td>\n",
       "      <td>200.0</td>\n",
       "      <td>1946.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98059</td>\n",
       "      <td>47.475631</td>\n",
       "      <td>-122.090274</td>\n",
       "      <td>2020.0</td>\n",
       "      <td>23958.0</td>\n",
       "      <td>27.386128</td>\n",
       "      <td>142.614866</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>6730700385</td>\n",
       "      <td>2014-10-22 00:00:00+00:00</td>\n",
       "      <td>205000.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>0.75</td>\n",
       "      <td>770.0</td>\n",
       "      <td>7000.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>4.0</td>\n",
       "      <td>770.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1942.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98024</td>\n",
       "      <td>47.566110</td>\n",
       "      <td>-121.887183</td>\n",
       "      <td>950.0</td>\n",
       "      <td>10500.0</td>\n",
       "      <td>27.748874</td>\n",
       "      <td>83.666003</td>\n",
       "      <td>9.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>3122069029</td>\n",
       "      <td>2014-06-19 00:00:00+00:00</td>\n",
       "      <td>120000.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>990.0</td>\n",
       "      <td>39964.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>4.0</td>\n",
       "      <td>990.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1945.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98042</td>\n",
       "      <td>47.357735</td>\n",
       "      <td>-122.085490</td>\n",
       "      <td>1560.0</td>\n",
       "      <td>8990.0</td>\n",
       "      <td>31.464265</td>\n",
       "      <td>199.909980</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>7203601405</td>\n",
       "      <td>2015-04-14 00:00:00+00:00</td>\n",
       "      <td>217000.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>730.0</td>\n",
       "      <td>2400.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>4.0</td>\n",
       "      <td>730.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1934.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98198</td>\n",
       "      <td>47.350042</td>\n",
       "      <td>-122.321550</td>\n",
       "      <td>1220.0</td>\n",
       "      <td>4382.0</td>\n",
       "      <td>27.018512</td>\n",
       "      <td>48.989795</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>7325600160</td>\n",
       "      <td>2014-06-04 00:00:00+00:00</td>\n",
       "      <td>299000.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.75</td>\n",
       "      <td>560.0</td>\n",
       "      <td>12120.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>4.0</td>\n",
       "      <td>560.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1967.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98014</td>\n",
       "      <td>47.675042</td>\n",
       "      <td>-121.854351</td>\n",
       "      <td>1300.0</td>\n",
       "      <td>19207.0</td>\n",
       "      <td>23.664319</td>\n",
       "      <td>110.090872</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>4048400185</td>\n",
       "      <td>2014-10-22 00:00:00+00:00</td>\n",
       "      <td>352000.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.75</td>\n",
       "      <td>760.0</td>\n",
       "      <td>33801.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>4.0</td>\n",
       "      <td>760.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1931.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98059</td>\n",
       "      <td>47.470317</td>\n",
       "      <td>-122.075855</td>\n",
       "      <td>1100.0</td>\n",
       "      <td>39504.0</td>\n",
       "      <td>27.568098</td>\n",
       "      <td>183.850483</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>0745000005</td>\n",
       "      <td>2014-08-25 00:00:00+00:00</td>\n",
       "      <td>145000.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.75</td>\n",
       "      <td>480.0</td>\n",
       "      <td>9750.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>4.0</td>\n",
       "      <td>480.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1948.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98146</td>\n",
       "      <td>47.498193</td>\n",
       "      <td>-122.361612</td>\n",
       "      <td>1550.0</td>\n",
       "      <td>9924.0</td>\n",
       "      <td>21.908902</td>\n",
       "      <td>98.742088</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>6896300380</td>\n",
       "      <td>2014-10-02 00:00:00+00:00</td>\n",
       "      <td>228000.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>390.0</td>\n",
       "      <td>5900.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>4.0</td>\n",
       "      <td>390.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1953.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98118</td>\n",
       "      <td>47.526040</td>\n",
       "      <td>-122.261428</td>\n",
       "      <td>2170.0</td>\n",
       "      <td>6000.0</td>\n",
       "      <td>19.748418</td>\n",
       "      <td>76.811457</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>2114700090</td>\n",
       "      <td>2015-03-01 00:00:00+00:00</td>\n",
       "      <td>151000.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.75</td>\n",
       "      <td>720.0</td>\n",
       "      <td>5040.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>4.0</td>\n",
       "      <td>720.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1949.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98106</td>\n",
       "      <td>47.532289</td>\n",
       "      <td>-122.346541</td>\n",
       "      <td>1290.0</td>\n",
       "      <td>4120.0</td>\n",
       "      <td>26.832816</td>\n",
       "      <td>70.992957</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>3332000195</td>\n",
       "      <td>2014-09-24 00:00:00+00:00</td>\n",
       "      <td>167500.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>760.0</td>\n",
       "      <td>3090.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>5.0</td>\n",
       "      <td>760.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1903.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98118</td>\n",
       "      <td>47.551326</td>\n",
       "      <td>-122.274718</td>\n",
       "      <td>1020.0</td>\n",
       "      <td>5356.0</td>\n",
       "      <td>27.568098</td>\n",
       "      <td>55.587768</td>\n",
       "      <td>9.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>2724089019</td>\n",
       "      <td>2014-05-23 00:00:00+00:00</td>\n",
       "      <td>527550.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.75</td>\n",
       "      <td>820.0</td>\n",
       "      <td>59677.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>5.0</td>\n",
       "      <td>820.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1999.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98065</td>\n",
       "      <td>47.531585</td>\n",
       "      <td>-121.764258</td>\n",
       "      <td>1590.0</td>\n",
       "      <td>14163.0</td>\n",
       "      <td>28.635642</td>\n",
       "      <td>244.288764</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>8658300315</td>\n",
       "      <td>2015-03-12 00:00:00+00:00</td>\n",
       "      <td>425000.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.75</td>\n",
       "      <td>1400.0</td>\n",
       "      <td>5071.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1400.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1916.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98014</td>\n",
       "      <td>47.649944</td>\n",
       "      <td>-121.908280</td>\n",
       "      <td>1200.0</td>\n",
       "      <td>7500.0</td>\n",
       "      <td>37.416574</td>\n",
       "      <td>71.210954</td>\n",
       "      <td>25.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>9435300030</td>\n",
       "      <td>2014-05-28 00:00:00+00:00</td>\n",
       "      <td>550000.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>1660.0</td>\n",
       "      <td>34848.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>5.0</td>\n",
       "      <td>930.0</td>\n",
       "      <td>730.0</td>\n",
       "      <td>1933.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98052</td>\n",
       "      <td>47.662149</td>\n",
       "      <td>-122.131997</td>\n",
       "      <td>2160.0</td>\n",
       "      <td>11467.0</td>\n",
       "      <td>40.743098</td>\n",
       "      <td>186.676190</td>\n",
       "      <td>16.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>3124089086</td>\n",
       "      <td>2014-10-02 00:00:00+00:00</td>\n",
       "      <td>300000.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>1730.0</td>\n",
       "      <td>177657.0</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1730.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1948.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98065</td>\n",
       "      <td>47.516274</td>\n",
       "      <td>-121.829079</td>\n",
       "      <td>1400.0</td>\n",
       "      <td>45175.0</td>\n",
       "      <td>41.593269</td>\n",
       "      <td>421.493772</td>\n",
       "      <td>16.0</td>\n",
       "      <td>2.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>5381000082</td>\n",
       "      <td>2015-01-08 00:00:00+00:00</td>\n",
       "      <td>185000.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>670.0</td>\n",
       "      <td>6750.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>5.0</td>\n",
       "      <td>670.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1947.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98188</td>\n",
       "      <td>47.452119</td>\n",
       "      <td>-122.283198</td>\n",
       "      <td>1700.0</td>\n",
       "      <td>11520.0</td>\n",
       "      <td>25.884358</td>\n",
       "      <td>82.158384</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>0421000215</td>\n",
       "      <td>2015-04-16 00:00:00+00:00</td>\n",
       "      <td>208000.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>700.0</td>\n",
       "      <td>5100.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>5.0</td>\n",
       "      <td>700.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1953.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98056</td>\n",
       "      <td>47.495713</td>\n",
       "      <td>-122.168370</td>\n",
       "      <td>970.0</td>\n",
       "      <td>5811.0</td>\n",
       "      <td>26.457513</td>\n",
       "      <td>71.414284</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>0859000110</td>\n",
       "      <td>2014-10-02 00:00:00+00:00</td>\n",
       "      <td>125000.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>500.0</td>\n",
       "      <td>7440.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>5.0</td>\n",
       "      <td>500.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1928.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98106</td>\n",
       "      <td>47.525206</td>\n",
       "      <td>-122.362116</td>\n",
       "      <td>1350.0</td>\n",
       "      <td>7440.0</td>\n",
       "      <td>22.360680</td>\n",
       "      <td>86.255435</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>9268200600</td>\n",
       "      <td>2014-05-19 00:00:00+00:00</td>\n",
       "      <td>413500.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>770.0</td>\n",
       "      <td>4000.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>5.0</td>\n",
       "      <td>770.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1924.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98117</td>\n",
       "      <td>47.695867</td>\n",
       "      <td>-122.364465</td>\n",
       "      <td>1420.0</td>\n",
       "      <td>5040.0</td>\n",
       "      <td>27.748874</td>\n",
       "      <td>63.245553</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>5101404170</td>\n",
       "      <td>2014-11-13 00:00:00+00:00</td>\n",
       "      <td>200000.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.75</td>\n",
       "      <td>680.0</td>\n",
       "      <td>9600.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>5.0</td>\n",
       "      <td>680.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1947.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98115</td>\n",
       "      <td>47.696416</td>\n",
       "      <td>-122.306414</td>\n",
       "      <td>1580.0</td>\n",
       "      <td>6624.0</td>\n",
       "      <td>26.076810</td>\n",
       "      <td>97.979590</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>8127700845</td>\n",
       "      <td>2015-02-19 00:00:00+00:00</td>\n",
       "      <td>375000.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>710.0</td>\n",
       "      <td>4618.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>5.0</td>\n",
       "      <td>710.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1925.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98199</td>\n",
       "      <td>47.640043</td>\n",
       "      <td>-122.393764</td>\n",
       "      <td>1810.0</td>\n",
       "      <td>4988.0</td>\n",
       "      <td>26.645825</td>\n",
       "      <td>67.955868</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>2767600171</td>\n",
       "      <td>2014-05-19 00:00:00+00:00</td>\n",
       "      <td>440000.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.50</td>\n",
       "      <td>1010.0</td>\n",
       "      <td>1968.0</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1010.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1906.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98107</td>\n",
       "      <td>47.675696</td>\n",
       "      <td>-122.384973</td>\n",
       "      <td>1760.0</td>\n",
       "      <td>4200.0</td>\n",
       "      <td>31.780497</td>\n",
       "      <td>44.362146</td>\n",
       "      <td>4.0</td>\n",
       "      <td>2.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>0421000285</td>\n",
       "      <td>2015-04-23 00:00:00+00:00</td>\n",
       "      <td>268000.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.50</td>\n",
       "      <td>1730.0</td>\n",
       "      <td>7020.0</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1730.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1953.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98056</td>\n",
       "      <td>47.493908</td>\n",
       "      <td>-122.166948</td>\n",
       "      <td>1110.0</td>\n",
       "      <td>7020.0</td>\n",
       "      <td>41.593269</td>\n",
       "      <td>83.785440</td>\n",
       "      <td>16.0</td>\n",
       "      <td>2.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>4045500510</td>\n",
       "      <td>2014-05-21 00:00:00+00:00</td>\n",
       "      <td>420850.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>960.0</td>\n",
       "      <td>40946.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>5.0</td>\n",
       "      <td>960.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1945.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98014</td>\n",
       "      <td>47.695091</td>\n",
       "      <td>-121.863533</td>\n",
       "      <td>1320.0</td>\n",
       "      <td>20350.0</td>\n",
       "      <td>30.983867</td>\n",
       "      <td>202.351180</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>0006200017</td>\n",
       "      <td>2014-11-12 00:00:00+00:00</td>\n",
       "      <td>281000.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>1340.0</td>\n",
       "      <td>21336.0</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1340.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1945.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98032</td>\n",
       "      <td>47.402256</td>\n",
       "      <td>-122.273161</td>\n",
       "      <td>1340.0</td>\n",
       "      <td>37703.0</td>\n",
       "      <td>36.606010</td>\n",
       "      <td>146.068477</td>\n",
       "      <td>9.0</td>\n",
       "      <td>2.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>0418000010</td>\n",
       "      <td>2015-04-22 00:00:00+00:00</td>\n",
       "      <td>227450.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>660.0</td>\n",
       "      <td>6509.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>5.0</td>\n",
       "      <td>660.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1952.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98056</td>\n",
       "      <td>47.493847</td>\n",
       "      <td>-122.170548</td>\n",
       "      <td>970.0</td>\n",
       "      <td>5713.0</td>\n",
       "      <td>25.690465</td>\n",
       "      <td>80.678374</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>0844000425</td>\n",
       "      <td>2014-12-23 00:00:00+00:00</td>\n",
       "      <td>199999.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>960.0</td>\n",
       "      <td>10815.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>5.0</td>\n",
       "      <td>960.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1900.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98010</td>\n",
       "      <td>47.309070</td>\n",
       "      <td>-122.005802</td>\n",
       "      <td>1330.0</td>\n",
       "      <td>10815.0</td>\n",
       "      <td>30.983867</td>\n",
       "      <td>103.995192</td>\n",
       "      <td>9.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50</th>\n",
       "      <td>0844001145</td>\n",
       "      <td>2015-03-26 00:00:00+00:00</td>\n",
       "      <td>208500.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>880.0</td>\n",
       "      <td>4814.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>5.0</td>\n",
       "      <td>880.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1906.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98010</td>\n",
       "      <td>47.310723</td>\n",
       "      <td>-121.998943</td>\n",
       "      <td>1010.0</td>\n",
       "      <td>6160.0</td>\n",
       "      <td>29.664794</td>\n",
       "      <td>69.382995</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>51</th>\n",
       "      <td>0121059007</td>\n",
       "      <td>2014-08-08 00:00:00+00:00</td>\n",
       "      <td>210000.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>1200.0</td>\n",
       "      <td>43560.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1200.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1968.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98042</td>\n",
       "      <td>47.337544</td>\n",
       "      <td>-122.122558</td>\n",
       "      <td>1400.0</td>\n",
       "      <td>54450.0</td>\n",
       "      <td>34.641016</td>\n",
       "      <td>208.710326</td>\n",
       "      <td>16.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>52</th>\n",
       "      <td>7116000425</td>\n",
       "      <td>2014-11-25 00:00:00+00:00</td>\n",
       "      <td>150000.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>720.0</td>\n",
       "      <td>4120.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>5.0</td>\n",
       "      <td>720.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1915.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98002</td>\n",
       "      <td>47.302989</td>\n",
       "      <td>-122.217469</td>\n",
       "      <td>940.0</td>\n",
       "      <td>6180.0</td>\n",
       "      <td>26.832816</td>\n",
       "      <td>64.187226</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>53</th>\n",
       "      <td>7227500020</td>\n",
       "      <td>2015-01-23 00:00:00+00:00</td>\n",
       "      <td>259950.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>1460.0</td>\n",
       "      <td>5825.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1260.0</td>\n",
       "      <td>200.0</td>\n",
       "      <td>1942.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98056</td>\n",
       "      <td>47.495767</td>\n",
       "      <td>-122.190743</td>\n",
       "      <td>1150.0</td>\n",
       "      <td>5926.0</td>\n",
       "      <td>38.209946</td>\n",
       "      <td>76.321688</td>\n",
       "      <td>9.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>54</th>\n",
       "      <td>8698100170</td>\n",
       "      <td>2015-02-11 00:00:00+00:00</td>\n",
       "      <td>111300.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>1060.0</td>\n",
       "      <td>6000.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1060.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1908.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98002</td>\n",
       "      <td>47.306602</td>\n",
       "      <td>-122.222607</td>\n",
       "      <td>940.0</td>\n",
       "      <td>6000.0</td>\n",
       "      <td>32.557641</td>\n",
       "      <td>77.459667</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>55</th>\n",
       "      <td>1735800050</td>\n",
       "      <td>2015-04-09 00:00:00+00:00</td>\n",
       "      <td>142500.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>690.0</td>\n",
       "      <td>6825.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>5.0</td>\n",
       "      <td>690.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1917.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98002</td>\n",
       "      <td>47.310923</td>\n",
       "      <td>-122.225241</td>\n",
       "      <td>1330.0</td>\n",
       "      <td>5381.0</td>\n",
       "      <td>26.267851</td>\n",
       "      <td>82.613558</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>56</th>\n",
       "      <td>2726049071</td>\n",
       "      <td>2014-12-11 00:00:00+00:00</td>\n",
       "      <td>510000.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>820.0</td>\n",
       "      <td>4206.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>5.0</td>\n",
       "      <td>820.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1949.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98125</td>\n",
       "      <td>47.707640</td>\n",
       "      <td>-122.283867</td>\n",
       "      <td>1810.0</td>\n",
       "      <td>7200.0</td>\n",
       "      <td>28.635642</td>\n",
       "      <td>64.853681</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>57</th>\n",
       "      <td>2726049071</td>\n",
       "      <td>2015-04-08 00:00:00+00:00</td>\n",
       "      <td>489950.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>820.0</td>\n",
       "      <td>4206.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>5.0</td>\n",
       "      <td>820.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1949.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98125</td>\n",
       "      <td>47.707640</td>\n",
       "      <td>-122.283867</td>\n",
       "      <td>1810.0</td>\n",
       "      <td>7200.0</td>\n",
       "      <td>28.635642</td>\n",
       "      <td>64.853681</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58</th>\n",
       "      <td>3806000005</td>\n",
       "      <td>2014-10-30 00:00:00+00:00</td>\n",
       "      <td>110000.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>760.0</td>\n",
       "      <td>4746.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>5.0</td>\n",
       "      <td>760.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1930.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98055</td>\n",
       "      <td>47.483586</td>\n",
       "      <td>-122.214469</td>\n",
       "      <td>1360.0</td>\n",
       "      <td>7810.0</td>\n",
       "      <td>27.568098</td>\n",
       "      <td>68.891219</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>59</th>\n",
       "      <td>3424069145</td>\n",
       "      <td>2014-09-25 00:00:00+00:00</td>\n",
       "      <td>343000.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>1400.0</td>\n",
       "      <td>5662.0</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1400.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1920.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98027</td>\n",
       "      <td>47.527053</td>\n",
       "      <td>-122.036354</td>\n",
       "      <td>1250.0</td>\n",
       "      <td>14375.0</td>\n",
       "      <td>37.416574</td>\n",
       "      <td>75.246262</td>\n",
       "      <td>9.0</td>\n",
       "      <td>2.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>60</th>\n",
       "      <td>7224000980</td>\n",
       "      <td>2014-06-10 00:00:00+00:00</td>\n",
       "      <td>100000.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>1120.0</td>\n",
       "      <td>2685.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>5.0</td>\n",
       "      <td>860.0</td>\n",
       "      <td>260.0</td>\n",
       "      <td>1939.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98055</td>\n",
       "      <td>47.490422</td>\n",
       "      <td>-122.203116</td>\n",
       "      <td>1120.0</td>\n",
       "      <td>4838.0</td>\n",
       "      <td>33.466401</td>\n",
       "      <td>51.816986</td>\n",
       "      <td>16.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>61</th>\n",
       "      <td>5634500170</td>\n",
       "      <td>2014-08-19 00:00:00+00:00</td>\n",
       "      <td>250000.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>950.0</td>\n",
       "      <td>11835.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>5.0</td>\n",
       "      <td>950.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1932.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98028</td>\n",
       "      <td>47.749404</td>\n",
       "      <td>-122.236772</td>\n",
       "      <td>1690.0</td>\n",
       "      <td>12586.0</td>\n",
       "      <td>30.822070</td>\n",
       "      <td>108.788786</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>62</th>\n",
       "      <td>7839300185</td>\n",
       "      <td>2015-02-06 00:00:00+00:00</td>\n",
       "      <td>225000.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>1340.0</td>\n",
       "      <td>4800.0</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1340.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1903.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98055</td>\n",
       "      <td>47.477017</td>\n",
       "      <td>-122.209228</td>\n",
       "      <td>1240.0</td>\n",
       "      <td>4800.0</td>\n",
       "      <td>36.606010</td>\n",
       "      <td>69.282032</td>\n",
       "      <td>9.0</td>\n",
       "      <td>2.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>63</th>\n",
       "      <td>1437500015</td>\n",
       "      <td>2014-07-09 00:00:00+00:00</td>\n",
       "      <td>150000.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>0.75</td>\n",
       "      <td>490.0</td>\n",
       "      <td>38500.0</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>5.0</td>\n",
       "      <td>490.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1959.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98014</td>\n",
       "      <td>47.711176</td>\n",
       "      <td>-121.315254</td>\n",
       "      <td>800.0</td>\n",
       "      <td>18297.0</td>\n",
       "      <td>22.135944</td>\n",
       "      <td>196.214169</td>\n",
       "      <td>9.0</td>\n",
       "      <td>2.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>64</th>\n",
       "      <td>0421000185</td>\n",
       "      <td>2014-06-11 00:00:00+00:00</td>\n",
       "      <td>200000.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>700.0</td>\n",
       "      <td>4700.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>5.0</td>\n",
       "      <td>700.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1953.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98056</td>\n",
       "      <td>47.495287</td>\n",
       "      <td>-122.168915</td>\n",
       "      <td>960.0</td>\n",
       "      <td>5200.0</td>\n",
       "      <td>26.457513</td>\n",
       "      <td>68.556546</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>65</th>\n",
       "      <td>7227800040</td>\n",
       "      <td>2014-06-04 00:00:00+00:00</td>\n",
       "      <td>190000.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>2.00</td>\n",
       "      <td>1750.0</td>\n",
       "      <td>10284.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1750.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1943.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98056</td>\n",
       "      <td>47.509393</td>\n",
       "      <td>-122.182224</td>\n",
       "      <td>1560.0</td>\n",
       "      <td>9010.0</td>\n",
       "      <td>41.833001</td>\n",
       "      <td>101.410059</td>\n",
       "      <td>25.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>66</th>\n",
       "      <td>7818700480</td>\n",
       "      <td>2015-04-09 00:00:00+00:00</td>\n",
       "      <td>314200.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>610.0</td>\n",
       "      <td>6000.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>5.0</td>\n",
       "      <td>610.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1918.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98117</td>\n",
       "      <td>47.691091</td>\n",
       "      <td>-122.366994</td>\n",
       "      <td>970.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>24.698178</td>\n",
       "      <td>77.459667</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>67</th>\n",
       "      <td>2122059127</td>\n",
       "      <td>2014-09-16 00:00:00+00:00</td>\n",
       "      <td>209900.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>1030.0</td>\n",
       "      <td>60720.0</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1030.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1912.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98042</td>\n",
       "      <td>47.374985</td>\n",
       "      <td>-122.166167</td>\n",
       "      <td>1330.0</td>\n",
       "      <td>10342.0</td>\n",
       "      <td>32.093613</td>\n",
       "      <td>246.414285</td>\n",
       "      <td>9.0</td>\n",
       "      <td>2.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>68</th>\n",
       "      <td>7802900380</td>\n",
       "      <td>2014-09-08 00:00:00+00:00</td>\n",
       "      <td>335000.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>1360.0</td>\n",
       "      <td>69260.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1360.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1937.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98065</td>\n",
       "      <td>47.522850</td>\n",
       "      <td>-121.837521</td>\n",
       "      <td>1460.0</td>\n",
       "      <td>69260.0</td>\n",
       "      <td>36.878178</td>\n",
       "      <td>263.172947</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69</th>\n",
       "      <td>5379800500</td>\n",
       "      <td>2014-09-30 00:00:00+00:00</td>\n",
       "      <td>255000.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.50</td>\n",
       "      <td>910.0</td>\n",
       "      <td>25500.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>5.0</td>\n",
       "      <td>910.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1943.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98188</td>\n",
       "      <td>47.456496</td>\n",
       "      <td>-122.275502</td>\n",
       "      <td>1580.0</td>\n",
       "      <td>10019.0</td>\n",
       "      <td>30.166206</td>\n",
       "      <td>159.687194</td>\n",
       "      <td>9.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>70</th>\n",
       "      <td>1670400090</td>\n",
       "      <td>2014-11-24 00:00:00+00:00</td>\n",
       "      <td>182000.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>1160.0</td>\n",
       "      <td>18055.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1160.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1950.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98168</td>\n",
       "      <td>47.477178</td>\n",
       "      <td>-122.268624</td>\n",
       "      <td>1340.0</td>\n",
       "      <td>10324.0</td>\n",
       "      <td>34.058773</td>\n",
       "      <td>134.368895</td>\n",
       "      <td>9.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>71</th>\n",
       "      <td>3224079005</td>\n",
       "      <td>2014-10-09 00:00:00+00:00</td>\n",
       "      <td>255000.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>920.0</td>\n",
       "      <td>43560.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>5.0</td>\n",
       "      <td>920.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1923.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98024</td>\n",
       "      <td>47.524489</td>\n",
       "      <td>-121.931496</td>\n",
       "      <td>1530.0</td>\n",
       "      <td>11875.0</td>\n",
       "      <td>30.331502</td>\n",
       "      <td>208.710326</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>72</th>\n",
       "      <td>6911700066</td>\n",
       "      <td>2014-06-04 00:00:00+00:00</td>\n",
       "      <td>175000.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>670.0</td>\n",
       "      <td>2378.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>5.0</td>\n",
       "      <td>670.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1919.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98126</td>\n",
       "      <td>47.576899</td>\n",
       "      <td>-122.372234</td>\n",
       "      <td>700.0</td>\n",
       "      <td>2970.0</td>\n",
       "      <td>25.884358</td>\n",
       "      <td>48.764741</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>73</th>\n",
       "      <td>5062300280</td>\n",
       "      <td>2015-04-16 00:00:00+00:00</td>\n",
       "      <td>150000.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>890.0</td>\n",
       "      <td>6488.0</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>5.0</td>\n",
       "      <td>890.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1928.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98014</td>\n",
       "      <td>47.708676</td>\n",
       "      <td>-121.351715</td>\n",
       "      <td>1330.0</td>\n",
       "      <td>16250.0</td>\n",
       "      <td>29.832868</td>\n",
       "      <td>80.548122</td>\n",
       "      <td>9.0</td>\n",
       "      <td>2.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>74</th>\n",
       "      <td>0323059167</td>\n",
       "      <td>2014-07-23 00:00:00+00:00</td>\n",
       "      <td>259000.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>1210.0</td>\n",
       "      <td>17389.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1210.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1948.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98059</td>\n",
       "      <td>47.504399</td>\n",
       "      <td>-122.147884</td>\n",
       "      <td>2140.0</td>\n",
       "      <td>14419.0</td>\n",
       "      <td>34.785054</td>\n",
       "      <td>131.867358</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75</th>\n",
       "      <td>1549500370</td>\n",
       "      <td>2014-05-05 00:00:00+00:00</td>\n",
       "      <td>210000.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>1340.0</td>\n",
       "      <td>306848.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1340.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1953.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98019</td>\n",
       "      <td>47.753356</td>\n",
       "      <td>-121.911773</td>\n",
       "      <td>1800.0</td>\n",
       "      <td>128066.0</td>\n",
       "      <td>36.606010</td>\n",
       "      <td>553.938625</td>\n",
       "      <td>9.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>76</th>\n",
       "      <td>3751605432</td>\n",
       "      <td>2014-05-13 00:00:00+00:00</td>\n",
       "      <td>239950.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>1900.0</td>\n",
       "      <td>33888.0</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1900.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1942.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98001</td>\n",
       "      <td>47.273839</td>\n",
       "      <td>-122.270646</td>\n",
       "      <td>1430.0</td>\n",
       "      <td>19200.0</td>\n",
       "      <td>43.588989</td>\n",
       "      <td>184.086936</td>\n",
       "      <td>9.0</td>\n",
       "      <td>2.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>77</th>\n",
       "      <td>7224000950</td>\n",
       "      <td>2014-11-03 00:00:00+00:00</td>\n",
       "      <td>238950.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>810.0</td>\n",
       "      <td>4838.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>5.0</td>\n",
       "      <td>810.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1938.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98055</td>\n",
       "      <td>47.490934</td>\n",
       "      <td>-122.203120</td>\n",
       "      <td>890.0</td>\n",
       "      <td>4838.0</td>\n",
       "      <td>28.460499</td>\n",
       "      <td>69.555733</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>78</th>\n",
       "      <td>0985000900</td>\n",
       "      <td>2014-11-05 00:00:00+00:00</td>\n",
       "      <td>198500.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.75</td>\n",
       "      <td>1520.0</td>\n",
       "      <td>7137.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1520.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1932.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98168</td>\n",
       "      <td>47.492359</td>\n",
       "      <td>-122.311373</td>\n",
       "      <td>1240.0</td>\n",
       "      <td>8602.0</td>\n",
       "      <td>38.987177</td>\n",
       "      <td>84.480767</td>\n",
       "      <td>9.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>79</th>\n",
       "      <td>8151600470</td>\n",
       "      <td>2014-08-04 00:00:00+00:00</td>\n",
       "      <td>121800.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>940.0</td>\n",
       "      <td>8384.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>5.0</td>\n",
       "      <td>940.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1947.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98146</td>\n",
       "      <td>47.506481</td>\n",
       "      <td>-122.363549</td>\n",
       "      <td>1290.0</td>\n",
       "      <td>8384.0</td>\n",
       "      <td>30.659419</td>\n",
       "      <td>91.564185</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>80</th>\n",
       "      <td>5379802181</td>\n",
       "      <td>2014-11-19 00:00:00+00:00</td>\n",
       "      <td>193000.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>680.0</td>\n",
       "      <td>8640.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>5.0</td>\n",
       "      <td>680.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1951.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98188</td>\n",
       "      <td>47.455914</td>\n",
       "      <td>-122.288727</td>\n",
       "      <td>1320.0</td>\n",
       "      <td>13140.0</td>\n",
       "      <td>26.076810</td>\n",
       "      <td>92.951600</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>81</th>\n",
       "      <td>5417600130</td>\n",
       "      <td>2014-10-10 00:00:00+00:00</td>\n",
       "      <td>244500.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>910.0</td>\n",
       "      <td>9000.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>5.0</td>\n",
       "      <td>910.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1923.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98065</td>\n",
       "      <td>47.526008</td>\n",
       "      <td>-121.809785</td>\n",
       "      <td>1290.0</td>\n",
       "      <td>9000.0</td>\n",
       "      <td>30.166206</td>\n",
       "      <td>94.868330</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>82</th>\n",
       "      <td>5417600130</td>\n",
       "      <td>2015-05-12 00:00:00+00:00</td>\n",
       "      <td>301000.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>910.0</td>\n",
       "      <td>9000.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>5.0</td>\n",
       "      <td>910.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1923.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98065</td>\n",
       "      <td>47.526008</td>\n",
       "      <td>-121.809785</td>\n",
       "      <td>1290.0</td>\n",
       "      <td>9000.0</td>\n",
       "      <td>30.166206</td>\n",
       "      <td>94.868330</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>83</th>\n",
       "      <td>8572900275</td>\n",
       "      <td>2014-06-25 00:00:00+00:00</td>\n",
       "      <td>286000.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>780.0</td>\n",
       "      <td>3475.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>5.0</td>\n",
       "      <td>780.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1930.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98045</td>\n",
       "      <td>47.494394</td>\n",
       "      <td>-121.789489</td>\n",
       "      <td>1210.0</td>\n",
       "      <td>6769.0</td>\n",
       "      <td>27.928480</td>\n",
       "      <td>58.949131</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>84</th>\n",
       "      <td>7335400345</td>\n",
       "      <td>2014-05-28 00:00:00+00:00</td>\n",
       "      <td>135000.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>780.0</td>\n",
       "      <td>6685.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>5.0</td>\n",
       "      <td>780.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1948.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98002</td>\n",
       "      <td>47.304958</td>\n",
       "      <td>-122.215070</td>\n",
       "      <td>880.0</td>\n",
       "      <td>6695.0</td>\n",
       "      <td>27.928480</td>\n",
       "      <td>81.761849</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>85</th>\n",
       "      <td>7227502155</td>\n",
       "      <td>2014-07-14 00:00:00+00:00</td>\n",
       "      <td>208000.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>820.0</td>\n",
       "      <td>5700.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>5.0</td>\n",
       "      <td>820.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1942.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98056</td>\n",
       "      <td>47.491473</td>\n",
       "      <td>-122.184276</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>5700.0</td>\n",
       "      <td>28.635642</td>\n",
       "      <td>75.498344</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>86</th>\n",
       "      <td>1151100010</td>\n",
       "      <td>2014-05-15 00:00:00+00:00</td>\n",
       "      <td>280000.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>1330.0</td>\n",
       "      <td>20562.0</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1330.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1959.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98045</td>\n",
       "      <td>47.480697</td>\n",
       "      <td>-121.775003</td>\n",
       "      <td>1350.0</td>\n",
       "      <td>20562.0</td>\n",
       "      <td>36.469165</td>\n",
       "      <td>143.394561</td>\n",
       "      <td>9.0</td>\n",
       "      <td>2.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>87</th>\n",
       "      <td>2856100185</td>\n",
       "      <td>2014-07-21 00:00:00+00:00</td>\n",
       "      <td>365000.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>680.0</td>\n",
       "      <td>2550.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>5.0</td>\n",
       "      <td>680.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1901.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98117</td>\n",
       "      <td>47.676676</td>\n",
       "      <td>-122.388306</td>\n",
       "      <td>1120.0</td>\n",
       "      <td>5100.0</td>\n",
       "      <td>26.076810</td>\n",
       "      <td>50.497525</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>88</th>\n",
       "      <td>7227800660</td>\n",
       "      <td>2014-05-22 00:00:00+00:00</td>\n",
       "      <td>300000.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>2.00</td>\n",
       "      <td>2040.0</td>\n",
       "      <td>10812.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>5.0</td>\n",
       "      <td>2040.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1943.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98056</td>\n",
       "      <td>47.491895</td>\n",
       "      <td>-122.180920</td>\n",
       "      <td>1440.0</td>\n",
       "      <td>10200.0</td>\n",
       "      <td>45.166359</td>\n",
       "      <td>103.980767</td>\n",
       "      <td>36.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>89</th>\n",
       "      <td>2085200545</td>\n",
       "      <td>2014-08-21 00:00:00+00:00</td>\n",
       "      <td>180000.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>840.0</td>\n",
       "      <td>5700.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>5.0</td>\n",
       "      <td>840.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1945.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98038</td>\n",
       "      <td>47.394776</td>\n",
       "      <td>-122.027768</td>\n",
       "      <td>1430.0</td>\n",
       "      <td>12600.0</td>\n",
       "      <td>28.982753</td>\n",
       "      <td>75.498344</td>\n",
       "      <td>9.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>90</th>\n",
       "      <td>1022049182</td>\n",
       "      <td>2015-04-28 00:00:00+00:00</td>\n",
       "      <td>175000.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>620.0</td>\n",
       "      <td>8685.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>5.0</td>\n",
       "      <td>620.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1976.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98198</td>\n",
       "      <td>47.409506</td>\n",
       "      <td>-122.290093</td>\n",
       "      <td>1300.0</td>\n",
       "      <td>12150.0</td>\n",
       "      <td>24.899799</td>\n",
       "      <td>93.193347</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>91</th>\n",
       "      <td>9275200080</td>\n",
       "      <td>2014-11-07 00:00:00+00:00</td>\n",
       "      <td>295000.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.50</td>\n",
       "      <td>720.0</td>\n",
       "      <td>7450.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>5.0</td>\n",
       "      <td>720.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1924.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98126</td>\n",
       "      <td>47.583975</td>\n",
       "      <td>-122.375163</td>\n",
       "      <td>2600.0</td>\n",
       "      <td>7360.0</td>\n",
       "      <td>26.832816</td>\n",
       "      <td>86.313383</td>\n",
       "      <td>9.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>92</th>\n",
       "      <td>0419000035</td>\n",
       "      <td>2014-10-15 00:00:00+00:00</td>\n",
       "      <td>187000.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>860.0</td>\n",
       "      <td>5400.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>5.0</td>\n",
       "      <td>860.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1953.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98056</td>\n",
       "      <td>47.492003</td>\n",
       "      <td>-122.170744</td>\n",
       "      <td>960.0</td>\n",
       "      <td>5400.0</td>\n",
       "      <td>29.325757</td>\n",
       "      <td>73.484692</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>93</th>\n",
       "      <td>4008400515</td>\n",
       "      <td>2015-01-20 00:00:00+00:00</td>\n",
       "      <td>190000.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.75</td>\n",
       "      <td>780.0</td>\n",
       "      <td>77603.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>5.0</td>\n",
       "      <td>780.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1945.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98058</td>\n",
       "      <td>47.439639</td>\n",
       "      <td>-122.103872</td>\n",
       "      <td>1750.0</td>\n",
       "      <td>30847.0</td>\n",
       "      <td>27.928480</td>\n",
       "      <td>278.573150</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94</th>\n",
       "      <td>8005100360</td>\n",
       "      <td>2014-09-16 00:00:00+00:00</td>\n",
       "      <td>169900.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>910.0</td>\n",
       "      <td>5800.0</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>5.0</td>\n",
       "      <td>910.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1900.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98022</td>\n",
       "      <td>47.206762</td>\n",
       "      <td>-121.991589</td>\n",
       "      <td>1400.0</td>\n",
       "      <td>6766.0</td>\n",
       "      <td>30.166206</td>\n",
       "      <td>76.157731</td>\n",
       "      <td>9.0</td>\n",
       "      <td>2.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>2475901105</td>\n",
       "      <td>2014-07-15 00:00:00+00:00</td>\n",
       "      <td>291000.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>1280.0</td>\n",
       "      <td>10500.0</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1280.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1941.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98024</td>\n",
       "      <td>47.566019</td>\n",
       "      <td>-121.893984</td>\n",
       "      <td>1410.0</td>\n",
       "      <td>10500.0</td>\n",
       "      <td>35.777088</td>\n",
       "      <td>102.469508</td>\n",
       "      <td>9.0</td>\n",
       "      <td>2.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>7227500865</td>\n",
       "      <td>2014-05-19 00:00:00+00:00</td>\n",
       "      <td>141800.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>930.0</td>\n",
       "      <td>4743.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>5.0</td>\n",
       "      <td>930.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1942.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98056</td>\n",
       "      <td>47.496556</td>\n",
       "      <td>-122.186791</td>\n",
       "      <td>930.0</td>\n",
       "      <td>4779.0</td>\n",
       "      <td>30.495901</td>\n",
       "      <td>68.869442</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>2734100835</td>\n",
       "      <td>2015-03-03 00:00:00+00:00</td>\n",
       "      <td>90000.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>780.0</td>\n",
       "      <td>4000.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>5.0</td>\n",
       "      <td>780.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1905.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98108</td>\n",
       "      <td>47.542426</td>\n",
       "      <td>-122.320864</td>\n",
       "      <td>1150.0</td>\n",
       "      <td>4000.0</td>\n",
       "      <td>27.928480</td>\n",
       "      <td>63.245553</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>3330500925</td>\n",
       "      <td>2015-02-24 00:00:00+00:00</td>\n",
       "      <td>258305.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.50</td>\n",
       "      <td>750.0</td>\n",
       "      <td>2964.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>5.0</td>\n",
       "      <td>750.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1919.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98118</td>\n",
       "      <td>47.551751</td>\n",
       "      <td>-122.277210</td>\n",
       "      <td>1350.0</td>\n",
       "      <td>3090.0</td>\n",
       "      <td>27.386128</td>\n",
       "      <td>54.442630</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>2354300845</td>\n",
       "      <td>2014-08-04 00:00:00+00:00</td>\n",
       "      <td>210000.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>1020.0</td>\n",
       "      <td>6000.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1020.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1900.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>98027</td>\n",
       "      <td>47.528115</td>\n",
       "      <td>-122.031388</td>\n",
       "      <td>2070.0</td>\n",
       "      <td>7200.0</td>\n",
       "      <td>31.937439</td>\n",
       "      <td>77.459667</td>\n",
       "      <td>9.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>                          </body>                                                          </html>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sales.sort(\"grade\", ascending=True).explore()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Create new features"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As in Week 2, we consider features that are some transformations of inputs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import log, sqrt\n",
    "sales['sqft_living_sqrt'] = sales['sqft_living'].apply(sqrt)\n",
    "sales['sqft_lot_sqrt'] = sales['sqft_lot'].apply(sqrt)\n",
    "sales['bedrooms_square'] = sales['bedrooms']*sales['bedrooms']\n",
    "\n",
    "# In the dataset, 'floors' was defined with type string, \n",
    "# so we'll convert them to float, before creating a new feature.\n",
    "sales['floors'] = sales['floors'].astype(float) \n",
    "sales['floors_square'] = sales['floors']*sales['floors']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Squaring bedrooms will increase the separation between not many bedrooms (e.g. 1) and lots of bedrooms (e.g. 4) since 1^2 = 1 but 4^2 = 16. Consequently this variable will mostly affect houses with many bedrooms.\n",
    "* On the other hand, taking square root of sqft_living will decrease the separation between big house and small house. The owner may not be exactly twice as happy for getting a house that is twice as big."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Learn regression weights with L1 penalty"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us fit a model with all the features available, plus the features we just created above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "all_features = ['bedrooms', 'bedrooms_square',\n",
    "                'bathrooms',\n",
    "                'sqft_living', 'sqft_living_sqrt',\n",
    "                'sqft_lot', 'sqft_lot_sqrt',\n",
    "                'floors', 'floors_square',\n",
    "                'waterfront', 'view', 'condition', 'grade',\n",
    "                'sqft_above',\n",
    "                'sqft_basement',\n",
    "                'yr_built', 'yr_renovated']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Applying L1 penalty requires adding an extra parameter (`l1_penalty`) to the linear regression call in Turi Create. (Other tools may have separate implementations of LASSO.)  Note that it's important to set `l2_penalty=0` to ensure we don't introduce an additional L2 penalty."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre>Linear regression:</pre>"
      ],
      "text/plain": [
       "Linear regression:"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>--------------------------------------------------------</pre>"
      ],
      "text/plain": [
       "--------------------------------------------------------"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of examples          : 21613</pre>"
      ],
      "text/plain": [
       "Number of examples          : 21613"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of features          : 17</pre>"
      ],
      "text/plain": [
       "Number of features          : 17"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of unpacked features : 17</pre>"
      ],
      "text/plain": [
       "Number of unpacked features : 17"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Number of coefficients    : 18</pre>"
      ],
      "text/plain": [
       "Number of coefficients    : 18"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Starting Accelerated Gradient (FISTA)</pre>"
      ],
      "text/plain": [
       "Starting Accelerated Gradient (FISTA)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>--------------------------------------------------------</pre>"
      ],
      "text/plain": [
       "--------------------------------------------------------"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Tuning step size. First iteration could take longer than subsequent iterations.</pre>"
      ],
      "text/plain": [
       "Tuning step size. First iteration could take longer than subsequent iterations."
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>+-----------+----------+-----------+--------------+--------------------+---------------------------------+</pre>"
      ],
      "text/plain": [
       "+-----------+----------+-----------+--------------+--------------------+---------------------------------+"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>| Iteration | Passes   | Step size | Elapsed Time | Training Max Error | Training Root-Mean-Square Error |</pre>"
      ],
      "text/plain": [
       "| Iteration | Passes   | Step size | Elapsed Time | Training Max Error | Training Root-Mean-Square Error |"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>+-----------+----------+-----------+--------------+--------------------+---------------------------------+</pre>"
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      "text/plain": [
       "+-----------+----------+-----------+--------------+--------------------+---------------------------------+"
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     },
     "metadata": {},
     "output_type": "display_data"
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    {
     "data": {
      "text/html": [
       "<pre>| 0         | 1        | 1.000000  | 1.012670     | 7700000.000000     | 653047.733994                   |</pre>"
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      "text/plain": [
       "| 0         | 1        | 1.000000  | 1.012670     | 7700000.000000     | 653047.733994                   |"
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    {
     "data": {
      "text/html": [
       "<pre>| 1         | 2        | 0.000002  | 1.334725     | 6962915.603493     | 426631.749026                   |</pre>"
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      "text/plain": [
       "| 1         | 2        | 0.000002  | 1.334725     | 6962915.603493     | 426631.749026                   |"
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     },
     "metadata": {},
     "output_type": "display_data"
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    {
     "data": {
      "text/html": [
       "<pre>| 2         | 3        | 0.000002  | 1.363248     | 6843144.200219     | 392488.929838                   |</pre>"
      ],
      "text/plain": [
       "| 2         | 3        | 0.000002  | 1.363248     | 6843144.200219     | 392488.929838                   |"
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     "metadata": {},
     "output_type": "display_data"
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    {
     "data": {
      "text/html": [
       "<pre>| 3         | 4        | 0.000002  | 1.391013     | 6831900.032123     | 385340.166783                   |</pre>"
      ],
      "text/plain": [
       "| 3         | 4        | 0.000002  | 1.391013     | 6831900.032123     | 385340.166783                   |"
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     "metadata": {},
     "output_type": "display_data"
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    {
     "data": {
      "text/html": [
       "<pre>| 4         | 5        | 0.000002  | 1.421434     | 6847166.848958     | 384842.383767                   |</pre>"
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      "text/plain": [
       "| 4         | 5        | 0.000002  | 1.421434     | 6847166.848958     | 384842.383767                   |"
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     },
     "metadata": {},
     "output_type": "display_data"
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    {
     "data": {
      "text/html": [
       "<pre>| 5         | 6        | 0.000002  | 1.453059     | 6869667.895833     | 385998.458623                   |</pre>"
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      "text/plain": [
       "| 5         | 6        | 0.000002  | 1.453059     | 6869667.895833     | 385998.458623                   |"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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    {
     "data": {
      "text/html": [
       "<pre>| 10        | 11       | 0.000002  | 1.591614     | 6842123.232651     | 364204.576180                   |</pre>"
      ],
      "text/plain": [
       "| 10        | 11       | 0.000002  | 1.591614     | 6842123.232651     | 364204.576180                   |"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>+-----------+----------+-----------+--------------+--------------------+---------------------------------+</pre>"
      ],
      "text/plain": [
       "+-----------+----------+-----------+--------------+--------------------+---------------------------------+"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>Completed (Iteration limit reached).</pre>"
      ],
      "text/plain": [
       "Completed (Iteration limit reached)."
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre>This model may not be optimal. To improve it, consider increasing `max_iterations`.</pre>"
      ],
      "text/plain": [
       "This model may not be optimal. To improve it, consider increasing `max_iterations`."
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model_all = turicreate.linear_regression.create(sales, target='price', features=all_features,\n",
    "                                                validation_set=None, \n",
    "                                                l2_penalty=0., l1_penalty=1e10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Find what features had non-zero weight."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Learned polynomial for degree 17:\n",
      "       14         13         5         4        3\n",
      "20.02 x  + 842.1 x  + 350.1 x + 24.42 x + 8469 x + 2.749e+05\n",
      "sqft_above grade sqft_living_sqrt sqft_living bathrooms\n"
     ]
    }
   ],
   "source": [
    "import turicreate\n",
    "import math\n",
    "import random\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline\n",
    "def print_coefficients(model):    \n",
    "    # Get the degree of the polynomial\n",
    "    deg = len(model.coefficients['value'])-1\n",
    "\n",
    "    # Get learned parameters as a list\n",
    "    w = list(model.coefficients['value'])\n",
    "\n",
    "    # Numpy has a nifty function to print out polynomials in a pretty way\n",
    "    # (We'll use it, but it needs the parameters in the reverse order)\n",
    "    print('Learned polynomial for degree ' + str(deg) + ':')\n",
    "    w.reverse()\n",
    "    print(np.poly1d(w))\n",
    "    \n",
    "print_coefficients(model_all)\n",
    "print(all_features[14-1], all_features[13-1], all_features[5-1], all_features[4-1], all_features[3-1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that a majority of the weights have been set to zero. So by setting an L1 penalty that's large enough, we are performing a subset selection. \n",
    "\n",
    "***QUIZ QUESTION***:\n",
    "According to this list of weights, which of the features have been chosen? \n",
    "\n",
    "** sqft_above grade sqft_living_sqrt sqft_living bathrooms"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Selecting an L1 penalty"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To find a good L1 penalty, we will explore multiple values using a validation set. Let us do three way split into train, validation, and test sets:\n",
    "* Split our sales data into 2 sets: training and test\n",
    "* Further split our training data into two sets: train, validation\n",
    "\n",
    "Be *very* careful that you use seed = 1 to ensure you get the same answer!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "(training_and_validation, testing) = sales.random_split(.9,seed=1) # initial train/test split\n",
    "(training, validation) = training_and_validation.random_split(0.5, seed=1) # split training into train and validate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we write a loop that does the following:\n",
    "* For `l1_penalty` in [10^1, 10^1.5, 10^2, 10^2.5, ..., 10^7] (to get this in Python, type `np.logspace(1, 7, num=13)`.)\n",
    "    * Fit a regression model with a given `l1_penalty` on TRAIN data. Specify `l1_penalty=l1_penalty` and `l2_penalty=0.` in the parameter list.\n",
    "    * Compute the RSS on VALIDATION data (here you will want to use `.predict()`) for that `l1_penalty`\n",
    "* Report which `l1_penalty` produced the lowest RSS on validation data.\n",
    "\n",
    "When you call `linear_regression.create()` make sure you set `validation_set = None`.\n",
    "\n",
    "Note: you can turn off the print out of `linear_regression.create()` with `verbose = False`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "625766285142460.5 10.0\n",
      "625766285362394.0 31.622776601683793\n",
      "625766286057885.4 100.0\n",
      "625766288257224.9 316.22776601683796\n",
      "625766295212186.0 1000.0\n",
      "625766317206080.8 3162.2776601683795\n",
      "625766386760658.0 10000.0\n",
      "625766606749278.6 31622.776601683792\n",
      "625767302791635.2 100000.0\n",
      "625769507643886.0 316227.7660168379\n",
      "625776517727024.4 1000000.0\n",
      "625799062845466.8 3162277.6601683795\n",
      "625883719085425.2 10000000.0\n",
      "10.0\n"
     ]
    }
   ],
   "source": [
    "min_rss = None\n",
    "best_l1_penalty = None\n",
    "\n",
    "for l1_penalty in np.logspace(1, 7, num=13):\n",
    "    next_mse = 0.0\n",
    "    # train model\n",
    "    model = turicreate.linear_regression.create(training[all_features+['price']],target='price', \n",
    "                                                l1_penalty=l1_penalty,\n",
    "                                                l2_penalty=0,\n",
    "                                                validation_set=None,verbose=False)\n",
    "    #print_coefficients(model)\n",
    "    # predict on validation set \n",
    "    y_test_predicted = model.predict(validation[all_features])\n",
    "    # compute squared error\n",
    "    rss = ((y_test_predicted-validation['price'])**2).sum()\n",
    "    print(rss, l1_penalty)\n",
    "    # save squared error in list of MSE for each l2_penalty\n",
    "    if min_rss is None or rss < min_rss:\n",
    "        min_rss = rss\n",
    "        best_l1_penalty = l1_penalty\n",
    "            \n",
    "print(best_l1_penalty)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "#training[all_features+['price']].explore()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*** QUIZ QUESTION. *** What was the best value for the `l1_penalty`?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***QUIZ QUESTION***\n",
    "Also, using this value of L1 penalty, how many nonzero weights do you have?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**May not be correct!**\n",
    "\n",
    "0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Limit the number of nonzero weights\n",
    "\n",
    "What if we absolutely wanted to limit ourselves to, say, 7 features? This may be important if we want to derive \"a rule of thumb\" --- an interpretable model that has only a few features in them."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this section, you are going to implement a simple, two phase procedure to achive this goal:\n",
    "1. Explore a large range of `l1_penalty` values to find a narrow region of `l1_penalty` values where models are likely to have the desired number of non-zero weights.\n",
    "2. Further explore the narrow region you found to find a good value for `l1_penalty` that achieves the desired sparsity.  Here, we will again use a validation set to choose the best value for `l1_penalty`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "max_nonzeros = 7"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exploring the larger range of values to find a narrow range with the desired sparsity\n",
    "\n",
    "Let's define a wide range of possible `l1_penalty_values`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "l1_penalty_values = np.logspace(8, 10, num=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, implement a loop that search through this space of possible `l1_penalty` values:\n",
    "\n",
    "* For `l1_penalty` in `np.logspace(8, 10, num=20)`:\n",
    "    * Fit a regression model with a given `l1_penalty` on TRAIN data. Specify `l1_penalty=l1_penalty` and `l2_penalty=0.` in the parameter list. When you call `linear_regression.create()` make sure you set `validation_set = None`\n",
    "    * Extract the weights of the model and count the number of nonzeros. Save the number of nonzeros to a list.\n",
    "        * *Hint: `model.coefficients['value']` gives you an SArray with the parameters you learned.  If you call the method `.nnz()` on it, you will find the number of non-zero parameters!* "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "627492659875075.2 100000000.0\n",
      "628210516770747.2 127427498.57031322\n",
      "629176689541061.4 162377673.91887242\n",
      "630650082718674.5 206913808.111479\n",
      "632940229286984.4 263665089.87303555\n",
      "636268140229529.2 335981828.6283788\n",
      "641261198311187.9 428133239.8719396\n",
      "648983455376337.2 545559478.1168514\n",
      "660962217696068.4 695192796.1775591\n",
      "677261520727858.6 885866790.4100832\n",
      "701046815867076.1 1128837891.6846883\n",
      "737850622829048.2 1438449888.2876658\n",
      "796163109639832.8 1832980710.8324375\n",
      "869018172893693.5 2335721469.0901213\n",
      "966925692362084.9 2976351441.6313133\n",
      "1081867592324112.2 3792690190.7322536\n",
      "1244927360324958.2 4832930238.571753\n",
      "1384161490235110.8 6158482110.6602545\n",
      "1230794720455646.5 7847599703.514623\n",
      "1229157160638600.2 10000000000.0\n",
      "100000000.0\n",
      "{100000000.0: 18, 127427498.57031322: 18, 162377673.91887242: 18, 206913808.111479: 18, 263665089.87303555: 17, 335981828.6283788: 17, 428133239.8719396: 17, 545559478.1168514: 17, 695192796.1775591: 17, 885866790.4100832: 16, 1128837891.6846883: 15, 1438449888.2876658: 15, 1832980710.8324375: 13, 2335721469.0901213: 12, 2976351441.6313133: 10, 3792690190.7322536: 6, 4832930238.571753: 5, 6158482110.6602545: 3, 7847599703.514623: 1, 10000000000.0: 1}\n"
     ]
    }
   ],
   "source": [
    "min_rss = None\n",
    "best_l1_penalty = None\n",
    "l1_penalty_2_nnz = {}\n",
    "\n",
    "for l1_penalty in l1_penalty_values:\n",
    "    model = turicreate.linear_regression.create(training[all_features+['price']],target='price', \n",
    "                                                l1_penalty=l1_penalty,\n",
    "                                                l2_penalty=0,\n",
    "                                                validation_set=None,verbose=False)\n",
    "    #print_coefficients(model)\n",
    "    # predict on validation set \n",
    "    y_test_predicted = model.predict(validation[all_features])\n",
    "    # compute squared error\n",
    "    rss = ((y_test_predicted-validation['price'])**2).sum()\n",
    "    print(rss, l1_penalty)\n",
    "    # save squared error in list of MSE for each l2_penalty\n",
    "    if min_rss is None or rss < min_rss:\n",
    "        min_rss = rss\n",
    "        best_l1_penalty = l1_penalty\n",
    "    l1_penalty_2_nnz[l1_penalty] = model.coefficients['value'].nnz()\n",
    "            \n",
    "print(best_l1_penalty)\n",
    "print(l1_penalty_2_nnz)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Out of this large range, we want to find the two ends of our desired narrow range of `l1_penalty`.  At one end, we will have `l1_penalty` values that have too few non-zeros, and at the other end, we will have an `l1_penalty` that has too many non-zeros.  \n",
    "\n",
    "More formally, find:\n",
    "* The largest `l1_penalty` that has more non-zeros than `max_nonzeros` (if we pick a penalty smaller than this value, we will definitely have too many non-zero weights)\n",
    "    * Store this value in the variable `l1_penalty_min` (we will use it later)\n",
    "* The smallest `l1_penalty` that has fewer non-zeros than `max_nonzeros` (if we pick a penalty larger than this value, we will definitely have too few non-zero weights)\n",
    "    * Store this value in the variable `l1_penalty_max` (we will use it later)\n",
    "\n",
    "\n",
    "*Hint: there are many ways to do this, e.g.:*\n",
    "* Programmatically within the loop above\n",
    "* Creating a list with the number of non-zeros for each value of `l1_penalty` and inspecting it to find the appropriate boundaries."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "#2976351441.6313133: 10, 3792690190.7322536: 6\n",
    "\n",
    "l1_penalty_min = 2976351441.6313133\n",
    "l1_penalty_max = 3792690190.7322536"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***QUIZ QUESTION.*** What values did you find for `l1_penalty_min` and `l1_penalty_max`, respectively? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exploring the narrow range of values to find the solution with the right number of non-zeros that has lowest RSS on the validation set \n",
    "\n",
    "We will now explore the narrow region of `l1_penalty` values we found:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "l1_penalty_values = np.linspace(l1_penalty_min,l1_penalty_max,20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* For `l1_penalty` in `np.linspace(l1_penalty_min,l1_penalty_max,20)`:\n",
    "    * Fit a regression model with a given `l1_penalty` on TRAIN data. Specify `l1_penalty=l1_penalty` and `l2_penalty=0.` in the parameter list. When you call `linear_regression.create()` make sure you set `validation_set = None`\n",
    "    * Measure the RSS of the learned model on the VALIDATION set\n",
    "\n",
    "Find the model that the lowest RSS on the VALIDATION set and has sparsity *equal* to `max_nonzeros`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "966925692362084.9 2976351441.6313133 10\n",
      "Learned polynomial for degree 17:\n",
      "      15         14        13             11        8         5\n",
      "12.8 x  + 32.74 x  + 3579 x  + 1.133e+04 x  + 3666 x + 789.3 x\n",
      "          4             3\n",
      " + 34.14 x + 1.796e+04 x + 2182 x + 1.961e+05\n",
      "974019450084554.9 3019316638.9524155 10\n",
      "Learned polynomial for degree 17:\n",
      "       15         14        13        11        8         5         4\n",
      "11.05 x  + 32.54 x  + 3528 x  + 9877 x  + 3358 x + 782.2 x + 34.02 x\n",
      "              3\n",
      " + 1.781e+04 x + 2067 x + 1.986e+05\n",
      "981188367942453.6 3062281836.2735176 10\n",
      "Learned polynomial for degree 17:\n",
      "       15         14        13        11        8       5        4\n",
      "9.306 x  + 32.33 x  + 3478 x  + 8419 x  + 3050 x + 775 x + 33.9 x\n",
      "              3\n",
      " + 1.766e+04 x + 1952 x + 2.01e+05\n",
      "989328342459473.2 3105247033.5946198 10\n",
      "Learned polynomial for degree 17:\n",
      "       15         14        13        11        8       5         4\n",
      "7.513 x  + 32.11 x  + 3421 x  + 6944 x  + 2717 x + 767 x + 33.76 x\n",
      "              3\n",
      " + 1.749e+04 x + 1826 x + 2.034e+05\n",
      "998783211265889.8 3148212230.915722 10\n",
      "Learned polynomial for degree 17:\n",
      "       15         14        13        11        8         5        4\n",
      "5.675 x  + 31.85 x  + 3358 x  + 5448 x  + 2342 x + 757.6 x + 33.6 x\n",
      "              3\n",
      " + 1.729e+04 x + 1683 x + 2.058e+05\n",
      "1008477167020093.4 3191177428.236824 10\n",
      "Learned polynomial for degree 17:\n",
      "       15         14        13        11        8         5         4\n",
      "3.833 x  + 31.59 x  + 3293 x  + 3950 x  + 1964 x + 748.2 x + 33.43 x\n",
      "              3\n",
      " + 1.709e+04 x + 1540 x + 2.082e+05\n",
      "1018298780553819.4 3234142625.557926 10\n",
      "Learned polynomial for degree 17:\n",
      "       15         14        13        11        8         5         4\n",
      "1.991 x  + 31.33 x  + 3229 x  + 2451 x  + 1585 x + 738.7 x + 33.27 x\n",
      "              3\n",
      " + 1.689e+04 x + 1396 x + 2.105e+05\n",
      "1028247992205977.1 3277107822.8790283 10\n",
      "Learned polynomial for degree 17:\n",
      "       15         14        13       11        8         5        4\n",
      "0.149 x  + 31.08 x  + 3165 x  + 953 x  + 1207 x + 729.3 x + 33.1 x\n",
      "              3\n",
      " + 1.669e+04 x + 1252 x + 2.129e+05\n",
      "1034616909232827.1 3320073020.2001305 8\n",
      "Learned polynomial for degree 17:\n",
      "       14        13         8         5         4            3\n",
      "30.82 x  + 3100 x  + 829.6 x + 719.9 x + 32.94 x + 1.65e+04 x + 1108 x + 2.152e+05\n",
      "1038554735941040.2 3363038217.5212326 8\n",
      "Learned polynomial for degree 17:\n",
      "       14        13         8         5         4            3\n",
      "30.56 x  + 3037 x  + 456.8 x + 710.5 x + 32.78 x + 1.63e+04 x + 966.4 x + 2.176e+05\n",
      "1043237237871701.6 3406003414.8423347 8\n",
      "Learned polynomial for degree 17:\n",
      "       14        13         8         5        4             3\n",
      "30.29 x  + 2969 x  + 64.82 x + 700.4 x + 32.6 x + 1.609e+04 x + 815.3 x + 2.199e+05\n",
      "1046937488751710.6 3448968612.163437 7\n",
      "Learned polynomial for degree 17:\n",
      "       14        13         5         4             3\n",
      "30.01 x  + 2899 x  + 690.1 x + 32.41 x + 1.587e+04 x + 661.7 x + 2.223e+05\n",
      "1051147625612862.1 3491933809.484539 7\n",
      "Learned polynomial for degree 17:\n",
      "       14        13         5        4             3\n",
      "29.72 x  + 2825 x  + 678.9 x + 32.2 x + 1.564e+04 x + 497 x + 2.245e+05\n",
      "1055992735342999.4 3534899006.805641 7\n",
      "Learned polynomial for degree 17:\n",
      "       14        13         5         4             3\n",
      "29.41 x  + 2748 x  + 666.9 x + 31.98 x + 1.539e+04 x + 322.1 x + 2.268e+05\n",
      "1060799531763287.2 3577864204.126743 7\n",
      "Learned polynomial for degree 17:\n",
      "      14        13         5         4             3\n",
      "29.1 x  + 2670 x  + 655.1 x + 31.76 x + 1.515e+04 x + 149.4 x + 2.291e+05\n",
      "1065707689498229.5 3620829401.447845 6\n",
      "Learned polynomial for degree 17:\n",
      "       14        13         5         4             3\n",
      "28.78 x  + 2591 x  + 642.9 x + 31.53 x + 1.489e+04 x + 2.313e+05\n",
      "1069464335425585.0 3663794598.768947 6\n",
      "Learned polynomial for degree 17:\n",
      "       14        13         5        4             3\n",
      "28.46 x  + 2511 x  + 630.6 x + 31.3 x + 1.464e+04 x + 2.336e+05\n",
      "1073504549585599.2 3706759796.0900493 6\n",
      "Learned polynomial for degree 17:\n",
      "       14        13         5         4             3\n",
      "28.14 x  + 2430 x  + 617.9 x + 31.05 x + 1.437e+04 x + 2.358e+05\n",
      "1077632775581415.1 3749724993.4111514 6\n",
      "Learned polynomial for degree 17:\n",
      "       14        13         5         4             3\n",
      "27.81 x  + 2348 x  + 605.1 x + 30.81 x + 1.411e+04 x + 2.381e+05\n",
      "1081867592324112.2 3792690190.7322536 6\n",
      "Learned polynomial for degree 17:\n",
      "       14        13         5         4             3\n",
      "27.49 x  + 2265 x  + 592.2 x + 30.56 x + 1.384e+04 x + 2.403e+05\n",
      "2976351441.6313133\n",
      "{2976351441.6313133: 10, 3019316638.9524155: 10, 3062281836.2735176: 10, 3105247033.5946198: 10, 3148212230.915722: 10, 3191177428.236824: 10, 3234142625.557926: 10, 3277107822.8790283: 10, 3320073020.2001305: 8, 3363038217.5212326: 8, 3406003414.8423347: 8, 3448968612.163437: 7, 3491933809.484539: 7, 3534899006.805641: 7, 3577864204.126743: 7, 3620829401.447845: 6, 3663794598.768947: 6, 3706759796.0900493: 6, 3749724993.4111514: 6, 3792690190.7322536: 6}\n"
     ]
    }
   ],
   "source": [
    "min_rss = None\n",
    "best_l1_penalty = None\n",
    "l1_penalty_2_nnz = {}\n",
    "\n",
    "for l1_penalty in l1_penalty_values:\n",
    "    model = turicreate.linear_regression.create(training[all_features+['price']],target='price', \n",
    "                                                l1_penalty=l1_penalty,\n",
    "                                                l2_penalty=0,\n",
    "                                                validation_set=None,verbose=False)\n",
    "\n",
    "    # predict on validation set \n",
    "    y_test_predicted = model.predict(validation[all_features])\n",
    "    # compute squared error\n",
    "    rss = ((y_test_predicted-validation['price'])**2).sum()\n",
    "\n",
    "    # save squared error in list of MSE for each l2_penalty\n",
    "    if min_rss is None or rss < min_rss:\n",
    "        min_rss = rss\n",
    "        best_l1_penalty = l1_penalty\n",
    "    \n",
    "    l1_penalty_2_nnz[l1_penalty] = model.coefficients['value'].nnz()\n",
    "    print(rss, l1_penalty, model.coefficients['value'].nnz())\n",
    "    print_coefficients(model)\n",
    "            \n",
    "print(best_l1_penalty)\n",
    "print(l1_penalty_2_nnz)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***QUIZ QUESTIONS***\n",
    "1. What value of `l1_penalty` in our narrow range has the lowest RSS on the VALIDATION set and has sparsity *equal* to `max_nonzeros`? **3448968612.163437**\n",
    "2. What features in this model have non-zero coefficients?\n",
    "\n",
    "```\n",
    "       14        13         5         4             3\n",
    "30.01 x  + 2899 x  + 690.1 x + 32.41 x + 1.587e+04 x + 661.7 x + 2.223e+05\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sqft_above grade sqft_living_sqrt sqft_living bathrooms bedrooms\n"
     ]
    }
   ],
   "source": [
    "# NOTE: this is 6 features + intercept, not clear if intercept should be included\n",
    "print(all_features[14-1], all_features[13-1], all_features[5-1], all_features[4-1], all_features[3-1], all_features[1-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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