Predicting House Prices Using Scikit-Learn.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Predicting House Prices Using Scikit-Learn\n",
    "\n",
    "In this notebook,we shall use data on 21,000+ houses in US to build a model to predict house prices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Let's start by importing a few modules/libraries that we will need\n",
    "import pandas as pd, numpy as np\n",
    "\n",
    "from sklearn import linear_model\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.preprocessing import StandardScaler, OneHotEncoder\n",
    "from sklearn.metrics import mean_squared_error\n",
    "\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step1:  Analyze the Data\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Read the data into Pandas, to keep the analysis fast and simple\n",
    "df=pd.read_csv(\"/data/house.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\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>...</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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>7129300520</td>\n",
       "      <td>20141013T000000</td>\n",
       "      <td>221900.0</td>\n",
       "      <td>3</td>\n",
       "      <td>1.00</td>\n",
       "      <td>1180</td>\n",
       "      <td>5650</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>7</td>\n",
       "      <td>1180</td>\n",
       "      <td>0</td>\n",
       "      <td>1955</td>\n",
       "      <td>0</td>\n",
       "      <td>98178</td>\n",
       "      <td>47.5112</td>\n",
       "      <td>-122.257</td>\n",
       "      <td>1340</td>\n",
       "      <td>5650</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>6414100192</td>\n",
       "      <td>20141209T000000</td>\n",
       "      <td>538000.0</td>\n",
       "      <td>3</td>\n",
       "      <td>2.25</td>\n",
       "      <td>2570</td>\n",
       "      <td>7242</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>7</td>\n",
       "      <td>2170</td>\n",
       "      <td>400</td>\n",
       "      <td>1951</td>\n",
       "      <td>1991</td>\n",
       "      <td>98125</td>\n",
       "      <td>47.7210</td>\n",
       "      <td>-122.319</td>\n",
       "      <td>1690</td>\n",
       "      <td>7639</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5631500400</td>\n",
       "      <td>20150225T000000</td>\n",
       "      <td>180000.0</td>\n",
       "      <td>2</td>\n",
       "      <td>1.00</td>\n",
       "      <td>770</td>\n",
       "      <td>10000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>6</td>\n",
       "      <td>770</td>\n",
       "      <td>0</td>\n",
       "      <td>1933</td>\n",
       "      <td>0</td>\n",
       "      <td>98028</td>\n",
       "      <td>47.7379</td>\n",
       "      <td>-122.233</td>\n",
       "      <td>2720</td>\n",
       "      <td>8062</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2487200875</td>\n",
       "      <td>20141209T000000</td>\n",
       "      <td>604000.0</td>\n",
       "      <td>4</td>\n",
       "      <td>3.00</td>\n",
       "      <td>1960</td>\n",
       "      <td>5000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>7</td>\n",
       "      <td>1050</td>\n",
       "      <td>910</td>\n",
       "      <td>1965</td>\n",
       "      <td>0</td>\n",
       "      <td>98136</td>\n",
       "      <td>47.5208</td>\n",
       "      <td>-122.393</td>\n",
       "      <td>1360</td>\n",
       "      <td>5000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1954400510</td>\n",
       "      <td>20150218T000000</td>\n",
       "      <td>510000.0</td>\n",
       "      <td>3</td>\n",
       "      <td>2.00</td>\n",
       "      <td>1680</td>\n",
       "      <td>8080</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>8</td>\n",
       "      <td>1680</td>\n",
       "      <td>0</td>\n",
       "      <td>1987</td>\n",
       "      <td>0</td>\n",
       "      <td>98074</td>\n",
       "      <td>47.6168</td>\n",
       "      <td>-122.045</td>\n",
       "      <td>1800</td>\n",
       "      <td>7503</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 21 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           id             date     price  bedrooms  bathrooms  sqft_living  \\\n",
       "0  7129300520  20141013T000000  221900.0         3       1.00         1180   \n",
       "1  6414100192  20141209T000000  538000.0         3       2.25         2570   \n",
       "2  5631500400  20150225T000000  180000.0         2       1.00          770   \n",
       "3  2487200875  20141209T000000  604000.0         4       3.00         1960   \n",
       "4  1954400510  20150218T000000  510000.0         3       2.00         1680   \n",
       "\n",
       "   sqft_lot  floors  waterfront  view     ...      grade  sqft_above  \\\n",
       "0      5650     1.0           0     0     ...          7        1180   \n",
       "1      7242     2.0           0     0     ...          7        2170   \n",
       "2     10000     1.0           0     0     ...          6         770   \n",
       "3      5000     1.0           0     0     ...          7        1050   \n",
       "4      8080     1.0           0     0     ...          8        1680   \n",
       "\n",
       "   sqft_basement  yr_built  yr_renovated  zipcode      lat     long  \\\n",
       "0              0      1955             0    98178  47.5112 -122.257   \n",
       "1            400      1951          1991    98125  47.7210 -122.319   \n",
       "2              0      1933             0    98028  47.7379 -122.233   \n",
       "3            910      1965             0    98136  47.5208 -122.393   \n",
       "4              0      1987             0    98074  47.6168 -122.045   \n",
       "\n",
       "   sqft_living15  sqft_lot15  \n",
       "0           1340        5650  \n",
       "1           1690        7639  \n",
       "2           2720        8062  \n",
       "3           1360        5000  \n",
       "4           1800        7503  \n",
       "\n",
       "[5 rows x 21 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Let's look at the data types that Pandas has infered"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "id                 int64\n",
       "date              object\n",
       "price            float64\n",
       "bedrooms           int64\n",
       "bathrooms        float64\n",
       "sqft_living        int64\n",
       "sqft_lot           int64\n",
       "floors           float64\n",
       "waterfront         int64\n",
       "view               int64\n",
       "condition          int64\n",
       "grade              int64\n",
       "sqft_above         int64\n",
       "sqft_basement      int64\n",
       "yr_built           int64\n",
       "yr_renovated       int64\n",
       "zipcode            int64\n",
       "lat              float64\n",
       "long             float64\n",
       "sqft_living15      int64\n",
       "sqft_lot15         int64\n",
       "dtype: object"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.dtypes "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Let's take a quick look at the properties of each column of data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>id</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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>2.161300e+04</td>\n",
       "      <td>2.161300e+04</td>\n",
       "      <td>21613.000000</td>\n",
       "      <td>21613.000000</td>\n",
       "      <td>21613.000000</td>\n",
       "      <td>2.161300e+04</td>\n",
       "      <td>21613.000000</td>\n",
       "      <td>21613.000000</td>\n",
       "      <td>21613.000000</td>\n",
       "      <td>21613.000000</td>\n",
       "      <td>21613.000000</td>\n",
       "      <td>21613.000000</td>\n",
       "      <td>21613.000000</td>\n",
       "      <td>21613.000000</td>\n",
       "      <td>21613.000000</td>\n",
       "      <td>21613.000000</td>\n",
       "      <td>21613.000000</td>\n",
       "      <td>21613.000000</td>\n",
       "      <td>21613.000000</td>\n",
       "      <td>21613.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>4.580302e+09</td>\n",
       "      <td>5.400881e+05</td>\n",
       "      <td>3.370842</td>\n",
       "      <td>2.114757</td>\n",
       "      <td>2079.899736</td>\n",
       "      <td>1.510697e+04</td>\n",
       "      <td>1.494309</td>\n",
       "      <td>0.007542</td>\n",
       "      <td>0.234303</td>\n",
       "      <td>3.409430</td>\n",
       "      <td>7.656873</td>\n",
       "      <td>1788.390691</td>\n",
       "      <td>291.509045</td>\n",
       "      <td>1971.005136</td>\n",
       "      <td>84.402258</td>\n",
       "      <td>98077.939805</td>\n",
       "      <td>47.560053</td>\n",
       "      <td>-122.213896</td>\n",
       "      <td>1986.552492</td>\n",
       "      <td>12768.455652</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>2.876566e+09</td>\n",
       "      <td>3.671272e+05</td>\n",
       "      <td>0.930062</td>\n",
       "      <td>0.770163</td>\n",
       "      <td>918.440897</td>\n",
       "      <td>4.142051e+04</td>\n",
       "      <td>0.539989</td>\n",
       "      <td>0.086517</td>\n",
       "      <td>0.766318</td>\n",
       "      <td>0.650743</td>\n",
       "      <td>1.175459</td>\n",
       "      <td>828.090978</td>\n",
       "      <td>442.575043</td>\n",
       "      <td>29.373411</td>\n",
       "      <td>401.679240</td>\n",
       "      <td>53.505026</td>\n",
       "      <td>0.138564</td>\n",
       "      <td>0.140828</td>\n",
       "      <td>685.391304</td>\n",
       "      <td>27304.179631</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.000102e+06</td>\n",
       "      <td>7.500000e+04</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>290.000000</td>\n",
       "      <td>5.200000e+02</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>290.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1900.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>98001.000000</td>\n",
       "      <td>47.155900</td>\n",
       "      <td>-122.519000</td>\n",
       "      <td>399.000000</td>\n",
       "      <td>651.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>2.123049e+09</td>\n",
       "      <td>3.219500e+05</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>1.750000</td>\n",
       "      <td>1427.000000</td>\n",
       "      <td>5.040000e+03</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>1190.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1951.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>98033.000000</td>\n",
       "      <td>47.471000</td>\n",
       "      <td>-122.328000</td>\n",
       "      <td>1490.000000</td>\n",
       "      <td>5100.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>3.904930e+09</td>\n",
       "      <td>4.500000e+05</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>2.250000</td>\n",
       "      <td>1910.000000</td>\n",
       "      <td>7.618000e+03</td>\n",
       "      <td>1.500000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>1560.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1975.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>98065.000000</td>\n",
       "      <td>47.571800</td>\n",
       "      <td>-122.230000</td>\n",
       "      <td>1840.000000</td>\n",
       "      <td>7620.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>7.308900e+09</td>\n",
       "      <td>6.450000e+05</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>2.500000</td>\n",
       "      <td>2550.000000</td>\n",
       "      <td>1.068800e+04</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>2210.000000</td>\n",
       "      <td>560.000000</td>\n",
       "      <td>1997.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>98118.000000</td>\n",
       "      <td>47.678000</td>\n",
       "      <td>-122.125000</td>\n",
       "      <td>2360.000000</td>\n",
       "      <td>10083.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>9.900000e+09</td>\n",
       "      <td>7.700000e+06</td>\n",
       "      <td>33.000000</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>13540.000000</td>\n",
       "      <td>1.651359e+06</td>\n",
       "      <td>3.500000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>13.000000</td>\n",
       "      <td>9410.000000</td>\n",
       "      <td>4820.000000</td>\n",
       "      <td>2015.000000</td>\n",
       "      <td>2015.000000</td>\n",
       "      <td>98199.000000</td>\n",
       "      <td>47.777600</td>\n",
       "      <td>-121.315000</td>\n",
       "      <td>6210.000000</td>\n",
       "      <td>871200.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 id         price      bedrooms     bathrooms   sqft_living  \\\n",
       "count  2.161300e+04  2.161300e+04  21613.000000  21613.000000  21613.000000   \n",
       "mean   4.580302e+09  5.400881e+05      3.370842      2.114757   2079.899736   \n",
       "std    2.876566e+09  3.671272e+05      0.930062      0.770163    918.440897   \n",
       "min    1.000102e+06  7.500000e+04      0.000000      0.000000    290.000000   \n",
       "25%    2.123049e+09  3.219500e+05      3.000000      1.750000   1427.000000   \n",
       "50%    3.904930e+09  4.500000e+05      3.000000      2.250000   1910.000000   \n",
       "75%    7.308900e+09  6.450000e+05      4.000000      2.500000   2550.000000   \n",
       "max    9.900000e+09  7.700000e+06     33.000000      8.000000  13540.000000   \n",
       "\n",
       "           sqft_lot        floors    waterfront          view     condition  \\\n",
       "count  2.161300e+04  21613.000000  21613.000000  21613.000000  21613.000000   \n",
       "mean   1.510697e+04      1.494309      0.007542      0.234303      3.409430   \n",
       "std    4.142051e+04      0.539989      0.086517      0.766318      0.650743   \n",
       "min    5.200000e+02      1.000000      0.000000      0.000000      1.000000   \n",
       "25%    5.040000e+03      1.000000      0.000000      0.000000      3.000000   \n",
       "50%    7.618000e+03      1.500000      0.000000      0.000000      3.000000   \n",
       "75%    1.068800e+04      2.000000      0.000000      0.000000      4.000000   \n",
       "max    1.651359e+06      3.500000      1.000000      4.000000      5.000000   \n",
       "\n",
       "              grade    sqft_above  sqft_basement      yr_built  yr_renovated  \\\n",
       "count  21613.000000  21613.000000   21613.000000  21613.000000  21613.000000   \n",
       "mean       7.656873   1788.390691     291.509045   1971.005136     84.402258   \n",
       "std        1.175459    828.090978     442.575043     29.373411    401.679240   \n",
       "min        1.000000    290.000000       0.000000   1900.000000      0.000000   \n",
       "25%        7.000000   1190.000000       0.000000   1951.000000      0.000000   \n",
       "50%        7.000000   1560.000000       0.000000   1975.000000      0.000000   \n",
       "75%        8.000000   2210.000000     560.000000   1997.000000      0.000000   \n",
       "max       13.000000   9410.000000    4820.000000   2015.000000   2015.000000   \n",
       "\n",
       "            zipcode           lat          long  sqft_living15     sqft_lot15  \n",
       "count  21613.000000  21613.000000  21613.000000   21613.000000   21613.000000  \n",
       "mean   98077.939805     47.560053   -122.213896    1986.552492   12768.455652  \n",
       "std       53.505026      0.138564      0.140828     685.391304   27304.179631  \n",
       "min    98001.000000     47.155900   -122.519000     399.000000     651.000000  \n",
       "25%    98033.000000     47.471000   -122.328000    1490.000000    5100.000000  \n",
       "50%    98065.000000     47.571800   -122.230000    1840.000000    7620.000000  \n",
       "75%    98118.000000     47.678000   -122.125000    2360.000000   10083.000000  \n",
       "max    98199.000000     47.777600   -121.315000    6210.000000  871200.000000  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "### Fix Data Types\n",
    "Observe the following columns and their datatypes\n",
    "\n",
    "id                 int64 <-- this is simply and ID for the record, drop this from analysis\n",
    "date              object <--- this should be converted to a date, to use the data meaningfully\n",
    "price            float64\n",
    "bedrooms           int64 <--- this can go eitherways e.g. is a 3 bed as far from a 2 bedroom as a 2 is from 1?Maybe/maybe-not\n",
    "bathrooms        float64 <--- this can go eitherways \n",
    "sqft_living        int64\n",
    "sqft_lot           int64\n",
    "floors           float64 <--- this can go eitherways \n",
    "waterfront         int64 <--- says 'int'. This is a categorical Yes/No variable. But because it is 0/1, we can let this slide\n",
    "view               int64 <- this is probably categorical, and will need to be coded as such\n",
    "condition          int64 <- this is probably categorical, and will need to be coded as such\n",
    "grade              int64 <- this is probably categorical, and will need to be coded as such\n",
    "sqft_above         int64\n",
    "sqft_basement      int64\n",
    "yr_built           int64\n",
    "yr_renovated       int64\n",
    "zipcode            int64 <- this is categorical, and will need to be coded as such. Note, this may cause large # of variables\n",
    "lat              float64 \n",
    "long             float64\n",
    "sqft_living15      int64\n",
    "sqft_lot15         int64"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "shape of data is  (21613, 21)\n"
     ]
    }
   ],
   "source": [
    "#simple checks\n",
    "print(\"shape of data is \", df.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### You may want to do a few simple plots for obvious patterns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f3d26b805f8>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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c+21WRN7n4jOfXDSnudbHgZ+52NEzwN0i0ueSBe4GnnHnfu6uXXx/Y53Q/qm8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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3cf1a8e438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Let's start simple\n",
    "plt.scatter(df['sqft_living'], df['price'],linewidths =0, alpha=0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f3cee338e48>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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gpapXAo8Cj7hrdQEPA7cCtwAPVwWuR4BHXZmUu0bTDfRvqZtHVOlKRNjZGefy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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3cee3b2e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(df['sqft_lot'], df['price'],linewidths =0, alpha=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Let's plot the correlation matrix to see linear relationships between columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.6/site-packages/matplotlib/font_manager.py:1297: UserWarning: findfont: Font family ['sans-serif'] not found. Falling back to DejaVu Sans\n",
      "  (prop.get_family(), self.defaultFamily[fontext]))\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f3cedad3438>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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hpxRjv2w/WiwWXnvtNf7yl7+wadMmBg0a5OhW3YiXlxcAVqsV2389ssTHx+eexuXt7e34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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3cee37ac88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "\n",
    "f, ax = plt.subplots(figsize=(10, 8))\n",
    "corr = df.corr()\n",
    "sns.heatmap(corr, mask=np.zeros_like(corr, dtype=np.bool), cmap=sns.diverging_palette(200, 10, as_cmap=True),\n",
    "            square=True, ax=ax)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# On to some quick modeling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "all_features_target=['price', 'bedrooms', 'bathrooms', 'sqft_living',\n",
    "       'sqft_lot', 'floors', 'waterfront', 'view', 'condition', 'grade',\n",
    "       'sqft_above', 'sqft_basement', 'yr_built', 'yr_renovated', 'zipcode',\n",
    "       'lat', 'long', 'sqft_living15', 'sqft_lot15']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Let's start simpe, with a few feature columns i.e. the usual suspects\n",
    "feature_set1=['bedrooms', 'bathrooms', 'sqft_living', 'sqft_lot', 'floors']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((21613, 5), (21613,))"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X=np.array(df[feature_set1])\n",
    "y=np.array(df['price'])\n",
    "s=StandardScaler()\n",
    "XX=s.fit_transform(X)\n",
    "XX.shape, y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "check zero mean [ 0. -0.  0.  0. -0.]\n",
      "check Unit Stdev [ 1.  1.  1.  1.  1.]\n"
     ]
    }
   ],
   "source": [
    "print(\"check zero mean\", np.round(XX.mean(axis=0),2) )\n",
    "print(\"check Unit Stdev\", np.round(XX.std(axis=0),2) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train test split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(16209, 5)\n",
      "(5404, 5)\n",
      "(16209,)\n",
      "(5404,)\n"
     ]
    }
   ],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(XX, y, test_size=0.25, random_state=42)\n",
    "for i in [X_train, X_test, y_train, y_test]: print(i.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Regular 'Score' that comes from most regression models in Scikit is r<sup>2</sup>. Let's define a function to print RMSE scores"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import math\n",
    "def print_rmse(model, x, y):\n",
    "    rmse=math.sqrt(mean_squared_error(model.predict(x), y))\n",
    "    print(\"RMSE is \", rmse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "r-square:  0.51235445976\n",
      "RMSE is  270084.68648585695\n",
      "CPU times: user 8 ms, sys: 0 ns, total: 8 ms\n",
      "Wall time: 46.3 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# Create linear regression object\n",
    "regr = linear_model.LinearRegression()\n",
    "regr.fit(X_train, y_train)\n",
    "print(\"r-square: \", regr.score( X_test, y_test))\n",
    "print_rmse(regr, X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "r-square:  0.551257547136\n",
      "RMSE is  259087.47066383396\n",
      "CPU times: user 340 ms, sys: 4 ms, total: 344 ms\n",
      "Wall time: 344 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "#create a K Neighbours model. Prediction is the average of the 10 nearest neighbours\n",
    "from sklearn.neighbors import KNeighborsRegressor\n",
    "KNN=KNeighborsRegressor(10)\n",
    "KNN.fit(X_train, y_train)\n",
    "print(\"r-square: \", KNN.score( X_test, y_test))\n",
    "print_rmse(KNN, X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "r-square:  0.565350185271\n",
      "RMSE is  254986.7314114229\n",
      "CPU times: user 4 s, sys: 0 ns, total: 4 s\n",
      "Wall time: 4.02 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "from sklearn.ensemble import GradientBoostingRegressor\n",
    "\n",
    "params = {'n_estimators': 500, 'max_depth': 4, 'min_samples_split': 2, 'learning_rate': 0.01, 'loss': 'ls'}\n",
    "gbr = GradientBoostingRegressor(**params)\n",
    "gbr.fit(X_train, y_train)\n",
    "print(\"r-square: \", gbr.score( X_test, y_test))\n",
    "print_rmse(gbr, X_test, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Let's improve the model, by increasing features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "feature_set2=['bedrooms', 'bathrooms', 'sqft_living', 'sqft_lot', 'floors', 'lat', 'long']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((21613, 7), (21613,))"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X=np.array(df[feature_set2])\n",
    "y=np.array(df['price'])\n",
    "s=StandardScaler()\n",
    "XX=s.fit_transform(X)\n",
    "XX.shape, y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(16209, 7)\n",
      "(5404, 7)\n",
      "(16209,)\n",
      "(5404,)\n"
     ]
    }
   ],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(XX, y, test_size=0.25, random_state=42)\n",
    "for i in [X_train, X_test, y_train, y_test]: print(i.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "r-square:  0.591135412034\n",
      "RMSE is  247307.6674549046\n",
      "CPU times: user 8 ms, sys: 0 ns, total: 8 ms\n",
      "Wall time: 5.6 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# Create linear regression object\n",
    "regr = linear_model.LinearRegression()\n",
    "regr.fit(X_train, y_train)\n",
    "print(\"r-square: \", regr.score( X_test, y_test))\n",
    "print_rmse(regr, X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "r-square:  0.750180888193\n",
      "RMSE is  193312.82276331823\n",
      "CPU times: user 624 ms, sys: 0 ns, total: 624 ms\n",
      "Wall time: 622 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "#create a K Neighbours model. Prediction is the average of the 10 nearest neighbours\n",
    "from sklearn.neighbors import KNeighborsRegressor\n",
    "KNN=KNeighborsRegressor(10)\n",
    "KNN.fit(X_train, y_train)\n",
    "print(\"r-square: \", KNN.score( X_test, y_test))\n",
    "print_rmse(KNN, X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "r-square:  0.778525931556\n",
      "RMSE is  182015.8777324025\n",
      "CPU times: user 5.75 s, sys: 0 ns, total: 5.75 s\n",
      "Wall time: 5.75 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "from sklearn.ensemble import GradientBoostingRegressor\n",
    "\n",
    "params = {'n_estimators': 500, 'max_depth': 4, 'min_samples_split': 2, 'learning_rate': 0.01, 'loss': 'ls'}\n",
    "gbr = GradientBoostingRegressor(**params)\n",
    "gbr.fit(X_train, y_train)\n",
    "print(\"r-square: \", gbr.score( X_test, y_test))\n",
    "print_rmse(gbr, X_test, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Let's include some categorial variables too"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "all_features_target=['price', 'bedrooms', 'bathrooms', 'sqft_living', 'sqft_lot', 'floors', \n",
    "                     'waterfront', 'view', 'condition', 'grade', 'sqft_above', 'sqft_basement', \n",
    "                     'yr_built', 'yr_renovated', 'zipcode', 'lat', 'long', 'sqft_living15', 'sqft_lot15']\n",
    "\n",
    "\n",
    "feature_set_num=['bedrooms', 'bathrooms', 'sqft_living', 'sqft_lot', 'floors', \n",
    "                 'lat', 'long', 'yr_built', 'yr_renovated', 'grade',\n",
    "                'sqft_above', 'sqft_basement', 'sqft_living15', 'sqft_lot15']\n",
    "\n",
    "\n",
    "feature_set_cat=['waterfront', 'view', 'condition', 'grade', 'zipcode']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((21613, 14), (21613,))"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X=np.array(df[feature_set_num])\n",
    "y=np.array(df['price'])\n",
    "s=StandardScaler()\n",
    "XX=s.fit_transform(X)\n",
    "XX.shape, y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(16209, 14)\n",
      "(5404, 14)\n",
      "(16209,)\n",
      "(5404,)\n"
     ]
    }
   ],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(XX, y, test_size=0.25, random_state=42)\n",
    "for i in [X_train, X_test, y_train, y_test]: print(i.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Regression\n",
      "r-square:  0.654343009624\n",
      "RMSE is  227389.55125424347\n",
      "CPU times: user 12 ms, sys: 0 ns, total: 12 ms\n",
      "Wall time: 12.8 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# Create linear regression object\n",
    "regr = linear_model.LinearRegression()\n",
    "regr.fit(X_train, y_train)\n",
    "print(\"Regression\")\n",
    "print(\"r-square: \", regr.score( X_test, y_test))\n",
    "print_rmse(regr, X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10-Nearest Neighbours\n",
      "r-square:  0.764069157128\n",
      "RMSE is  187862.5409408664\n",
      "CPU times: user 2.32 s, sys: 4 ms, total: 2.32 s\n",
      "Wall time: 2.32 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "#create a K Neighbours model. Prediction is the average of the 10 nearest neighbours\n",
    "from sklearn.neighbors import KNeighborsRegressor\n",
    "KNN=KNeighborsRegressor(10)\n",
    "KNN.fit(X_train, y_train)\n",
    "print(\"10-Nearest Neighbours\")\n",
    "print(\"r-square: \", KNN.score( X_test, y_test))\n",
    "print_rmse(KNN, X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Boosted Gradient\n",
      "r-square:  0.816182392813\n",
      "RMSE is  165821.70897386884\n",
      "CPU times: user 10 s, sys: 8 ms, total: 10 s\n",
      "Wall time: 10 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "params = {'n_estimators': 500, 'max_depth': 4, 'min_samples_split': 2, 'learning_rate': 0.01, 'loss': 'ls'}\n",
    "gbr = GradientBoostingRegressor(**params)\n",
    "gbr.fit(X_train, y_train)\n",
    "print(\"Boosted Gradient\")\n",
    "print(\"r-square: \", gbr.score( X_test, y_test))\n",
    "print_rmse(gbr, X_test, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Let's try a gradient boosting run with 1000 estimators and max-depth 6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Boosted Gradient\n",
      "r-square:  0.838072466427\n",
      "RMSE is  155635.327156142\n",
      "CPU times: user 37.5 s, sys: 12 ms, total: 37.5 s\n",
      "Wall time: 37.5 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "params = {'n_estimators': 1000, 'max_depth': 6, 'min_samples_split': 2, 'learning_rate': 0.01, 'loss': 'ls'}\n",
    "gbr = GradientBoostingRegressor(**params)\n",
    "gbr.fit(X_train, y_train)\n",
    "print(\"Boosted Gradient\")\n",
    "print(\"r-square: \", gbr.score( X_test, y_test))\n",
    "print_rmse(gbr, X_test, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Let's now add categorical variables as well\n",
    "\n",
    "We need to preprocess them, for Scikit-Learn purposes. Let's first see what they look like"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>waterfront</th>\n",
       "      <th>view</th>\n",
       "      <th>condition</th>\n",
       "      <th>grade</th>\n",
       "      <th>zipcode</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>21613.000000</td>\n",
       "      <td>21613.000000</td>\n",
       "      <td>21613.000000</td>\n",
       "      <td>21613.000000</td>\n",
       "      <td>21613.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.007542</td>\n",
       "      <td>0.234303</td>\n",
       "      <td>3.409430</td>\n",
       "      <td>7.656873</td>\n",
       "      <td>98077.939805</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.086517</td>\n",
       "      <td>0.766318</td>\n",
       "      <td>0.650743</td>\n",
       "      <td>1.175459</td>\n",
       "      <td>53.505026</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>98001.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>98033.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>98065.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>98118.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>13.000000</td>\n",
       "      <td>98199.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         waterfront          view     condition         grade       zipcode\n",
       "count  21613.000000  21613.000000  21613.000000  21613.000000  21613.000000\n",
       "mean       0.007542      0.234303      3.409430      7.656873  98077.939805\n",
       "std        0.086517      0.766318      0.650743      1.175459     53.505026\n",
       "min        0.000000      0.000000      1.000000      1.000000  98001.000000\n",
       "25%        0.000000      0.000000      3.000000      7.000000  98033.000000\n",
       "50%        0.000000      0.000000      3.000000      7.000000  98065.000000\n",
       "75%        0.000000      0.000000      4.000000      8.000000  98118.000000\n",
       "max        1.000000      4.000000      5.000000     13.000000  98199.000000"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "feature_set_cat=['waterfront', 'view', 'condition', 'grade', 'zipcode']\n",
    "df[feature_set_cat].describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(21613, 20)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def OneHotDropOne(df, colnames):\n",
    "    first=1\n",
    "    for col in colnames:\n",
    "        Hot=OneHotEncoder()\n",
    "        coded_vals=Hot.fit_transform(df[[col]])[:,:-1].todense()\n",
    "        if not first:\n",
    "            retval=np.hstack((retval, coded_vals))\n",
    "        else:\n",
    "            retval=coded_vals.copy()\n",
    "            first=0\n",
    "    return retval\n",
    "\n",
    "# Let's include all categorical variables except Zipcode\n",
    "\n",
    "r=OneHotDropOne(df, colnames=[ 'waterfront','view', 'condition', 'grade'])\n",
    "r.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "feature_set_num=['bedrooms', 'bathrooms', 'sqft_living', 'sqft_lot', 'floors', \n",
    "                 'lat', 'long', 'yr_built', 'yr_renovated', 'grade',\n",
    "                'sqft_above', 'sqft_basement', 'sqft_living15', 'sqft_lot15']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((21613, 14), (21613,))"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X=np.array(df[feature_set_num])\n",
    "y=np.array(df['price'])\n",
    "s=StandardScaler()\n",
    "XX=s.fit_transform(X)\n",
    "XX.shape, y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(21613, 34)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "XXX=np.hstack((XX, r))\n",
    "XXX.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(16209, 34)\n",
      "(5404, 34)\n",
      "(16209,)\n",
      "(5404,)\n"
     ]
    }
   ],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(XXX, y, test_size=0.25, random_state=42)\n",
    "for i in [X_train, X_test, y_train, y_test]: print(i.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Regression\n",
      "r-square:  0.732910473027\n",
      "RMSE is  199883.18543684244\n",
      "CPU times: user 16 ms, sys: 8 ms, total: 24 ms\n",
      "Wall time: 30.4 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# Create linear regression object\n",
    "regr = linear_model.LinearRegression()\n",
    "regr.fit(X_train, y_train)\n",
    "print(\"Regression\")\n",
    "print(\"r-square: \", regr.score( X_test, y_test))\n",
    "print_rmse(regr, X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10-Nearest Neighbours\n",
      "r-square:  0.765126618476\n",
      "RMSE is  187441.06049062504\n",
      "CPU times: user 5.25 s, sys: 4 ms, total: 5.26 s\n",
      "Wall time: 5.25 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "#create a K Neighbours model. Prediction is the average of the 10 nearest neighbours\n",
    "from sklearn.neighbors import KNeighborsRegressor\n",
    "KNN=KNeighborsRegressor(10)\n",
    "KNN.fit(X_train, y_train)\n",
    "print(\"10-Nearest Neighbours\")\n",
    "print(\"r-square: \", KNN.score( X_test, y_test))\n",
    "print_rmse(KNN, X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Boosted Gradient\n",
      "r-square:  0.852985282161\n",
      "RMSE is  148295.59124071474\n",
      "CPU times: user 16.3 s, sys: 4 ms, total: 16.3 s\n",
      "Wall time: 16.3 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "params = {'n_estimators': 500, 'max_depth': 4, 'min_samples_split': 2, 'learning_rate': 0.01, 'loss': 'ls'}\n",
    "gbr = GradientBoostingRegressor(**params)\n",
    "gbr.fit(X_train, y_train)\n",
    "print(\"Boosted Gradient\")\n",
    "print(\"r-square: \", gbr.score( X_test, y_test))\n",
    "print_rmse(gbr, X_test, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Predict function to predict House Prices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "this is not tested\n",
    "\n",
    "def predict_price(house_features, s, model):\n",
    "    \"\"\" Takes as input a dictionary 'house_features' with following features to predict house price:\n",
    "    \n",
    "    (Numerical): bedrooms, bathrooms,sqft_living, sqft_lot, floors, lat, long,'yr_built, yr_renovated,\n",
    "    sqft_above, sqft_basement, sqft_living15, sqft_lot15, \n",
    "    \n",
    "    (categorical):  waterfront,view, condition, grade\n",
    "    \"\"\"\n",
    "    feature_set_num=['bedrooms', 'bathrooms', 'sqft_living', 'sqft_lot', 'floors', \n",
    "                 'lat', 'long', 'yr_built', 'yr_renovated', 'grade',\n",
    "                'sqft_above', 'sqft_basement', 'sqft_living15', 'sqft_lot15']\n",
    "    \n",
    "    feature_set_cat=[ 'waterfront','view', 'condition', 'grade']\n",
    "    \n",
    "    \n",
    "    df=pd.DataFrame(house_features)\n",
    "    \n",
    "    inp1=s.fit_transform(np.array(df[feature_set_num]))\n",
    "    inp2=OneHotDropOne(df, colnames=feature_set_cat)\n",
    "    \n",
    "    inp=np.hstack((inp1, inp2))\n",
    "    \n",
    "    return model.predict(inp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "house={'bedrooms', 'bathrooms', 'sqft_living', 'sqft_lot', 'floors', \n",
    "       'lat', 'long', 'yr_built', 'yr_renovated', 'grade',\n",
    "       'sqft_above', 'sqft_basement', 'sqft_living15', 'sqft_lot15',\n",
    "       'waterfront','view', 'condition', 'grade'\n",
    "      }\n",
    "\n",
    "predict_price(house, s, gbr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hyperparameter Optimization\n",
    "\n",
    "We know that the Gradient Boosting is outperforming the other two algorithms on the test data and also takes a lot longer, as expected. Let's see if we can further improve the GB model by selecting a good set of hyper-paramaters. \n",
    "\n",
    "We shall use a GridSearch with a 5-Fold cross validation for this search\n",
    "\n",
    "\n",
    "<span style=\"color:red\">This will take time, run on rorocloud </span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(21613, 34) (21613,)\n"
     ]
    }
   ],
   "source": [
    "print(XXX.shape, y.shape) #quick verify the features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 20.2 s, sys: 32 ms, total: 20.2 s\n",
      "Wall time: 20.2 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "from sklearn.model_selection import  GridSearchCV\n",
    "\n",
    "parameters = {'n_estimators':[250,500, 750, 1000], 'max_depth':[2,4,6,8], \n",
    "              'min_samples_split':[2, 4 ,6], 'learning_rate':[0.001, 0.01, 0.1]}\n",
    "\n",
    "parameters = {'n_estimators':[250], 'max_depth':[2], \n",
    "              'min_samples_split':[4], 'learning_rate':[0.01]}\n",
    "\n",
    "clf = GradientBoostingRegressor()\n",
    "opt= GridSearchCV(clf,param_grid=parameters, cv=5)\n",
    "opt.fit(XXX, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.matrixlib.defmatrix.matrix"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(XXX)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "XXX.tofile(\"XXX.data\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CIFAR10.ipynb\t       Traffic_Sign_Classifier.ipynb  XXX.data\t   helper.py\r\n",
      "MNIST_CNN.ipynb        Traffic_Signs_roro.ipynb       __pycache__\r\n",
      "Test_Regression.ipynb  Untitled.ipynb\t\t      anand.ipynb\r\n"
     ]
    }
   ],
   "source": [
    "!ls"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y.tofile(\"y.data\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Writing hyper.py\n"
     ]
    }
   ],
   "source": [
    "%%file hyper.py\n",
    "from sklearn.model_selection import  GridSearchCV\n",
    "\n",
    "XXX = np.fromfile(\"XXX.data\")\n",
    "y = np.fromfile(\"y.data\")\n",
    "\n",
    "parameters = {'n_estimators':[250,500, 750, 1000], 'max_depth':[2,4,6,8], \n",
    "              'min_samples_split':[2, 4 ,6], 'learning_rate':[0.001, 0.01, 0.1]}\n",
    "\n",
    "clf = GradientBoostingRegressor()\n",
    "opt= GridSearchCV(clf,param_grid=parameters, n_jobs=16, cv=5)\n",
    "opt.fit(XXX, y)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "!rorocloud run -i C16 hyper.py"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Option B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%%time\n",
    "from sklearn.model_selection import  GridSearchCV\n",
    "from rorocloud.model_selection import GridSearchCV\n",
    "\n",
    "parameters = {'n_estimators':[250,500, 750, 1000], 'max_depth':[2,4,6,8], \n",
    "              'min_samples_split':[2, 4 ,6], 'learning_rate':[0.001, 0.01, 0.1]}\n",
    "\n",
    "clf = GradientBoostingRegressor()\n",
    "opt= GridSearchCV(clf,param_grid=parameters, cv=5)\n",
    "opt.fit(XXX, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "ename": "ModuleNotFoundError",
     "evalue": "No module named 'rorocloud'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-49-466d99d6cb7f>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0;32mimport\u001b[0m \u001b[0mrorocloud\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'rorocloud'"
     ]
    }
   ],
   "source": [
    "import rorocloud "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%%rorocloud-enable"
   ]
  }
 ],
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   "codemirror_mode": {
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   "file_extension": ".py",
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   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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