data_wrangling.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import necessary modules/libraries\n",
    "\n",
    "import numpy as  np\n",
    "import pandas as pd\n",
    "\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "from scipy import stats\n",
    "from scipy.stats import pearsonr\n",
    "\n",
    "from matplotlib import rcParams\n",
    "sns.set_style(\"whitegrid\")\n",
    "sns.set_context(\"talk\", font_scale=0.7)\n",
    "sns.set_palette(\"Greens_r\")\n",
    "#set_palette(\"Set1\", 8, .75) # makes plot lines red\n",
    "\n",
    "from ipywidgets import interact, widgets\n",
    "\n",
    "from sklearn.preprocessing import Imputer # to impute missing data\n",
    "\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.preprocessing import MinMaxScaler\n",
    "\n",
    "import sklearn\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.ensemble import RandomForestRegressor\n",
    "from sklearn.linear_model import Lasso\n",
    "from sklearn.linear_model import Ridge\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.model_selection import cross_val_score\n",
    "from sklearn.model_selection import GridSearchCV\n",
    "from sklearn.metrics import mean_squared_error\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Washington housing dataset has 4600 data points with 18 variables each.\n"
     ]
    },
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></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>sqft_above</th>\n",
       "      <th>sqft_basement</th>\n",
       "      <th>yr_built</th>\n",
       "      <th>yr_renovated</th>\n",
       "      <th>street</th>\n",
       "      <th>city</th>\n",
       "      <th>statezip</th>\n",
       "      <th>country</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2014-05-02 00:00:00</td>\n",
       "      <td>313000.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.5</td>\n",
       "      <td>1340</td>\n",
       "      <td>7912</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>1340</td>\n",
       "      <td>0</td>\n",
       "      <td>1955</td>\n",
       "      <td>2005</td>\n",
       "      <td>18810 Densmore Ave N</td>\n",
       "      <td>Shoreline</td>\n",
       "      <td>WA 98133</td>\n",
       "      <td>USA</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2014-05-02 00:00:00</td>\n",
       "      <td>2384000.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>2.5</td>\n",
       "      <td>3650</td>\n",
       "      <td>9050</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>3370</td>\n",
       "      <td>280</td>\n",
       "      <td>1921</td>\n",
       "      <td>0</td>\n",
       "      <td>709 W Blaine St</td>\n",
       "      <td>Seattle</td>\n",
       "      <td>WA 98119</td>\n",
       "      <td>USA</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  date      price  bedrooms  bathrooms  sqft_living  sqft_lot  \\\n",
       "0  2014-05-02 00:00:00   313000.0       3.0        1.5         1340      7912   \n",
       "1  2014-05-02 00:00:00  2384000.0       5.0        2.5         3650      9050   \n",
       "\n",
       "   floors  waterfront  view  condition  sqft_above  sqft_basement  yr_built  \\\n",
       "0     1.5           0     0          3        1340              0      1955   \n",
       "1     2.0           0     4          5        3370            280      1921   \n",
       "\n",
       "   yr_renovated                street       city  statezip country  \n",
       "0          2005  18810 Densmore Ave N  Shoreline  WA 98133     USA  \n",
       "1             0       709 W Blaine St    Seattle  WA 98119     USA  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Load the Washington housing dataset\n",
    "df1 = pd.read_csv('house_price_prediction.csv')\n",
    "print(\"The Washington housing dataset has {} data points with {} variables each.\".format(*df1.shape))\n",
    "df1.head(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EDA and Summary Statistics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 4600 entries, 0 to 4599\n",
      "Data columns (total 18 columns):\n",
      "date             4600 non-null object\n",
      "price            4600 non-null float64\n",
      "bedrooms         4600 non-null float64\n",
      "bathrooms        4600 non-null float64\n",
      "sqft_living      4600 non-null int64\n",
      "sqft_lot         4600 non-null int64\n",
      "floors           4600 non-null float64\n",
      "waterfront       4600 non-null int64\n",
      "view             4600 non-null int64\n",
      "condition        4600 non-null int64\n",
      "sqft_above       4600 non-null int64\n",
      "sqft_basement    4600 non-null int64\n",
      "yr_built         4600 non-null int64\n",
      "yr_renovated     4600 non-null int64\n",
      "street           4600 non-null object\n",
      "city             4600 non-null object\n",
      "statezip         4600 non-null object\n",
      "country          4600 non-null object\n",
      "dtypes: float64(4), int64(9), object(5)\n",
      "memory usage: 647.0+ KB\n"
     ]
    }
   ],
   "source": [
    "# inspecting structure of dataframe & number of null values (if any)\n",
    "df1.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></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>sqft_above</th>\n",
       "      <th>sqft_basement</th>\n",
       "      <th>yr_built</th>\n",
       "      <th>yr_renovated</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>4.600000e+03</td>\n",
       "      <td>4600.000000</td>\n",
       "      <td>4600.000000</td>\n",
       "      <td>4600.000000</td>\n",
       "      <td>4.600000e+03</td>\n",
       "      <td>4600.000000</td>\n",
       "      <td>4600.000000</td>\n",
       "      <td>4600.000000</td>\n",
       "      <td>4600.000000</td>\n",
       "      <td>4600.000000</td>\n",
       "      <td>4600.000000</td>\n",
       "      <td>4600.000000</td>\n",
       "      <td>4600.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>5.519630e+05</td>\n",
       "      <td>3.400870</td>\n",
       "      <td>2.160815</td>\n",
       "      <td>2139.346957</td>\n",
       "      <td>1.485252e+04</td>\n",
       "      <td>1.512065</td>\n",
       "      <td>0.007174</td>\n",
       "      <td>0.240652</td>\n",
       "      <td>3.451739</td>\n",
       "      <td>1827.265435</td>\n",
       "      <td>312.081522</td>\n",
       "      <td>1970.786304</td>\n",
       "      <td>808.608261</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>5.638347e+05</td>\n",
       "      <td>0.908848</td>\n",
       "      <td>0.783781</td>\n",
       "      <td>963.206916</td>\n",
       "      <td>3.588444e+04</td>\n",
       "      <td>0.538288</td>\n",
       "      <td>0.084404</td>\n",
       "      <td>0.778405</td>\n",
       "      <td>0.677230</td>\n",
       "      <td>862.168977</td>\n",
       "      <td>464.137228</td>\n",
       "      <td>29.731848</td>\n",
       "      <td>979.414536</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>370.000000</td>\n",
       "      <td>6.380000e+02</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>370.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1900.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>3.228750e+05</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>1.750000</td>\n",
       "      <td>1460.000000</td>\n",
       "      <td>5.000750e+03</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>1190.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1951.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>4.609435e+05</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>2.250000</td>\n",
       "      <td>1980.000000</td>\n",
       "      <td>7.683000e+03</td>\n",
       "      <td>1.500000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>1590.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1976.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>6.549625e+05</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>2.500000</td>\n",
       "      <td>2620.000000</td>\n",
       "      <td>1.100125e+04</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>2300.000000</td>\n",
       "      <td>610.000000</td>\n",
       "      <td>1997.000000</td>\n",
       "      <td>1999.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>2.659000e+07</td>\n",
       "      <td>9.000000</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>13540.000000</td>\n",
       "      <td>1.074218e+06</td>\n",
       "      <td>3.500000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>9410.000000</td>\n",
       "      <td>4820.000000</td>\n",
       "      <td>2014.000000</td>\n",
       "      <td>2014.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              price     bedrooms    bathrooms   sqft_living      sqft_lot  \\\n",
       "count  4.600000e+03  4600.000000  4600.000000   4600.000000  4.600000e+03   \n",
       "mean   5.519630e+05     3.400870     2.160815   2139.346957  1.485252e+04   \n",
       "std    5.638347e+05     0.908848     0.783781    963.206916  3.588444e+04   \n",
       "min    0.000000e+00     0.000000     0.000000    370.000000  6.380000e+02   \n",
       "25%    3.228750e+05     3.000000     1.750000   1460.000000  5.000750e+03   \n",
       "50%    4.609435e+05     3.000000     2.250000   1980.000000  7.683000e+03   \n",
       "75%    6.549625e+05     4.000000     2.500000   2620.000000  1.100125e+04   \n",
       "max    2.659000e+07     9.000000     8.000000  13540.000000  1.074218e+06   \n",
       "\n",
       "            floors   waterfront         view    condition   sqft_above  \\\n",
       "count  4600.000000  4600.000000  4600.000000  4600.000000  4600.000000   \n",
       "mean      1.512065     0.007174     0.240652     3.451739  1827.265435   \n",
       "std       0.538288     0.084404     0.778405     0.677230   862.168977   \n",
       "min       1.000000     0.000000     0.000000     1.000000   370.000000   \n",
       "25%       1.000000     0.000000     0.000000     3.000000  1190.000000   \n",
       "50%       1.500000     0.000000     0.000000     3.000000  1590.000000   \n",
       "75%       2.000000     0.000000     0.000000     4.000000  2300.000000   \n",
       "max       3.500000     1.000000     4.000000     5.000000  9410.000000   \n",
       "\n",
       "       sqft_basement     yr_built  yr_renovated  \n",
       "count    4600.000000  4600.000000   4600.000000  \n",
       "mean      312.081522  1970.786304    808.608261  \n",
       "std       464.137228    29.731848    979.414536  \n",
       "min         0.000000  1900.000000      0.000000  \n",
       "25%         0.000000  1951.000000      0.000000  \n",
       "50%         0.000000  1976.000000      0.000000  \n",
       "75%       610.000000  1997.000000   1999.000000  \n",
       "max      4820.000000  2014.000000   2014.000000  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1.describe()\n",
    "\n",
    "#notice: price, bedrooms, & bathrooms have min of 0. Needs furthern investigation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice `price`, `bedrooms`, & `bathroom` have a minimum value of 0. Needs further investigation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Some statistics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Statistics for Washington housing dataset:\n",
      "\n",
      "Minimum price: $0.0\n",
      "Maximum price: $26590000.0\n",
      "Mean price: $551962.99\n",
      "Median price $460943.46\n",
      "Standard deviation of prices: $563773.41\n"
     ]
    }
   ],
   "source": [
    "# Minimum price of the data\n",
    "minimum_price = round(np.amin(df1[\"price\"]), 2)\n",
    "\n",
    "# Maximum price of the data\n",
    "maximum_price = round(np.amax(df1[\"price\"]), 2)\n",
    "\n",
    "# Mean price of the data\n",
    "mean_price = round(np.mean(df1[\"price\"]), 2)\n",
    "\n",
    "# Median price of the data\n",
    "median_price = round(np.median(df1[\"price\"]), 2)\n",
    "\n",
    "# Standard deviation of prices of the data\n",
    "std_price = round(np.std(df1[\"price\"]), 2)\n",
    "\n",
    "# Show the calculated statistics\n",
    "print(\"Statistics for Washington housing dataset:\\n\")\n",
    "print(\"Minimum price: ${}\".format(minimum_price)) \n",
    "print(\"Maximum price: ${}\".format(maximum_price))\n",
    "print(\"Mean price: ${}\".format(mean_price))\n",
    "print(\"Median price ${}\".format(median_price))\n",
    "print(\"Standard deviation of prices: ${}\".format(std_price))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Feature Observation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Confirm sqft_living is sqft_above + sqft_basement?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Notice sqft_above & sqft_basement add up to sqft_living.\n",
    "(df1.sqft_living == df1.sqft_above + df1.sqft_basement).all()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Feature Engineering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "df2 = df1.copy()\n",
    "\n",
    "# change date col to datetime\n",
    "df2['date'] = pd.to_datetime(df2['date'])\n",
    "\n",
    "# change data types of 'waterfront' & 'condition' to categorical\n",
    "df2[['waterfront', 'condition']] = df1[['waterfront', 'condition']].astype('category')\n",
    "\n",
    "# splittig statezip into state & zipcode features & removing statezip\n",
    "df2['state'] = df2['statezip'].apply(lambda x: x.split(' ')[0])\n",
    "df2['zipcode'] = df2['statezip'].apply(lambda x: int(x.split(' ')[1]))\n",
    "df2 = df2.drop('statezip', axis='columns')\n",
    "\n",
    "# creating total_sqft feature: sqft_above + sqft_lot\n",
    "df2['total_sqft'] = df2.sqft_living + df2.sqft_lot\n",
    "\n",
    "# creating month feature\n",
    "df2['month'] = pd.DatetimeIndex(df2['date']).month"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Missing/zero values & outliers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Zero/Missing Values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "date                0\n",
       "price              49\n",
       "bedrooms            2\n",
       "bathrooms           2\n",
       "sqft_living         0\n",
       "sqft_lot            0\n",
       "floors              0\n",
       "waterfront       4567\n",
       "view             4140\n",
       "condition           0\n",
       "sqft_above          0\n",
       "sqft_basement    2745\n",
       "yr_built            0\n",
       "yr_renovated     2735\n",
       "street              0\n",
       "city                0\n",
       "country             0\n",
       "state               0\n",
       "zipcode             0\n",
       "total_sqft          0\n",
       "month               0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df3 = df2.copy()\n",
    "\n",
    "# counting the number of zero values in each column\n",
    "df3.isin([0]).sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice: `waterfront` & `view` have categorical values of 0 & 1.  \n",
    "Nearly half of `yr_renovated` are 0.  \n",
    "Inspect the 0s in `bedrooms` & `bathrooms`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "There are 49 houses worth $0, which are 1.1% of entire data. Therefore created a column of boolean arrays with 1s for when price is $0 & 0s for when price is not $0.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# 0 Price\n",
    "\n",
    "price_zero_len = round((len(df3[df3.price == 0])/len(df3)) * 100, 1)\n",
    "print('There are {} houses worth $0, which are {}% of entire data. Therefore created a column of boolean arrays with 1s for when price is $0 & 0s for when price is not $0.'.format(len(df3[df3.price == 0]), price_zero_len))\n",
    "print('')\n",
    "\n",
    "df3['price_is_zero'] = (df3['price'] == 0).astype(int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "59.5% of yr_renovated column has 0 values, therefore added a column of boolean arrays with 1s for when yr_renov is 0 & 0s for others.\n"
     ]
    }
   ],
   "source": [
    "# 0 yr_renovated\n",
    "\n",
    "# percentage of 'yr_renovated' col with 0 entries\n",
    "yr_renov_0 = round((len(df3[df3['yr_renovated'] == 0]) / len(df3)) * 100, 1)\n",
    "print(\"{}% of yr_renovated column has 0 values, therefore added a column of boolean arrays with 1s for when yr_renov is 0 & 0s for others.\".format(yr_renov_0))\n",
    "\n",
    "df3['renov_date_is_zero'] = (df3['yr_renovated'] == 0).astype(int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></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>...</th>\n",
       "      <th>yr_renovated</th>\n",
       "      <th>street</th>\n",
       "      <th>city</th>\n",
       "      <th>country</th>\n",
       "      <th>state</th>\n",
       "      <th>zipcode</th>\n",
       "      <th>total_sqft</th>\n",
       "      <th>month</th>\n",
       "      <th>price_is_zero</th>\n",
       "      <th>renov_date_is_zero</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2365</th>\n",
       "      <td>2014-06-12</td>\n",
       "      <td>1095000.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3064</td>\n",
       "      <td>4764</td>\n",
       "      <td>3.5</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>...</td>\n",
       "      <td>2009</td>\n",
       "      <td>814 E Howe St</td>\n",
       "      <td>Seattle</td>\n",
       "      <td>USA</td>\n",
       "      <td>WA</td>\n",
       "      <td>98102</td>\n",
       "      <td>7828</td>\n",
       "      <td>6</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3209</th>\n",
       "      <td>2014-06-24</td>\n",
       "      <td>1295648.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>4810</td>\n",
       "      <td>28008</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>...</td>\n",
       "      <td>2009</td>\n",
       "      <td>20418 NE 64th Pl</td>\n",
       "      <td>Redmond</td>\n",
       "      <td>USA</td>\n",
       "      <td>WA</td>\n",
       "      <td>98053</td>\n",
       "      <td>32818</td>\n",
       "      <td>6</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2 rows × 23 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           date      price  bedrooms  bathrooms  sqft_living  sqft_lot  \\\n",
       "2365 2014-06-12  1095000.0       0.0        0.0         3064      4764   \n",
       "3209 2014-06-24  1295648.0       0.0        0.0         4810     28008   \n",
       "\n",
       "      floors waterfront  view condition  ...  yr_renovated            street  \\\n",
       "2365     3.5          0     2         3  ...          2009     814 E Howe St   \n",
       "3209     2.0          0     0         3  ...          2009  20418 NE 64th Pl   \n",
       "\n",
       "         city  country state zipcode total_sqft month  price_is_zero  \\\n",
       "2365  Seattle      USA    WA   98102       7828     6              0   \n",
       "3209  Redmond      USA    WA   98053      32818     6              0   \n",
       "\n",
       "      renov_date_is_zero  \n",
       "2365                   0  \n",
       "3209                   0  \n",
       "\n",
       "[2 rows x 23 columns]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 0 bedrooms & bathrooms\n",
    "\n",
    "df3[df3.bedrooms == 0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are 2 houses with 0s as their bedrooms & bathrooms shown above.  \n",
    "We can see that the houses are both worth over 1 mil, therefore the 0s must be errors.  \n",
    "Will replace 0s with the mean bedroom & bathroom values of 3 & 2 respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "df3[\"bedrooms\"].replace({0: round(df3[\"bedrooms\"].mean(), 0)}, inplace=True)\n",
    "df3[\"bathrooms\"].replace({0: round(df3[\"bathrooms\"].mean(), 0)}, inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# removing price outliers\n",
    "df_no_outs = df3[df3.price < 10000000].copy()\n",
    "\n",
    "# removing zero price\n",
    "df_no_zeros = df_no_outs[df_no_outs[\"price\"] != 0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Outliers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Relationship between Bedrooms and Price')"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Price\n",
    "\n",
    "plt.scatter(df3[\"bedrooms\"], df3[\"price\"].div(1000000), alpha = 0.3 ,s=60 , edgecolors='g')\n",
    "plt.xlabel(\"Number of bedrooms\")\n",
    "plt.ylabel(\"House Price ($M)\")\n",
    "plt.title(\"Relationship between Bedrooms and Price\")\n",
    "#plt.grid('on')\n",
    "#ax.set_facecolor('grey')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice 2 outliers priced around \\\\$13 M & \\\\$26 M, both with 3 bedrooms."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Relationship between Bedrooms and Price')"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# normalized / scaled scatter plot of bedrooms vs price\n",
    "X = df3[\"price\"].values.reshape(-1,1)\n",
    "X = MinMaxScaler().fit_transform(X)\n",
    "plt.scatter(df3[\"bedrooms\"], X, s=60, alpha=0.3, edgecolors='g')\n",
    "plt.xlabel(\"Number of bedrooms\")\n",
    "plt.ylabel(\"Scaled House Price\")\n",
    "plt.title(\"Relationship between Bedrooms and Price\")\n",
    "#plt.grid('on')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see in the above plot that even after scaling the data, the outliers remain outliers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Relationship between Bedrooms and Price (Without Outliers)')"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot with removed price outliers\n",
    "plt.scatter(df_no_outs[\"bedrooms\"], np.divide(df_no_outs[\"price\"], 1000000), alpha = 0.3 ,s=60 , edgecolors='g')\n",
    "plt.xlabel(\"Number of bedrooms\")\n",
    "plt.ylabel(\"House Price ($M)\")\n",
    "plt.title(\"Relationship between Bedrooms and Price (Without Outliers)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A polynomial (quadratic) regression might fit the data better.  \n",
    "(squared 'bedrooms' when modelling)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></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>...</th>\n",
       "      <th>yr_renovated</th>\n",
       "      <th>street</th>\n",
       "      <th>city</th>\n",
       "      <th>country</th>\n",
       "      <th>state</th>\n",
       "      <th>zipcode</th>\n",
       "      <th>total_sqft</th>\n",
       "      <th>month</th>\n",
       "      <th>price_is_zero</th>\n",
       "      <th>renov_date_is_zero</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>4346</th>\n",
       "      <td>2014-06-23</td>\n",
       "      <td>12899000.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.5</td>\n",
       "      <td>2190</td>\n",
       "      <td>11394</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>...</td>\n",
       "      <td>2001</td>\n",
       "      <td>5426 40th Ave W</td>\n",
       "      <td>Seattle</td>\n",
       "      <td>USA</td>\n",
       "      <td>WA</td>\n",
       "      <td>98199</td>\n",
       "      <td>13584</td>\n",
       "      <td>6</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4350</th>\n",
       "      <td>2014-07-03</td>\n",
       "      <td>26590000.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1180</td>\n",
       "      <td>7793</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>12005 SE 219th Ct</td>\n",
       "      <td>Kent</td>\n",
       "      <td>USA</td>\n",
       "      <td>WA</td>\n",
       "      <td>98031</td>\n",
       "      <td>8973</td>\n",
       "      <td>7</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2 rows × 23 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           date       price  bedrooms  bathrooms  sqft_living  sqft_lot  \\\n",
       "4346 2014-06-23  12899000.0       3.0        2.5         2190     11394   \n",
       "4350 2014-07-03  26590000.0       3.0        2.0         1180      7793   \n",
       "\n",
       "      floors waterfront  view condition  ...  yr_renovated             street  \\\n",
       "4346     1.0          0     0         3  ...          2001    5426 40th Ave W   \n",
       "4350     1.0          0     0         4  ...             0  12005 SE 219th Ct   \n",
       "\n",
       "         city  country state zipcode total_sqft month  price_is_zero  \\\n",
       "4346  Seattle      USA    WA   98199      13584     6              0   \n",
       "4350     Kent      USA    WA   98031       8973     7              0   \n",
       "\n",
       "      renov_date_is_zero  \n",
       "4346                   0  \n",
       "4350                   1  \n",
       "\n",
       "[2 rows x 23 columns]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df3[df3.price > 10000000]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "House price of greater than $10 milion might be too high for a 3 bedroom house. Do they have higher square footage than the other houses?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'House Size vs Price')"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(data=df3, x='sqft_living', y='price', fit_reg=True, scatter_kws={'s':20})\n",
    "plt.title(\"House Size vs Price\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see in the above plot that the size of the houses priced over $10 mil does not explain why they're priced very high. Might be an error. Therefore consider modeling the data with the 2 price outliers removed."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}