Kaggle_House_price_Github_3_17.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this project, I read the following kernels: <br>\n",
    "https://www.kaggle.com/pmarcelino/comprehensive-data-exploration-with-python <br>\n",
    "https://www.kaggle.com/juliencs/a-study-on-regression-applied-to-the-ames-dataset <br>\n",
    "https://www.kaggle.com/apapiu/regularized-linear-models <br>\n",
    "https://www.kaggle.com/serigne/stacked-regressions-top-4-on-leaderboard"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Import python Analysis tools and read the data from CSV."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import preprocessing\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import os \n",
    "import tarfile \n",
    "from sklearn.ensemble import RandomForestRegressor\n",
    "from scipy.stats import norm\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from scipy import stats\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "%matplotlib inline\n",
    "from sklearn.preprocessing import LabelEncoder\n",
    "from scipy.stats import norm, skew\n",
    "from sklearn import linear_model as lm\n",
    "from sklearn.linear_model import ElasticNet, Lasso,  BayesianRidge, LassoLarsIC\n",
    "from sklearn.ensemble import RandomForestRegressor,  GradientBoostingRegressor\n",
    "from sklearn.kernel_ridge import KernelRidge\n",
    "from sklearn.pipeline import make_pipeline\n",
    "from sklearn.preprocessing import RobustScaler\n",
    "from sklearn.base import BaseEstimator, TransformerMixin, RegressorMixin, clone\n",
    "from sklearn.model_selection import KFold, cross_val_score, train_test_split\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.feature_selection import SelectKBest\n",
    "from sklearn.feature_selection import SelectFromModel\n",
    "from sklearn.feature_selection import chi2, f_regression\n",
    "import xgboost as xgb\n",
    "from sklearn.model_selection import GridSearchCV \n",
    "from sklearn.neighbors import KNeighborsRegressor\n",
    "import lightgbm as lgb\n",
    "import statsmodels.api as sm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "train = pd.read_csv(\"/Users/rileychiu/Desktop/Kaggle/house price/train.csv\")\n",
    "test = pd.read_csv(\"/Users/rileychiu/Desktop/Kaggle/house price/test.csv\")\n",
    "sample = pd.read_csv('/Users/rileychiu/Desktop/Kaggle/house price/sample_submission.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 1460 entries, 0 to 1459\n",
      "Data columns (total 81 columns):\n",
      "Id               1460 non-null int64\n",
      "MSSubClass       1460 non-null int64\n",
      "MSZoning         1460 non-null object\n",
      "LotFrontage      1201 non-null float64\n",
      "LotArea          1460 non-null int64\n",
      "Street           1460 non-null object\n",
      "Alley            91 non-null object\n",
      "LotShape         1460 non-null object\n",
      "LandContour      1460 non-null object\n",
      "Utilities        1460 non-null object\n",
      "LotConfig        1460 non-null object\n",
      "LandSlope        1460 non-null object\n",
      "Neighborhood     1460 non-null object\n",
      "Condition1       1460 non-null object\n",
      "Condition2       1460 non-null object\n",
      "BldgType         1460 non-null object\n",
      "HouseStyle       1460 non-null object\n",
      "OverallQual      1460 non-null int64\n",
      "OverallCond      1460 non-null int64\n",
      "YearBuilt        1460 non-null int64\n",
      "YearRemodAdd     1460 non-null int64\n",
      "RoofStyle        1460 non-null object\n",
      "RoofMatl         1460 non-null object\n",
      "Exterior1st      1460 non-null object\n",
      "Exterior2nd      1460 non-null object\n",
      "MasVnrType       1452 non-null object\n",
      "MasVnrArea       1452 non-null float64\n",
      "ExterQual        1460 non-null object\n",
      "ExterCond        1460 non-null object\n",
      "Foundation       1460 non-null object\n",
      "BsmtQual         1423 non-null object\n",
      "BsmtCond         1423 non-null object\n",
      "BsmtExposure     1422 non-null object\n",
      "BsmtFinType1     1423 non-null object\n",
      "BsmtFinSF1       1460 non-null int64\n",
      "BsmtFinType2     1422 non-null object\n",
      "BsmtFinSF2       1460 non-null int64\n",
      "BsmtUnfSF        1460 non-null int64\n",
      "TotalBsmtSF      1460 non-null int64\n",
      "Heating          1460 non-null object\n",
      "HeatingQC        1460 non-null object\n",
      "CentralAir       1460 non-null object\n",
      "Electrical       1459 non-null object\n",
      "1stFlrSF         1460 non-null int64\n",
      "2ndFlrSF         1460 non-null int64\n",
      "LowQualFinSF     1460 non-null int64\n",
      "GrLivArea        1460 non-null int64\n",
      "BsmtFullBath     1460 non-null int64\n",
      "BsmtHalfBath     1460 non-null int64\n",
      "FullBath         1460 non-null int64\n",
      "HalfBath         1460 non-null int64\n",
      "BedroomAbvGr     1460 non-null int64\n",
      "KitchenAbvGr     1460 non-null int64\n",
      "KitchenQual      1460 non-null object\n",
      "TotRmsAbvGrd     1460 non-null int64\n",
      "Functional       1460 non-null object\n",
      "Fireplaces       1460 non-null int64\n",
      "FireplaceQu      770 non-null object\n",
      "GarageType       1379 non-null object\n",
      "GarageYrBlt      1379 non-null float64\n",
      "GarageFinish     1379 non-null object\n",
      "GarageCars       1460 non-null int64\n",
      "GarageArea       1460 non-null int64\n",
      "GarageQual       1379 non-null object\n",
      "GarageCond       1379 non-null object\n",
      "PavedDrive       1460 non-null object\n",
      "WoodDeckSF       1460 non-null int64\n",
      "OpenPorchSF      1460 non-null int64\n",
      "EnclosedPorch    1460 non-null int64\n",
      "3SsnPorch        1460 non-null int64\n",
      "ScreenPorch      1460 non-null int64\n",
      "PoolArea         1460 non-null int64\n",
      "PoolQC           7 non-null object\n",
      "Fence            281 non-null object\n",
      "MiscFeature      54 non-null object\n",
      "MiscVal          1460 non-null int64\n",
      "MoSold           1460 non-null int64\n",
      "YrSold           1460 non-null int64\n",
      "SaleType         1460 non-null object\n",
      "SaleCondition    1460 non-null object\n",
      "SalePrice        1460 non-null int64\n",
      "dtypes: float64(3), int64(35), object(43)\n",
      "memory usage: 924.0+ KB\n"
     ]
    }
   ],
   "source": [
    "train.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that there are 1460 examples in the train set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 1459 entries, 0 to 1458\n",
      "Data columns (total 80 columns):\n",
      "Id               1459 non-null int64\n",
      "MSSubClass       1459 non-null int64\n",
      "MSZoning         1455 non-null object\n",
      "LotFrontage      1232 non-null float64\n",
      "LotArea          1459 non-null int64\n",
      "Street           1459 non-null object\n",
      "Alley            107 non-null object\n",
      "LotShape         1459 non-null object\n",
      "LandContour      1459 non-null object\n",
      "Utilities        1457 non-null object\n",
      "LotConfig        1459 non-null object\n",
      "LandSlope        1459 non-null object\n",
      "Neighborhood     1459 non-null object\n",
      "Condition1       1459 non-null object\n",
      "Condition2       1459 non-null object\n",
      "BldgType         1459 non-null object\n",
      "HouseStyle       1459 non-null object\n",
      "OverallQual      1459 non-null int64\n",
      "OverallCond      1459 non-null int64\n",
      "YearBuilt        1459 non-null int64\n",
      "YearRemodAdd     1459 non-null int64\n",
      "RoofStyle        1459 non-null object\n",
      "RoofMatl         1459 non-null object\n",
      "Exterior1st      1458 non-null object\n",
      "Exterior2nd      1458 non-null object\n",
      "MasVnrType       1443 non-null object\n",
      "MasVnrArea       1444 non-null float64\n",
      "ExterQual        1459 non-null object\n",
      "ExterCond        1459 non-null object\n",
      "Foundation       1459 non-null object\n",
      "BsmtQual         1415 non-null object\n",
      "BsmtCond         1414 non-null object\n",
      "BsmtExposure     1415 non-null object\n",
      "BsmtFinType1     1417 non-null object\n",
      "BsmtFinSF1       1458 non-null float64\n",
      "BsmtFinType2     1417 non-null object\n",
      "BsmtFinSF2       1458 non-null float64\n",
      "BsmtUnfSF        1458 non-null float64\n",
      "TotalBsmtSF      1458 non-null float64\n",
      "Heating          1459 non-null object\n",
      "HeatingQC        1459 non-null object\n",
      "CentralAir       1459 non-null object\n",
      "Electrical       1459 non-null object\n",
      "1stFlrSF         1459 non-null int64\n",
      "2ndFlrSF         1459 non-null int64\n",
      "LowQualFinSF     1459 non-null int64\n",
      "GrLivArea        1459 non-null int64\n",
      "BsmtFullBath     1457 non-null float64\n",
      "BsmtHalfBath     1457 non-null float64\n",
      "FullBath         1459 non-null int64\n",
      "HalfBath         1459 non-null int64\n",
      "BedroomAbvGr     1459 non-null int64\n",
      "KitchenAbvGr     1459 non-null int64\n",
      "KitchenQual      1458 non-null object\n",
      "TotRmsAbvGrd     1459 non-null int64\n",
      "Functional       1457 non-null object\n",
      "Fireplaces       1459 non-null int64\n",
      "FireplaceQu      729 non-null object\n",
      "GarageType       1383 non-null object\n",
      "GarageYrBlt      1381 non-null float64\n",
      "GarageFinish     1381 non-null object\n",
      "GarageCars       1458 non-null float64\n",
      "GarageArea       1458 non-null float64\n",
      "GarageQual       1381 non-null object\n",
      "GarageCond       1381 non-null object\n",
      "PavedDrive       1459 non-null object\n",
      "WoodDeckSF       1459 non-null int64\n",
      "OpenPorchSF      1459 non-null int64\n",
      "EnclosedPorch    1459 non-null int64\n",
      "3SsnPorch        1459 non-null int64\n",
      "ScreenPorch      1459 non-null int64\n",
      "PoolArea         1459 non-null int64\n",
      "PoolQC           3 non-null object\n",
      "Fence            290 non-null object\n",
      "MiscFeature      51 non-null object\n",
      "MiscVal          1459 non-null int64\n",
      "MoSold           1459 non-null int64\n",
      "YrSold           1459 non-null int64\n",
      "SaleType         1458 non-null object\n",
      "SaleCondition    1459 non-null object\n",
      "dtypes: float64(11), int64(26), object(43)\n",
      "memory usage: 912.0+ KB\n"
     ]
    }
   ],
   "source": [
    "test.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that there are 1459 examples in the test set."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are 80 features. (data field)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data field"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's a brief version of what you'll find in the data description file.\n",
    "\n",
    "SalePrice - the property's sale price in dollars. This is the target variable that you're trying to predict.<br>\n",
    "MSSubClass: The building class<br>\n",
    "MSZoning: The general zoning classification<br>\n",
    "LotFrontage: Linear feet of street connected to property<br>\n",
    "LotArea: Lot size in square feet<br>\n",
    "Street: Type of road access<br>\n",
    "Alley: Type of alley access<br>\n",
    "LotShape: General shape of property<br>\n",
    "LandContour: Flatness of the property<br>\n",
    "Utilities: Type of utilities available<br>\n",
    "LotConfig: Lot configuration<br>\n",
    "LandSlope: Slope of property<br>\n",
    "Neighborhood: Physical locations within Ames city limits<br>\n",
    "Condition1: Proximity to main road or railroad<br>\n",
    "Condition2: Proximity to main road or railroad (if a second is present)<br>\n",
    "BldgType: Type of dwelling<br>\n",
    "HouseStyle: Style of dwelling<br>\n",
    "OverallQual: Overall material and finish quality<br>\n",
    "OverallCond: Overall condition rating<br>\n",
    "YearBuilt: Original construction date<br>\n",
    "YearRemodAdd: Remodel date<br>\n",
    "RoofStyle: Type of roof<br>\n",
    "RoofMatl: Roof material<br>\n",
    "Exterior1st: Exterior covering on house<br>\n",
    "Exterior2nd: Exterior covering on house (if more than one material)<br>\n",
    "MasVnrType: Masonry veneer type<br>\n",
    "MasVnrArea: Masonry veneer area in square feet<br>\n",
    "ExterQual: Exterior material quality<br>\n",
    "ExterCond: Present condition of the material on the exterior<br>\n",
    "Foundation: Type of foundation<br>\n",
    "BsmtQual: Height of the basement<br>\n",
    "BsmtCond: General condition of the basement<br>\n",
    "BsmtExposure: Walkout or garden level basement walls<br>\n",
    "BsmtFinType1: Quality of basement finished area<br>\n",
    "BsmtFinSF1: Type 1 finished square feet<br>\n",
    "BsmtFinType2: Quality of second finished area (if present)<br>\n",
    "BsmtFinSF2: Type 2 finished square feet<br>\n",
    "BsmtUnfSF: Unfinished square feet of basement area<br>\n",
    "TotalBsmtSF: Total square feet of basement area<br>\n",
    "Heating: Type of heating<br>\n",
    "HeatingQC: Heating quality and condition<br>\n",
    "CentralAir: Central air conditioning<br>\n",
    "Electrical: Electrical system<br>\n",
    "1stFlrSF: First Floor square feet<br>\n",
    "2ndFlrSF: Second floor square feet<br>\n",
    "LowQualFinSF: Low quality finished square feet (all floors)<br>\n",
    "GrLivArea: Above grade (ground) living area square feet<br>\n",
    "BsmtFullBath: Basement full bathrooms<br>\n",
    "BsmtHalfBath: Basement half bathrooms<br>\n",
    "FullBath: Full bathrooms above grade<br>\n",
    "HalfBath: Half baths above grade<br>\n",
    "Bedroom: Number of bedrooms above basement level<br>\n",
    "Kitchen: Number of kitchens<br>\n",
    "KitchenQual: Kitchen quality<br>\n",
    "TotRmsAbvGrd: Total rooms above grade (does not include bathrooms)<br>\n",
    "Functional: Home functionality rating<br>\n",
    "Fireplaces: Number of fireplaces<br>\n",
    "FireplaceQu: Fireplace quality<br>\n",
    "GarageType: Garage location<br>\n",
    "GarageYrBlt: Year garage was built<br>\n",
    "GarageFinish: Interior finish of the garage<br>\n",
    "GarageCars: Size of garage in car capacity<br>\n",
    "GarageArea: Size of garage in square feet<br>\n",
    "GarageQual: Garage quality<br>\n",
    "GarageCond: Garage condition<br>\n",
    "PavedDrive: Paved driveway<br>\n",
    "WoodDeckSF: Wood deck area in square feet<br>\n",
    "OpenPorchSF: Open porch area in square feet<br>\n",
    "EnclosedPorch: Enclosed porch area in square feet<br>\n",
    "3SsnPorch: Three season porch area in square feet<br>\n",
    "ScreenPorch: Screen porch area in square feet<br>\n",
    "PoolArea: Pool area in square feet<br>\n",
    "PoolQC: Pool quality<br>\n",
    "Fence: Fence quality<br>\n",
    "MiscFeature: Miscellaneous feature not covered in other categories<br>\n",
    "MiscVal: $Value of miscellaneous feature<br>\n",
    "MoSold: Month Sold<br>\n",
    "YrSold: Year Sold<br>\n",
    "SaleType: Type of sale<br>\n",
    "SaleCondition: Condition of sale<br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Save the 'Id' column\n",
    "train_ID = train['Id']\n",
    "test_ID = test['Id']\n",
    "\n",
    "#Now drop the  'Id' colum since it's unnecessary for  the prediction process.\n",
    "train.drop(\"Id\", axis = 1, inplace = True)\n",
    "test.drop(\"Id\", axis = 1, inplace = True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Get the first sense of the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SalePrice        1.000000\n",
      "OverallQual      0.790982\n",
      "GrLivArea        0.708624\n",
      "GarageCars       0.640409\n",
      "GarageArea       0.623431\n",
      "TotalBsmtSF      0.613581\n",
      "1stFlrSF         0.605852\n",
      "FullBath         0.560664\n",
      "TotRmsAbvGrd     0.533723\n",
      "YearBuilt        0.522897\n",
      "YearRemodAdd     0.507101\n",
      "GarageYrBlt      0.486362\n",
      "MasVnrArea       0.477493\n",
      "Fireplaces       0.466929\n",
      "BsmtFinSF1       0.386420\n",
      "LotFrontage      0.351799\n",
      "WoodDeckSF       0.324413\n",
      "2ndFlrSF         0.319334\n",
      "OpenPorchSF      0.315856\n",
      "HalfBath         0.284108\n",
      "LotArea          0.263843\n",
      "BsmtFullBath     0.227122\n",
      "BsmtUnfSF        0.214479\n",
      "BedroomAbvGr     0.168213\n",
      "ScreenPorch      0.111447\n",
      "PoolArea         0.092404\n",
      "MoSold           0.046432\n",
      "3SsnPorch        0.044584\n",
      "BsmtFinSF2      -0.011378\n",
      "BsmtHalfBath    -0.016844\n",
      "MiscVal         -0.021190\n",
      "LowQualFinSF    -0.025606\n",
      "YrSold          -0.028923\n",
      "OverallCond     -0.077856\n",
      "MSSubClass      -0.084284\n",
      "EnclosedPorch   -0.128578\n",
      "KitchenAbvGr    -0.135907\n",
      "Name: SalePrice, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "corr = train.corr()\n",
    "corr.sort_values([\"SalePrice\"], ascending = False, inplace = True)\n",
    "print(corr.SalePrice)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check and remove the outlier."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "plt.scatter(train.GrLivArea, train.SalePrice, c = \"blue\", marker = \"s\")\n",
    "plt.title(\"Looking for outliers\")\n",
    "plt.xlabel(\"GrLivArea\")\n",
    "plt.ylabel(\"SalePrice\")\n",
    "plt.show()\n",
    "\n",
    "train = train[train.GrLivArea < 4500]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'SalePrice distribution')"
      ]
     },
     "execution_count": 8,
     "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.distplot(train['SalePrice'] , fit=norm);\n",
    "\n",
    "#Now plot the distribution\n",
    "plt.ylabel('Frequency')\n",
    "plt.title('SalePrice distribution')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To make the SalePrice have normal distribution. We use the numpy fuction log1p which  applies log(1+x) to all elements of the column. Don't forget to transform back after getting the prediction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "train[\"SalePrice\"] = np.log1p(train[\"SalePrice\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'SalePrice distribution')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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hOpwzhWUAdGnmSiPr2EEObd/A2Kn3EhzaclOnAwzoHE6N07Di4FmmT59Onz59ePnll6+Y8FApX6NFQ3U4ZwrKESC+mU7wNR+/TXBYBGNuu7vFM3SNCiI+3NVEZbPZePLJJzl9+jTz5s1r8XMp1ZK0aKgO50xBGbFhAfg7Gv/vn3P6GMf2bGXMbXcTEHR104x4wibCbQMSWHM4j7LKGm655RYGDhzIrFmzqKmpafHzKdVStGioDie7sIwuzXw2Y+OiD/EPDGLkpDu8luO2gfGUVzlZdyQPEeGxxx7j9OnTLF682GvnVOp6adFQHUpJRTVF5dV0jmi8aarg3Fn2bV7NiAnTCAoJ81qWsT06ERbgYOXBXAAmT55Mz549ef3113V6EeWztGioDuVMgbsTvIkrjc1LPkJEGDPlHq9m8bPbGNerE+uOnMMYg81m48tf/jKHDh1iy5YtXj23UtdKpxFRHUp2QdMjp0pLitixZhGDxk4iPDq22ePVn57kat3cJ5Yl+85yLO8iveJCmT59Or/97W95++23GTNmzHUdWylv0CsN1aGcKSwnKtiPIH97g+u3rphPVWUFN0y/t1Xy3NzbVZjWHs4DIDAwkM997nOsWrWKrCy9kaXyPVo0VIeS3cQnwZ01NWxf9Qm9howirmu3VsmTFB1Mj5gQ1h7Jq112//33IyK8++67rZJBqauhRUN1GFU1Ts6XVJLQSCf44Z2bKS44z4jrnJTwat3UO4ZNx89TXuUaatu5c2cmT57MnDlzKCsra9UsSjVHi4bqMHKLKjA0/qG+7asWEB4dQ+8ho1s11819YimvcrL1ZH7tsoceeojCwkLmz5/fqlmUao4WDdVh5BSVAzQ4HXp+Xg7H9m1n2M3TsNkb7u/wlrE9OuFnl8uaqFJTU+nbty/vvPOODr9VPkWLhuowzhaV47AJnUL9r1i3Y81CBGH4zVNaPVdIgIPUlOjaznAAEeHBBx/k8OHD7N69u9UzKdUYLRqqw8gpKicuPABbvXt711RXsXPtEnoPG+3RMNuW8u7m07WP8CA/DuYU85fVx2qH8U6fPp3AwEC9JazyKVo0VIdxtrC8waapQ9s3crGogJG3eG/KkOb0jgsF4EhuSe2y0NBQbrvtNhYuXKgd4spnaNFQHcLFimqKK6ob7ATfsWYREZ3i6TFohAXJXBIiAgkNcHAkt/iy5ffccw8lJSUsW7bMomRKXU6LhuoQGusEL8o/x/H9OxgyfjI2W+t2gNdlE6F3XChHc0tw1un4HjVqFImJicydO9eybErVpUVDdQhn3UUjvt5nNPZuXAnGMGTcrVbEukzv+FBKK2tq58cCsNlszJw5k02bNuknxJVP0KKhOoScwnKC/e2EBfx3ujVjDLs3rCCxV3+i47tamM6lV5xrRt26/RoAM2fORET0akP5BK8WDRGZKiKHROSoiDzbwPpkEVklIjtEZLeITPdmHtVxnS0qJz48EKkzcurs6ePkZZ5ksA9cZQCEBjjoEhnIkbOX92t07dqVsWPHMnfuXJxOp0XplHLxWtEQETvwCjANGAA8ICID6m32Y2C2MWY4cD/wqrfyqI7L6TScLa64oj9j94bl2OwOBo6eYFGyK/WOC+P0hVKKyy+/V/jdd9/NmTNn2L59u0XJlHLx5pXGaOCoMea4MaYS+Dcwo942Bgh3P48Azngxj+qgsgrKqKx2XjZyyllTw96Nq+g9bAxBoeFN7N26eseH4jSw4dj5y5ZPmjSJwMBAFixYYFEypVy8WTS6Ahl1Xme6l9X1U+DzIpIJLAS+2dCBROQxEdkqIlvz8vIa2kSpRh3McTX3JIQH1C47vm87F4vyfaIDvK7k6GD8HbbLPh0OEBISwqRJk1iyZAlVVVWN7K2U91ndEf4A8E9jTCIwHXhbRK7IZIyZZYxJNcakxsa23id2VftwKKcIuHyiwt0blhMUEkavIaOsitUgh81GT/dU6fXnnLr99tspKChgw4YNFqVTyrtFIwtIqvM60b2srq8AswGMMRuBQCDGi5lUB3Qwp5ioYD8C/Fyfw6iqKOfw9o30H3UTDr8r56GyWu/4MDIulHHyfOlly8ePH09ERASffPKJRcmU8m7RSAd6i0h3EfHH1dE9r942p4FbAUSkP66ioe1PqkUdyim+7Crj6O50qiorGDjGdzrA67o0pUj9Jip/f3/S0tJYsWKFTiuiLOO1omGMqQaeAJYAB3CNktonIj8Xkbvcmz0NfFVEdgHvAV80Og+0akEV1TUcP3fxspFT+9PXEhIeSXLfwRYma1yn0ABSOgVfUTQA7rjjDkpLS1m9enXrB1MKcDS/ybUzxizE1cFdd9lzdZ7vB270ZgbVsR3LvUiN09R+EryyopwjOzczZHyapdOGNOfm3rHM2Z5JZbUTf8d//7ZLTU0lLi6OTz75hGnTplmYUHVUVneEK+VVh866OsEvXWkc3bWFqsoKBoy62cpYzbq5TyyllTVsO5V/2XK73c60adNYu3YtRUVFFqVTHZkWDdWuHcopwc8uxIS6htvu37KWkPAokvsOsjhZ027o2QmHTVjTQBPVtGnTqKqqYtWqVRYkUx2dFg3Vrh3KKaJnbCh2m7iapnZvof+o8T7dNAWuKUVGd49m+YGzV6wbMmQInTt3ZunSpRYkUx2dR0VDRHyzx1CpZhzKKaZfgnsiwF2bqa6sYIAPTRvSlGmDEjiaW3LFXFQiQlpaGuvXr+fixYsWpVMdladXGq+KyBYR+R8RifBqIqVaSGFZFWcKy+njLhr7t6wlNCKapN71p0DzTVMGJiACi/bmXLHutttuo7KyUkdRqVbnUdEwxtwEPITrw3rbRORdEUnzajKlrtNh91/o/RLCqCwv4+iuLfRP9f2mqUviwgMZmRzVYNEYPnw4sbGx2kSlWp3HfRrGmCO4ZqV9BpgAvCwiB0XkHm+FU+p6XJpzqm9COId3bqa6qpIBo3171FR9UwclcCC7iJPnLm+GstlspKWlsXbtWkpLSxvZW6mW52mfxhAR+QOuD+lNAu40xvR3P/+DF/Mpdc0O5RQRFuCgS0Qg+9PXEhoZTVLvgVbHuirTBncGGm6imjJlCuXl5axfv761Y6kOzNMrjT8B24GhxphvGGO2AxhjzuC6+lDK5xzMLqZf5zBKS0s5tjudAaNuRmxta8Bg18gghiZGsHhv9hXrRo4cSXR0NEuWLLEgmeqoPP0Juh141xhTBiAiNhEJBjDGvO2tcEpdK2MMB3OK6d85nNWrV1NdVUn/UTdZHeuaTBvcmV2ZhZw6f3kTld1uZ/LkyaxevZqKigqL0qmOxtOisRwIqvM62L1MKZ+UmV9GSUU1/RLCWbZsmWvUVK+2MWqqvhnDuiACc7a7Jol+d/Pp2odf8jBKS0v59T8+rl2mlDd5WjQCjTG1d7t3Pw/2TiSlrt+BbNcUGz2i/Vm3bh19ho9tc01Tl3SOCGJ8rxjmbMvE6bx8Ps+UfkMJDAnlQPo6i9KpjsbTn6KLIjLi0gsRGQno3MzKZx3MKUYE8k/spbS0lH4j2/a8mPeOTCSroIxNJy6/Dazd4aDviHEc3rGJ6qpKi9KpjsTTovFt4AMRWSci64H3cU17rpRPOpBdREp0MOvXrCIsLIxu/YdaHem6TBmYQFiAgw+3ZV6xrn/qTVSUXeTE/p0WJFMdjacf7ksH+gFfBx4H+htjtnkzmFLX42BOMX3jQ1i1ahUTJkzA7vCzOtJ1CfSzc8fQLizak0NFVc1l67oPGEZAUDAHtmoTlfK+q2nkHQUMAUYAD4jIF7wTSanrU1pZzcnzF4m8mEV+fj6TJ0+2OlKLuHdkImVVNezJKrxsucPPn97DxnJ4xyacNTWN7K1Uy/DoJkwi8jbQE9gJXPpfaYC3vJRLqatSd9RQxoVSjIH9W9djd/iRHdgN37sT+NUbkRxJ3/gwNh0/z8iUKESkdl2/kTeyd+NKTh/eA+O6W5hStXee3rkvFRigt2JVbUFOYTkYQ86BdHoMGol/YFDzO7UBIsIXxqXwo7l7OX2hlJROIbXreg5OxeHnz8FtG+CLdzVxFKWuj6fNU3uBBG8GUaqlZBeVEVCSTUl+Hv1GjrM6Tou6e3hXAv1sbDh2+Sgq/4BAeg5O5dD2T9G/7ZQ3eVo0YoD9IrJEROZdengzmFLXKqewnNDzBxCx0WfYWKvjtKhgfwepKdHsO1NIYVnVZev6jhxH0YVz7N2716J0qiPwtHnqp94MoVRLMcaQU1ROYOZukvsOIjis/d3+ZWyPTnx69BxbTpwnbcB/GwD6DB2DzW5n2bJlDB6s901T3uFR0TDGrBGRFKC3MWa5e96ptnFTAtWhFJRVUZF/FjmfRb+pbbdtv6npQKJD/OmbEMaWk/nc0jcOh93VYBAUGk5KvyEsW7aM73znO5d1lCvVUjydGv2rwIfAX92LugIfeyuUUtcqp7Ace7areabviPbVn1HXDT07cbGi+orht/1G3sjJkyc5duyYRclUe+dpn8Y3gBuBIqi9IVOct0Ipda1yilxFIz6lFxGd2u9/0V6xocSGBrDx+OUd4n2HuwrlsmXLrIilOgBPi0aFMaZ2YhsRceD6nIZSPiXjTA62/FP0b+NzTTVHRBjbsxOZ+WVkXPjvnfvCojoxbNgwli/XSaiVd3haNNaIyA+BIPe9wT8A5nsvllLXJnt/OuAaSdTejUiKJMBhY8Oxc5ctT0tLY//+/WRlZVmUTLVnnhaNZ4E8YA/wNWAhesc+5WMqq52UndxJYFQ8sV1SrI7jdQF+dkakRLE3q4ji8v8Ov700bYpebShv8HTCQqcx5nVjzGeNMfe6nzfbPCUiU0XkkIgcFZFnG9nmcyKyX0T2ici7V/sNKHVJxtlz2M4dJXnwmA4zcuiG7p2oMYb0kxdqlyUnJ9O3b1/t11Be4enoqRMicrz+o5l97MArwDRgAK5JDgfU26Y38APgRmPMQFxTsCt1TfZu3YgYJ4NGjbc6SquJCQugd1woW05coKbODZomT57M9u3bOXfuXBN7K3X1PG2eSsU1y+0o4CbgZeBfzewzGjhqjDnu7kT/NzCj3jZfBV4xxuQDGGNyPQ2uVH2n9mzGBIbTb8Agq6O0qrE9OlFUXs1+990KwdWvYYxh5cqVFiZT7ZGnzVPn6zyyjDH/B9zezG5dgYw6rzPdy+rqA/QRkU9FZJOITG3oQCLymIhsFZGteXl5nkRWHUxVZQVFJ/cQ1G0odnvH+txp34QwIoP92FRn+G2fPn1ISkrSfg3V4jxtnhpR55EqIo/j+RQkTXEAvYGJwAPA6yISWX8jY8wsY0yqMSY1Nja2BU6r2ptje7ZhqitJ6Dfa6iitzibCmO6dOHHuImeLygHXkNy0tDQ2bdpEcXGxxQlVe+Jp89T/1nm8AIwEPtfMPllAUp3Xie5ldWUC84wxVcaYE8BhXEVEqauyJ30dxi+IngPb9m1dr1VqShQOm1x2tTF58mSqqqpYu3athclUe+Np89QtdR5pxpivGmMONbNbOtBbRLqLiD9wP1B/ZtyPcV1lICIxuJqrmuxgV6q+6upqju/eQk18f7pGh1odxxIhAQ6GJEawI6Ogdvjt0KFDiYmJ0VFUqkV5eue+p5pab4z5fQPLqkXkCWAJrskN3zDG7BORnwNbjTHz3OtuE5H9uO4I+D1jzPn6x1KqKVu3bqWytISagYOJDw+0Oo5lxvboxPbTBXy0PYtHxnXDZrNx6623Mn/+fMrLywkM7LjvjWo5VzN66uu4OrK7Ao/juld4mPvRIGPMQmNMH2NMT2PMr9zLnnMXDIzLU8aYAcaYwcaYf1/PN6M6puXLlyN2PyK7DyLQr2N1gteVGBVMYlQQb208WXsjprS0NEpLS9mwYYO14VS74WnRSARGGGOeNsY8jatPI9kY8zNjzM+8F0+pphljWLFiBZLQj8TYK8ZQdDhje3TiWN7F2jv7jR49mvDwcG2iUi3G06IRD1TWeV3pXqaUpfbt20dOTg7lcQPoEtE+7gV+PQZ3jSA6xJ+3Np4EwM/Pj4kTJ7Jq1Sqqqqqa3FcpT3haNN4CtojIT0Xkp8Bm4E2vpVLKQ8uXL8dms1OTMJCuUVo0/Ow2PpeaxLL9Z8kpdA2/TUtLo7CwkK1VidtRAAAgAElEQVRbt1qcTrUHno6e+hXwJSDf/fiSMebX3gymlCeWL19Ol94DwT9YrzTc7h+VhNPAnO2ZANx4440EBgbqB/1Ui/D0SgMgGCgyxvwRyBSR7l7KpJRHTpw4wbFjxwjuNpyoYD+C/DtuJ3hd3WJCGNM9mtlbM3A6DUFBQdx0000sX74cp9NpdTzVxnn6ifDngWdwTS4I4Efzc08p5VWX/nI+F9GHrpF6lVHXfaOSOHW+lM0nXLPfTp48mdzcXPbs2WNxMtXWeXqlcTdwF3ARwBhzhiaG2irVGpYvX86AgYPIqgigixaNy0wb1JmwQAezt7qmf5s4cSIOh0NHUanr5mnRqHTfP8MAiEiI9yIp1byzZ8+ye/du+rnv0KdXGpcL8rczY1gXFu7JprCsivDwcMaMGcOyZctqP8Oh1LXwtGjMFpG/ApEi8lVgOfC692Ip1bRLTVNhPYcD0FmLxhXuS02motrJvJ2uKd/S0tI4ffo0R44csTiZass8HT31O+BDYA7QF3jOGPMnbwZTqinLly+nR48enKmJoEtEIKEBLTHpcvsyqGs4/TuH8767iWrSpEmIiI6iUtel2aIhInYRWWWMWWaM+Z4x5rvGGG0YVZYpKCggPT2dyZMnsyerkEFdI6yO5JNEhPtHJbE3q4i9WYXExsYyfPhwLRrqujRbNIwxNYBTRPQnU/mE1atXU1NTw+gbJ3Di3EWGJev0IY2ZOawr/g5bbYf45MmTOXDgAJmZmRYnU22Vp30aJcAeEfm7iLx86eHNYEo1Zvny5SQkJFAR7roR5LAkLRqNiQj2Y+rABD7ekUV5VQ2TJ08G0KsNdc08LRofAT8B1gLb6jyUalUlJSWsW7eOtLQ0dmUUIgJDErVoNOW+UUkUlVezeG8OSUlJ9OvXT4uGumZNFg0RSQYwxrzZ0KN1Iir1X6tXr6ayspKpU6eyM6OAPnFh2gnejBt6dCIpOoj30//bRLV9+3by8vIsTqbaouauND6+9ERE5ng5i1LNWrx4MfHx8QwdOpRdmQUM1/6MZtlswudGJrHx+HlOny8lLS0NYwwrV660Oppqg5orGlLneQ9vBlGqORcvXmTdunXcdtttnM4vp6C0SvszPPSZkYmIwIfbMujduzfJycnaRKWuSXPX9aaR50q1ulWrVlFZWcmUKVPYmZEPoCOnGvDu5tMNLu8VG8qH2zJ5cnIf0tLSePPNNykqKiI8PLyVE6q2rLkrjaEiUiQixcAQ9/MiESkWkaLWCKjUJYsXLyYuLo7hw4ez43QBIf52esfpFGieGpkSxZnCcj49eo7JkydTXV3NmjVrrI6l2pgmi4Yxxm6MCTfGhBljHO7nl17rnyeq1dRtmrLZbOzMKGBwYgR2mzS/swJgQOdwIoP9mL01gyFDhhAXF6cTGKqrdjX301DKMpdGTU2ZMoXyqhoOZBcxLCnK6lhtisNuY+awrizdd5ai8mpuvfVW1q9fT1lZmdXRVBuiRUO1CYsXLyY2NpYRI0awN6uQqhqjI6euQWiAg8oaJz/+eC/2pKGUlZXxwj/+02g/iFL1adFQPu9S09SUKVOw2Wy1NxYa1S3a4mRtT5fIILpEBrLtVD7JfQYTFBrO/nTt11Ce06KhfN7q1aupqKhgypQpAGw+cYE+8aFEh/hbnKxtGpkSTXZhOWdLquifOp7D2zdSWVFudSzVRmjRUD5vyZIltU1T1TVOtp28wJjunayO1WYNTYzAYRO2nspn4JiJVFVWcGTXZqtjqTZCi4byaRcvXmTt2rW1o6b2niniYmUNY3po09S1CvZ3MKBLOLsyCujcawChkdHs26xNVMozXi0aIjJVRA6JyFERebaJ7T4jIkZEUr2ZR7U9q1aturxp6vh5AEZ316JxPUamRFFWVcPBsxcZMOpmju7aQnFxsdWxVBvgtaIhInbgFWAaMAB4QEQGNLBdGPAkoNfH6goLFiygc+fOjBw5EoAtJy7QIyaEuLBAi5O1bT1jQ4kM9iP95AUGjb2FmuoqVqxYYXUs1QZ480pjNHDUGHPcGFMJ/BuY0cB2vwB+A2hPnLpMfn4+n376KdOnT8dms1HjNGw5eUGbplqATYRR3aI5nncR/7huRMbEs3DhQqtjqTbAm0WjK5BR53Wme1ktERkBJBljPmnqQCLymIhsFZGtOp1zx7F48WKqq6u58847ATiQXURxebV2greQkSlR2AS2nsxnwJiJbNiwgQsXLlgdS/k4yzrCRcQG/B54urltjTGzjDGpxpjU2NhY74dTPmHBggX07t2bvn37Aq6mKdD+jJYSHuhH/87hbDudT99RN1NTU8OSJUusjqV8nDeLRhaQVOd1onvZJWHAIGC1iJwExgLztDNcAWRlZbF9+3buuOOO2mXrjuSR0imYLpFBFiZrX0Z3i6a0soY8Wyd69uzJggULrI6kfJw3i0Y60FtEuouIP3A/MO/SSmNMoTEmxhjTzRjTDdgE3GWM2erFTKqN+OQTV4vl7bffDkBZZQ0bjp3nlr5xVsZqd3rGuT4kmX7yAjNmzGD79u2cPq1TiqjGea1oGGOqgSeAJcABYLYxZp+I/FxE7vLWeVXbZ4xh/vz5jBgxgq5dXd1gG4+fo6LayaR+WjRakk2E0d2iOXm+lH5jJiIizJs3r/kdVYfl1T4NY8xCY0wfY0xPY8yv3MueM8Zc8b/SGDNRrzIUwKFDhzh69OhlTVMrD+YS7G/XkVNekNotCj+7MP9wKWPGjGHevHkYo/dcUw3TT4Qrn/Pxxx/j5+fH1KlTAdeVx8oDuYzvFUOAw25xuvYn2N/B8KQoPt55hlun3k5GRgY7duywOpbyUVo0lE+pqqpi/vz53HLLLURFue6XcehsMWcKy7Vpyotu6NmJymoneeF9CQoK4j//+Y/VkZSP0qKhfMratWu5cOECd999d+2ylQdzAbhFi4bXxIcHMr5XDO/vyOXWWyezePFiKioqrI6lfJDD6gBK1TV37lxiYmIYP3587bJVB3MZ1DWcFQdyLUzW/n3pxm585c2txA0eT9GC+axevbp2zi+lLtErDeUzzp8/z5o1a7jrrrtwOFx/z+QUlrPtVD639ou3OF37d0vfOHrHhbIsL5z4+Hg++ugjqyMpH6RFQ/mM+fPnU11dfVnT1NwdWTgN3D28axN7qpZgswlfn9iTw3kXGTY+jfXr15OdnW11LOVjtGgon2CMYe7cuQwZMoRevXrVLpuzPZNR3aLoFhNiccKO4c6hXegaGcTRkIE4nU692lBX0KKhfML+/fs5fPgwM2fOrF22K7OQo7klfGZEooXJOhY/u43HJ/Rgb6EfA4alMmfOHGpqaqyOpXyIFg3lE2bPnk1gYCDTp0+vXfbhtgwC/WxMH9LZwmQdz2dTk4gJDaAscTTZ2dls3LjR6kjKh2jRUJYrKSlhwYIFTJ8+nYiICADKq2qYvyubKQMTCA/0szhhxxLoZ+fxCT3YTzKh4RF8+OGHVkdSPkSLhrLcvHnzKC0t5b777qtdtnhvDoVlVdo0ZZHPj00hLjKEgJ5jWLFiBefPn7c6kvIR+jkNZSljDO+//z4DBgxg8ODBADidhldWHaVPfCjje8VYnLBjCvSz881JvXjuzFACq5fy8ccfEzQordHtHxyT3IrplJX0SkNZaufOnRw+fJj77rsPEQFg0d4cjuSW8M1JvbHZxOKEHdd9o5LpktSNwM69eP/993E6tUNcadFQFnvvvfcICQmpvW+G02l4ecUResaGMH2wdoBbyd9h48nJvSnqOpaMjAyO7k63OpLyAVo0lGXy8/NZsmQJd911FyEhrs9hLN2fw6GzxXxzUm/sepVhuc+MSKTXsHHYgiPZskwnMVTap6Fa2bub/3tXuA0LZ1NZWUnYgJt5d/NpqmqcvLXxJN1jQrhzaBfrQqpadpvw3IzBPLJ+LCf2LebcmdPEdNH+i45MrzSUJWqqq9my7D906z+M+KQeAKw+lMuxvIv89K6BepXhQ27sFcO4tDswNjsblurVRkenRUNZYn/6WorzzzF2yj0AZBeWseZwHvcM78qEPrEWp1P1Pf/ZMTi7DmPPp8uoKLtodRxlIW2eUq3OGMOmxXPolJBIryGjqHEa5u7IIsjPzoDO4Zc1YSnf0DM2lP7jb+fwe9tYv3wht975WasjKYvolYZqdacP7yXn1FHGTLkHsdlYefAsmfll3DG0C8EB+neMr7pz4hhMdDc2L/0Yp85H1WFp0VCtbvOSjwgKDWfIuFs5mlvC6kN5jEyOYmhipNXRVBOCAxwMnjSTmuJzrFi+1Oo4yiJaNFSrunA2i0M7NjLyljsoM3be35pBbFiAjpZqI+6YkoaEx7Nl0Wyqa5xWx1EW0KKhWtXGRR9itzsYMel2ZqdnUFldwwOjk/F36H/FtsDPz8HI2z6Ds+AMC5autDqOsoD+pKpWc+bMGXauW8qwm6ewNaeG4+cuctfQLsSHB1odTV2F26ZOxx4axe4Vcygsq7I6jmplWjRUq/nb3/4GQOLYO1h5MJfhSZGMSI6yOJW6WnaHHzdMvRc5d5w5S9dZHUe1Mi0aqlWcPXuWDz/8kEHjJvPJsXJiQgO4a1iX2kkKVdtyY9odOAJDOb1hHofPFlsdR7Uir45vFJGpwB8BO/A3Y8yL9dY/BTwKVAN5wJeNMae8mUlZ4+9//ztOp5OyHhO5WFjNF27oRoDDbnUsVcfVfD7GPyCQcdPuYe3ct/h4xac8O60fgX7679kReO1KQ0TswCvANGAA8ICIDKi32Q4g1RgzBPgQeMlbeZR18vLymD17NmNvmcLuAgc39Y6la2SQ1bHUdbphyj0EhIRTun0+f11z3Oo4qpV4s3lqNHDUGHPcGFMJ/BuYUXcDY8wqY0yp++UmQG/T1g69/vrrVFVVsT9iFDGh/kzqF2d1JNUC/AODmDDjQeznjvLK7IWcOq/Ti3QE3iwaXYGMOq8z3csa8xVgUUMrROQxEdkqIlvz8vJaMKLytlOnTvHee+/RZ+xkzlSHcffwRPzs2pXWXoyceDuhUTHY9y3ihx/twRhjdSTlZT7x0ysinwdSgd82tN4YM8sYk2qMSY2N1cnsfN27m0/XPr7zk18hdgd7I25gSGIE3WNCrI6nWpDD35+JMz8PF06xcf1a/rVJuyTbO28WjSwgqc7rRPeyy4jIZOBHwF3GmAov5lGtLPPoAQ6kryN8SBomMJwpAxKsjqS8YMiNaaSkpBB5fCm/XrCPk+e0mao982bRSAd6i0h3EfEH7gfm1d1ARIYDf8VVMHK9mEW1MmMMy2e/TlBYJJlxY7mxVwxRIf5Wx1JeYHc4ePrppyk7l4Xt5Eae/mCXTjHSjnmtaBhjqoEngCXAAWC2MWafiPxcRO5yb/ZbIBT4QER2isi8Rg6n2phD2zeScXgffkOmExIcrPfIaOcmT57MDTfcgP+hJWw7nMHvlh62OpLyEq9+TsMYsxBYWG/Zc3WeT/bm+ZU1KivKWfruX4iITyQneii3943TMfztnIjwwx/+kJkzZ9L//Hr+siaUkSlRpA2ItzqaamE+0RGu2pe1//kXhefPIiM/R3hwAKO7R1sdSbWCXr168dBDD3Fq6wp6+xfw1OydOgy3HdKioVrU4cOH2bzkI7qnTiLbrwsT+sbpENsO5Bvf+AZRUVGEH5iHDcOX/plOQWml1bFUC9LbpKkW43Q6ef755wkMCqWw1xQi8GNUik5I2JGEh4fzve99jx/84Ac8OO4Eb5/rxmNvb+OOwZ1xNPLHw4Njkls5pboe+iegajEffPABO3fuZOC0z5NVZmdS37hGf1Go9mvGjBlMmDCBj96axTPjo9ly4gIfbs/EqR/8axf0J1q1iJMnT/LSSy8xduxYjgT1IyrYjxF6ldEhiQg///nP8ff3Z9U7f+KZKX3YnVnIxzuytHC0A1o01HWrqqrimWeewc/Pj6lfeorswgom9YvHbtNpzzuquLg4fvCDH7Bt2zaCT29gUr84tp7KZ/6uMzrVSBunRUNdt1dffZXdu3fz/PPP84/t+XQK8WdYUqTVsZTFZsyYwcSJE/nDH/7AoOASbu4dw+YTF1i4J1sLRxumRUNdl23btjFr1izuuecearoO5WBOMbf2j9OrDIWI8Mtf/pKIiAjmvPpLJnQP44aenfj02HmW7j+rhaON0qKhrllubi5PPfUUiYmJfPf7z/LbJYfoEx/KkES9ylAunTp14g9/+AP5eTkseOP33D4ogdHdollzOI8VB3XmoLZIh9yqa1JRUcE3v/lNSkpKmDVrFnP3nOPU+VL++aVRnCkotzqeamVN3/Uvhsmfe5Rl/57FlmUfc9dtd1PjNKx0F40HRifpbX/bEL3SUFfNGMNzzz3H7t27efHFF0lI7sHLK48wvleMzjGlGjRmyj30G3kjy99/nWO707l7RFdSU6JYeTCX3y87rE1VbYgWDXXV3njjDebNm8cTTzxBWloar646SmFZFT+Y3k//YlQNEhHuevS7xCf1YM4rvyTn5BFmDncVjj+tPMrvlh7SwtFGaNFQV+WDDz7gd7/7HVOnTuXrX/86B7KL+Pv6E3xmRCIDu0RYHU/5sICgYB74zi8ICY/k33/4CYV5Ocwc3pUHRifzyqpjvLREC0dboEVDeeyTTz7h+eef56abbuI3v/kNNQa+9+EuIoP9+dH0/lbHU21AaGQ0Dzz9K5w1Nbz7vz+kpOA8v5o5iAfHJPPa6mO8uPigFg4fp0VDeWT58uU888wzjBo1ipdffhl/f3/+uuYYe7OK+OXMgXqDJeWxmM5J3P+dn1NSWMBbv/4u2dln+OWMQXx+bDJ/XXOcFxZp4fBlWjRUs+bMmcO3v/1tBg4cyKuvvkpgYCC7Mwt4ecVRbh/SmamDOlsdUbUxib0G8Pnvv0DZxWI+//nPc/r0KX4xYxBfuCGFWWuP84sFB3A6tXD4Ii0aqlHGGF555RV+/OMfM3bsWN544w1CQkLIzC/ly//cSmxYAD+/a6DVMVUb1bVHPx5+9iWKLpZx730P8rv3ltE3PoxxPTvxxqcnuPcvG6jS28b6HC0aqkEVFRX85Cc/4c9//jMzZszgtddeIyQkhMKyKr70j3Qqqmv455dG0Sk0wOqoqg1LSO7JIz/4HX4BAbz5wnfZvX4Ztw/uzOT+cWw/XcDjb2+jtLLa6piqDi0a6gonTpzg/vvvZ86cOTz++OO88MIL+Pn5kXGhlAdf38TJ8xf568Mj6R0fZnVU1Q7EdEnmK8//ieQ+A5n39/9l6bt/YUKvaGYM68KqQ7l85rWNZBWUWR1TuWnRULWMMcyfP597772X7OxsXnvtNZ588klEhHVH8rjrz+s5faGUWQ+nMq5njNVxVTsSHBrOg0//mtFpM9my7GP+/rNv0c1RyBtfHEXmhVJm/Hk9m4+ftzqmQouGcsvMzORrX/sa3//+9+nbty9z585l4sSJ7M0q5NE303n471uIDQtg3hPjuaVfnNVxVTtks9uZ8tDX+dyTP6WkMJ+//fSbHFo9lw++NpqwQD8eeH0T/7v0kPZzWEza2tC21NRUs3XrVqtjtBtlZWW8/fbbvPbaa9hsNh7/nycYPukONh4vYNmBs+zOLCQ80MFXb+rBl8d3JySg+enKmp6HSKnmlRYXsvCtP3EgfR3dunXjiSe/w8qiOOZsz2JIYgS/mDGIoTr9/lURkW3GmNTrPo4WjY6prLyCb/3qVdIXz6aipIDgbsOoGXo3BYTUbjM8OZIpAxN4cEwy4YF+l+2vhUG1hiM7N7Ps/dc5n51BSr8hJI2/hw2FEZRW1jAyJYo/PjCcrpFBVsdsE7RoqKuSf7GStUfyWL3rOOmrFnJu9yqkrJCaTj2o7j+VTin9iY8IJCE8gITwQJKigwmrVyiUskJNdTXbVy9k7X/+RWlxIZ279yFoUBoHJBmb3cGdQ7vwyLhuDE2M0LnPmqBFQzXJGMO+M0X8ccURDmblc+bQTmxZO3Cc2Q3OGsKSB9Bv4kwGDR9FfHggfnbt3lK+raqygl3rl7Jp0Rzy87IJDo8iefjNHAzoS1lQHIlRQUwdmMDYHp0YmRKlsxTUo0VDXaG4vIpPj55j1cE8Vu4+wYUTe7HlHsIvZx+mshT/oBCG3HgroybdSUyXZKvjKnVNnM4aDu/YzK71Szm+J53q6mpiuyTjlzSY04HdqQpPApuduLAAUjoFkxwdQkqnYFI6BZMYFUTXyGDiwgKwdbC7S7ZU0dCbMLWgS+381U4n5VVOqmqcVNcYbAL3jEwkLNBBWICjxS6hjTEczS1hxYFsFm/Yw759eyE/A0fBacjPxB+Df1AIfVNvYODoCfQYNAK7Q5ucVNtms9npN3Ic/UaOY0qvEBYuXMjKlSvZunUJjupqQoOCiO3Wl/KIbmTmJnIwMJZigqHOz53dJkQE+REZ7EdUkL/ra7A/USH+RAX78bUJPfWWxY3w6pWGiEwF/gjYgb8ZY16stz4AeAsYCZwH7jPGnGzqmL5wpVFeVUNmfimnzrsepy+4HnuyCikur6K8qvEhgQ6bEOouHqEBDiKC/YgM8mf6kM50jQyiS2QgUcH+BPrZa/cxxpBfUsax09nsPnqaPYeOcejoCTIyTlNVmIsU5SA1la7jBwTSOaU33QcMo+egEXTp3heb3d5YHKXatAfH/PeKuaioiE8//ZT09HS2bdvG4cOHa9cFhYYT1TmF4NhEbKExOIMiqQiIpNQRQUG1nZKKmsuO62cXukQGkRQVTFJ0EJ1CAggLdBAa6GB3RiEBfjb87K6Hwyaur3bhvlFJBDhshPg7fO5Kxuebp0TEDhwG0oBMIB14wBizv842/wMMMcY8LiL3A3cbY+5r6rgtVTScTkO101DjNFQ7nTidUFZVQ3F5FUXl1RSVVVJUVkVucTnZ+WVkF7ofBWXkFpdjDGBcxSHYz0ZSdDBiDGGBfgT72wiwg4MaxNRQU11NdVUVZeUVXCyvoLS8gtLyStfrsjKqKsqhugKpcn+trsBWU46tohjKizHlxUhV/U/ECoERnQiOjicxpTvde/enc/c+dErois2mRUKpsovF5Gac4GzGCXIzjnM28wTnzpymsvzynyWHnz9BoeH4B4fhCApFAkKJjIqkHH9Kqu0UVcHFGjvG7o+x+4HdHxz+GJsDxOZ62Oy1X43YEJuNkAB/woMDCAsKICzIj/Agf8IDHa6vQQ4igvzdz/1cj0A/woMchAf6ERrowGGTFu3YbwvNU6OBo8aY4wAi8m9gBrC/zjYzgJ+6n38I/FlExHihki1dupRvP/09nMZA7eENGPdXAGMQmj91YL3XBrjWAagC1O2uc/gH4B8YhCMgmIDQCAITehIcHkl0dDSxsbH0Su7MqEF96N+rOwEBATr0ValGBIWEkdJvCCn9htQuM8ZQdrGYwnNnKTh3lsJzZykpzKe0pJDS4iLKSoooPZ9BduZ+iouLcTpdfxheS6NuDZDvfnjC4C4QtYVCXL8g6iz/8he/xPe/+51rSNNyvHmlcS8w1RjzqPv1w8AYY8wTdbbZ694m0/36mHubc/WO9RjwmPvlIGCvV0K3rBjgXLNbWU9ztizN2bLaQs62kBGgrzHmuieMaxMd4caYWcAsABHZ2hKXWN6mOVuW5mxZmrPltIWM4MrZEsfx5uD8LCCpzutE97IGtxERBxCBq0NcKaWUD/Jm0UgHeotIdxHxB+4H5tXbZh7wiPv5vcBKb/RnKKWUahlea54yxlSLyBPAElxDbt8wxuwTkZ8DW40x84C/A2+LyFHgAq7C0pxZ3srcwjRny9KcLUtztpy2kBFaKGeb+0S4Ukop6+iEQ0oppTymRUMppZTHfKZoiMgbIpLr/uzGpWXRIrJMRI64v0Y1su8j7m2OiMgjDW3jIzlrRGSn+1F/UEBr5PysiOwTEaeINDpEUESmisghETkqIs/6cM6TIrLH/X56dW6ZRnL+VkQOishuEZkrIg3eFcgH3k9Pc1r9fv7CnXGniCwVkS6N7NsqP+/XmdHSn/U6654WESMiDd6f+ZreS2OMTzyAm4ERwN46y14CnnU/fxb4TQP7RQPH3V+j3M+jfC2ne12Jxe9nf6AvsBpIbWQ/O3AM6IHrw+q7gAG+ltO93UkgxsL38zbA4X7+m0b+f/rC+9lsTh95P8PrPP8W8JcG9mu1n/drzeheZ+nPunt5Eq6BSKca+ne91vfSZ640jDFrcY2gqmsG8Kb7+ZvAzAZ2nQIsM8ZcMMbkA8uAqT6Ys1U1lNMYc8AYc6iZXWunfzHGVAKXpn/xiuvI2aoaybnUGFPtfrkJ12eR6vOF99OTnK2qkZxFdV6GQINz+rTaz/t1ZGxVjfxOAvgD8H0az3hN76XPFI1GxBtjst3Pc4D4BrbpCmTUeZ3pXtaaPMkJECgiW0Vkk4hYXlga4Qvvp6cMsFREtrmnmrHSl4FFDSz3tfezsZzgA++niPxKRDKAh4DnGtjE8vfTg4xg8c+6iMwAsowxu5rY7JreS18vGrWM63rK8qrenGZyphjXdAMPAv8nIj1bL1m7NN4YMwKYBnxDRG62IoSI/AioBt6x4vye8iCn5e+nMeZHxpgkXBmfaG57K3iY0bKfdREJBn5I4wXtuvh60TgrIp0B3F9zG9jGk+lKvM2TnBhjstxfj+Nqrx/eWgGvgi+8nx6p837mAnNxNQW1KhH5InAH8JD7D4b6fOL99CCnT7yfdbwDfKaB5T7xfro1ltHqn/WeQHdgl4icxPUebReRhHrbXdN76etFo+40I48A/2lgmyXAbSIS5R61dJt7WWtqNqc7X4D7eQxwI5dPE+8rPJn+xXIiEiIiYZee4/p3b9XZj8V1k7HvA3cZY0ob2ez/27ufF6vKOI7j7w+kVgwUhUINgQtFIilpJqIooo2LUCLQVhWlkP0DtlEqgmjRDyIrZjbhJkQoXASBViAuatevYaAfIwUFGs0icIKmkE+L5xySaoIAAAM4SURBVDk0Xa55vF7nHrifFxyYe+9zzv3eA2e+nOc8z/cZ+flsE2dHzufmFS8fBr7t02yk13ubGEd9rdues73B9kbbGyndTnfaPtvTdLBzuVpP+FuMADgCnAH+rj9yL3Aj8CnwA/AJcENtO01ZCbDZdw+wULenuhgncC8wRxk9MwfsHUGcj9S/l4FfgeO17c3ARyv2fYiygNZp4EAX46SMRvq6bvMjinOB0if8Vd1mOno+LxpnR87nB5RE9Q3wITDZex3V16tyvQ8aYxeu9Z7Pf6KOnhrGuUwZkYiIaK3r3VMREdEhSRoREdFakkZERLSWpBEREa0laURERGtJGjGWJB2olXSbiqV3/0/bw5J2XeR4hyX9WI/1haR7LtDuGUlPXG78EaNyxZZ7jeiq+g99B2XC03KdgLV2CIfeb/t9SduBWeD2nu+9yvbMEL4nYmSSNGIc3QQs2l4GsL0IIOk5YCdwDfAZsM89E5kkTQGvAxPAIvCk/y1W2TgFbKrtT1Im1N0HHKmzrpdsvyppEzADrAfOA7ttn5a0H3gUWAccs/38kH9/xMDSPRXj6ARwi6TvJb0j6YH6/lu277K9lZI4dqzcSdIa4BCwy/YU8C7wUp/j76TMBG6stT1t+7Wedu8Bb9u+gzKL+Ey9S9lMqfu0DZgaVSHGiH5ypxFjx/ZSvWO4H3gQOKqyot45Sc8C11IWppmnlIpobAG2Ah9LgrLA0sq7jFckHQR+o5ScaBztjaHecUzaPlZj+rO+v51SA+jL2nSCkkROXc5vjhiWJI0YS7bPU6qPnpQ0B+yjPIOYtv2zpBeAq3t2EzBvu+9DbuozjT7v/3EJoQl42fbsJewTsWrSPRVjR9KWnmql24BmpcBFSRNAv9FS3wHrm5FRktZIum2QGGyfA35pFuiRtK6ug3Ac2FNjQNKkpA2DfEfElZA7jRhHE8AhSddTFiVaAJ4GfqdUMD1LKWn+H7b/qkNv35R0HeX6eYPSjTWIx4FZSS9SKpTutn1C0q3A57ULbAl4jAus0RKx2lLlNiIiWkv3VEREtJakERERrSVpREREa0kaERHRWpJGRES0lqQRERGtJWlERERr/wAdDayfJ+HloQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Check the new distribution \n",
    "sns.distplot(train['SalePrice'] , fit=norm);\n",
    "\n",
    "#Now plot the distribution\n",
    "plt.ylabel('Frequency')\n",
    "plt.title('SalePrice distribution')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Combine train and test for data processing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "ntrain = train.shape[0]\n",
    "ntest = test.shape[0]\n",
    "y_train = train.SalePrice.values\n",
    "all_data = pd.concat((train, test)).reset_index(drop=True)\n",
    "#all_data.drop(['SalePrice'], axis=1, inplace=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Feature Engineering"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Imputing missing values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Handle missing values for features where median/mean or most common value doesn't make sense\n",
    "\n",
    "# Alley : data description says NA means \"no alley access\"\n",
    "all_data.loc[:, \"Alley\"] = all_data.loc[:, \"Alley\"].fillna(\"None\")\n",
    "# BedroomAbvGr : NA most likely means 0\n",
    "all_data.loc[:, \"BedroomAbvGr\"] = all_data.loc[:, \"BedroomAbvGr\"].fillna(0)\n",
    "# BsmtQual etc : data description says NA for basement features is \"no basement\"\n",
    "all_data.loc[:, \"BsmtQual\"] = all_data.loc[:, \"BsmtQual\"].fillna(\"No\")\n",
    "all_data.loc[:, \"BsmtCond\"] = all_data.loc[:, \"BsmtCond\"].fillna(\"No\")\n",
    "all_data.loc[:, \"BsmtExposure\"] = all_data.loc[:, \"BsmtExposure\"].fillna(\"No\")\n",
    "all_data.loc[:, \"BsmtFinType1\"] = all_data.loc[:, \"BsmtFinType1\"].fillna(\"No\")\n",
    "all_data.loc[:, \"BsmtFinType2\"] = all_data.loc[:, \"BsmtFinType2\"].fillna(\"No\")\n",
    "all_data.loc[:, \"BsmtFullBath\"] = all_data.loc[:, \"BsmtFullBath\"].fillna(0)\n",
    "all_data.loc[:, \"BsmtHalfBath\"] = all_data.loc[:, \"BsmtHalfBath\"].fillna(0)\n",
    "all_data.loc[:, \"BsmtUnfSF\"] = all_data.loc[:, \"BsmtUnfSF\"].fillna(0)\n",
    "all_data.loc[:, \"BsmtFinSF1\"] = all_data.loc[:, \"BsmtFinSF1\"].fillna(0)\n",
    "all_data.loc[:, \"BsmtFinSF2\"] = all_data.loc[:, \"BsmtFinSF2\"].fillna(0)\n",
    "# CentralAir : NA most likely means No\n",
    "all_data.loc[:, \"CentralAir\"] = all_data.loc[:, \"CentralAir\"].fillna(\"N\")\n",
    "# Condition : NA most likely means Normal\n",
    "all_data.loc[:, \"Condition1\"] = all_data.loc[:, \"Condition1\"].fillna(\"Norm\")\n",
    "all_data.loc[:, \"Condition2\"] = all_data.loc[:, \"Condition2\"].fillna(\"Norm\")\n",
    "# EnclosedPorch : NA most likely means no enclosed porch\n",
    "all_data.loc[:, \"EnclosedPorch\"] = all_data.loc[:, \"EnclosedPorch\"].fillna(0)\n",
    "# External stuff : NA most likely means average\n",
    "all_data.loc[:, \"ExterCond\"] = all_data.loc[:, \"ExterCond\"].fillna(\"TA\")\n",
    "all_data.loc[:, \"ExterQual\"] = all_data.loc[:, \"ExterQual\"].fillna(\"TA\")\n",
    "# Fence : data description says NA means \"no fence\"\n",
    "all_data.loc[:, \"Fence\"] = all_data.loc[:, \"Fence\"].fillna(\"No\")\n",
    "# FireplaceQu : data description says NA means \"no fireplace\"\n",
    "all_data.loc[:, \"FireplaceQu\"] = all_data.loc[:, \"FireplaceQu\"].fillna(\"No\")\n",
    "all_data.loc[:, \"Fireplaces\"] = all_data.loc[:, \"Fireplaces\"].fillna(0)\n",
    "# Functional : data description says NA means typical\n",
    "all_data.loc[:, \"Functional\"] = all_data.loc[:, \"Functional\"].fillna(\"Typ\")\n",
    "# GarageType etc : data description says NA for garage features is \"no garage\"\n",
    "all_data.loc[:, \"GarageType\"] = all_data.loc[:, \"GarageType\"].fillna(\"No\")\n",
    "all_data.loc[:, \"GarageFinish\"] = all_data.loc[:, \"GarageFinish\"].fillna(\"No\")\n",
    "all_data.loc[:, \"GarageQual\"] = all_data.loc[:, \"GarageQual\"].fillna(\"No\")\n",
    "all_data.loc[:, \"GarageCond\"] = all_data.loc[:, \"GarageCond\"].fillna(\"No\")\n",
    "all_data.loc[:, \"GarageArea\"] = all_data.loc[:, \"GarageArea\"].fillna(0)\n",
    "all_data.loc[:, \"GarageCars\"] = all_data.loc[:, \"GarageCars\"].fillna(0)\n",
    "all_data.loc[:, \"GarageYrBlt\"] = all_data.loc[:, \"GarageYrBlt\"].fillna(0)\n",
    "# HalfBath : NA most likely means no half baths above grade\n",
    "all_data.loc[:, \"HalfBath\"] = all_data.loc[:, \"HalfBath\"].fillna(0)\n",
    "# HeatingQC : NA most likely means typical\n",
    "all_data.loc[:, \"HeatingQC\"] = all_data.loc[:, \"HeatingQC\"].fillna(\"TA\")\n",
    "# KitchenAbvGr : NA most likely means 0\n",
    "all_data.loc[:, \"KitchenAbvGr\"] = all_data.loc[:, \"KitchenAbvGr\"].fillna(0)\n",
    "# KitchenQual : NA most likely means typical\n",
    "all_data.loc[:, \"KitchenQual\"] = all_data.loc[:, \"KitchenQual\"].fillna(\"TA\")\n",
    "# LotFrontage : NA most likely means no lot frontage\n",
    "all_data.loc[:, \"LotFrontage\"] = all_data.loc[:, \"LotFrontage\"].fillna(0)\n",
    "# LotShape : NA most likely means regular\n",
    "all_data.loc[:, \"LotShape\"] = all_data.loc[:, \"LotShape\"].fillna(\"Reg\")\n",
    "# MasVnrType : NA most likely means no veneer\n",
    "all_data.loc[:, \"MasVnrType\"] = all_data.loc[:, \"MasVnrType\"].fillna(\"None\")\n",
    "all_data.loc[:, \"MasVnrArea\"] = all_data.loc[:, \"MasVnrArea\"].fillna(0)\n",
    "# MiscFeature : data description says NA means \"no misc feature\"\n",
    "all_data.loc[:, \"MiscFeature\"] = all_data.loc[:, \"MiscFeature\"].fillna(\"No\")\n",
    "all_data.loc[:, \"MiscVal\"] = all_data.loc[:, \"MiscVal\"].fillna(0)\n",
    "# OpenPorchSF : NA most likely means no open porch\n",
    "all_data.loc[:, \"OpenPorchSF\"] = all_data.loc[:, \"OpenPorchSF\"].fillna(0)\n",
    "# PavedDrive : NA most likely means not paved\n",
    "all_data.loc[:, \"PavedDrive\"] = all_data.loc[:, \"PavedDrive\"].fillna(\"N\")\n",
    "# PoolQC : data description says NA means \"no pool\"\n",
    "all_data.loc[:, \"PoolQC\"] = all_data.loc[:, \"PoolQC\"].fillna(\"No\")\n",
    "all_data.loc[:, \"PoolArea\"] = all_data.loc[:, \"PoolArea\"].fillna(0)\n",
    "# SaleCondition : NA most likely means normal sale\n",
    "all_data.loc[:, \"SaleCondition\"] = all_data.loc[:, \"SaleCondition\"].fillna(\"Normal\")\n",
    "# ScreenPorch : NA most likely means no screen porch\n",
    "all_data.loc[:, \"ScreenPorch\"] = all_data.loc[:, \"ScreenPorch\"].fillna(0)\n",
    "# TotalBsmtSF : NA most likely means no Bsmt\n",
    "all_data.loc[:, \"TotalBsmtSF\"] = all_data.loc[:, \"TotalBsmtSF\"].fillna(0)\n",
    "# TotRmsAbvGrd : NA most likely means 0\n",
    "all_data.loc[:, \"TotRmsAbvGrd\"] = all_data.loc[:, \"TotRmsAbvGrd\"].fillna(0)\n",
    "# Utilities : NA most likely means all public utilities\n",
    "all_data.loc[:, \"Utilities\"] = all_data.loc[:, \"Utilities\"].fillna(\"AllPub\")\n",
    "# WoodDeckSF : NA most likely means no wood deck\n",
    "all_data.loc[:, \"WoodDeckSF\"] = all_data.loc[:, \"WoodDeckSF\"].fillna(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Transforming some numerical variables that are actually categorical"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "all_data.drop([\"MSSubClass\"], axis=1, inplace=True)\n",
    "all_data = all_data.replace({\"MoSold\" : {1 : \"Jan\", 2 : \"Feb\", 3 : \"Mar\", 4 : \"Apr\", 5 : \"May\", 6 : \"Jun\",\n",
    "                                   7 : \"Jul\", 8 : \"Aug\", 9 : \"Sep\", 10 : \"Oct\", 11 : \"Nov\", 12 : \"Dec\"}\n",
    "                      })"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Encode some categorical features as ordered numbers when there is information in the order"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "all_data = all_data.replace({\"Alley\" : {\"Grvl\" : 1, \"Pave\" : 2},\n",
    "                       \"BsmtCond\" : {\"No\" : 0, \"Po\" : 1, \"Fa\" : 2, \"TA\" : 3, \"Gd\" : 4, \"Ex\" : 5},\n",
    "                       \"BsmtExposure\" : {\"No\" : 0, \"Mn\" : 1, \"Av\": 2, \"Gd\" : 3},\n",
    "                       \"BsmtFinType1\" : {\"No\" : 0, \"Unf\" : 1, \"LwQ\": 2, \"Rec\" : 3, \"BLQ\" : 4, \n",
    "                                         \"ALQ\" : 5, \"GLQ\" : 6},\n",
    "                       \"BsmtFinType2\" : {\"No\" : 0, \"Unf\" : 1, \"LwQ\": 2, \"Rec\" : 3, \"BLQ\" : 4, \n",
    "                                         \"ALQ\" : 5, \"GLQ\" : 6},\n",
    "                       \"BsmtQual\" : {\"No\" : 0, \"Po\" : 1, \"Fa\" : 2, \"TA\": 3, \"Gd\" : 4, \"Ex\" : 5},\n",
    "                       \"ExterCond\" : {\"Po\" : 1, \"Fa\" : 2, \"TA\": 3, \"Gd\": 4, \"Ex\" : 5},\n",
    "                       \"ExterQual\" : {\"Po\" : 1, \"Fa\" : 2, \"TA\": 3, \"Gd\": 4, \"Ex\" : 5},\n",
    "                       \"FireplaceQu\" : {\"No\" : 0, \"Po\" : 1, \"Fa\" : 2, \"TA\" : 3, \"Gd\" : 4, \"Ex\" : 5},\n",
    "                       \"Functional\" : {\"Sal\" : 1, \"Sev\" : 2, \"Maj2\" : 3, \"Maj1\" : 4, \"Mod\": 5, \n",
    "                                       \"Min2\" : 6, \"Min1\" : 7, \"Typ\" : 8},\n",
    "                       \"GarageCond\" : {\"No\" : 0, \"Po\" : 1, \"Fa\" : 2, \"TA\" : 3, \"Gd\" : 4, \"Ex\" : 5},\n",
    "                       \"GarageQual\" : {\"No\" : 0, \"Po\" : 1, \"Fa\" : 2, \"TA\" : 3, \"Gd\" : 4, \"Ex\" : 5},\n",
    "                       \"HeatingQC\" : {\"Po\" : 1, \"Fa\" : 2, \"TA\" : 3, \"Gd\" : 4, \"Ex\" : 5},\n",
    "                       \"KitchenQual\" : {\"Po\" : 1, \"Fa\" : 2, \"TA\" : 3, \"Gd\" : 4, \"Ex\" : 5},\n",
    "                       \"LandSlope\" : {\"Sev\" : 1, \"Mod\" : 2, \"Gtl\" : 3},\n",
    "                       \"LotShape\" : {\"IR3\" : 1, \"IR2\" : 2, \"IR1\" : 3, \"Reg\" : 4},\n",
    "                       \"PavedDrive\" : {\"N\" : 0, \"P\" : 1, \"Y\" : 2},\n",
    "                       \"PoolQC\" : {\"No\" : 0, \"Fa\" : 1, \"TA\" : 2, \"Gd\" : 3, \"Ex\" : 4},\n",
    "                       \"Street\" : {\"Grvl\" : 1, \"Pave\" : 2},\n",
    "                       \"Utilities\" : {\"ELO\" : 1, \"NoSeWa\" : 2, \"NoSewr\" : 3, \"AllPub\" : 4}}\n",
    "                     )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Simplifications of existing features (prevent overfitting)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "all_data[\"SimplOverallQual\"] = all_data.OverallQual.replace({1 : 1, 2 : 1, 3 : 1, # bad\n",
    "                                                       4 : 2, 5 : 2, 6 : 2, # average\n",
    "                                                       7 : 3, 8 : 3, 9 : 3, 10 : 3 # good\n",
    "                                                      })\n",
    "all_data[\"SimplOverallCond\"] = all_data.OverallCond.replace({1 : 1, 2 : 1, 3 : 1, # bad\n",
    "                                                       4 : 2, 5 : 2, 6 : 2, # average\n",
    "                                                       7 : 3, 8 : 3, 9 : 3, 10 : 3 # good\n",
    "                                                      })\n",
    "all_data[\"SimplPoolQC\"] = all_data.PoolQC.replace({1 : 1, 2 : 1, # average\n",
    "                                             3 : 2, 4 : 2 # good\n",
    "                                            })\n",
    "all_data[\"SimplGarageCond\"] = all_data.GarageCond.replace({1 : 1, # bad\n",
    "                                                     2 : 1, 3 : 1, # average\n",
    "                                                     4 : 2, 5 : 2 # good\n",
    "                                                    })\n",
    "all_data[\"SimplGarageQual\"] = all_data.GarageQual.replace({1 : 1, # bad\n",
    "                                                     2 : 1, 3 : 1, # average\n",
    "                                                     4 : 2, 5 : 2 # good\n",
    "                                                    })\n",
    "all_data[\"SimplFireplaceQu\"] = all_data.FireplaceQu.replace({1 : 1, # bad\n",
    "                                                       2 : 1, 3 : 1, # average\n",
    "                                                       4 : 2, 5 : 2 # good\n",
    "                                                      })\n",
    "all_data[\"SimplFireplaceQu\"] = all_data.FireplaceQu.replace({1 : 1, # bad\n",
    "                                                       2 : 1, 3 : 1, # average\n",
    "                                                       4 : 2, 5 : 2 # good\n",
    "                                                      })\n",
    "all_data[\"SimplFunctional\"] = all_data.Functional.replace({1 : 1, 2 : 1, # bad\n",
    "                                                     3 : 2, 4 : 2, # major\n",
    "                                                     5 : 3, 6 : 3, 7 : 3, # minor\n",
    "                                                     8 : 4 # typical\n",
    "                                                    })\n",
    "all_data[\"SimplKitchenQual\"] = all_data.KitchenQual.replace({1 : 1, # bad\n",
    "                                                       2 : 1, 3 : 1, # average\n",
    "                                                       4 : 2, 5 : 2 # good\n",
    "                                                      })\n",
    "all_data[\"SimplHeatingQC\"] = all_data.HeatingQC.replace({1 : 1, # bad\n",
    "                                                   2 : 1, 3 : 1, # average\n",
    "                                                   4 : 2, 5 : 2 # good\n",
    "                                                  })\n",
    "all_data[\"SimplBsmtFinType1\"] = all_data.BsmtFinType1.replace({1 : 1, # unfinished\n",
    "                                                         2 : 1, 3 : 1, # rec room\n",
    "                                                         4 : 2, 5 : 2, 6 : 2 # living quarters\n",
    "                                                        })\n",
    "all_data[\"SimplBsmtFinType2\"] = all_data.BsmtFinType2.replace({1 : 1, # unfinished\n",
    "                                                         2 : 1, 3 : 1, # rec room\n",
    "                                                         4 : 2, 5 : 2, 6 : 2 # living quarters\n",
    "                                                        })\n",
    "all_data[\"SimplBsmtCond\"] = all_data.BsmtCond.replace({1 : 1, # bad\n",
    "                                                 2 : 1, 3 : 1, # average\n",
    "                                                 4 : 2, 5 : 2 # good\n",
    "                                                })\n",
    "all_data[\"SimplBsmtQual\"] = all_data.BsmtQual.replace({1 : 1, # bad\n",
    "                                                 2 : 1, 3 : 1, # average\n",
    "                                                 4 : 2, 5 : 2 # good\n",
    "                                                })\n",
    "all_data[\"SimplExterCond\"] = all_data.ExterCond.replace({1 : 1, # bad\n",
    "                                                   2 : 1, 3 : 1, # average\n",
    "                                                   4 : 2, 5 : 2 # good\n",
    "                                                  })\n",
    "all_data[\"SimplExterQual\"] = all_data.ExterQual.replace({1 : 1, # bad\n",
    "                                                   2 : 1, 3 : 1, # average\n",
    "                                                   4 : 2, 5 : 2 # good\n",
    "                                                  })\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Combinations of existing features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 2* Combinations of existing features\n",
    "# Overall quality of the house\n",
    "all_data[\"OverallGrade\"] = all_data[\"OverallQual\"] * all_data[\"OverallCond\"]\n",
    "# Overall quality of the garage\n",
    "all_data[\"GarageGrade\"] = all_data[\"GarageQual\"] * all_data[\"GarageCond\"]\n",
    "# Overall quality of the exterior\n",
    "all_data[\"ExterGrade\"] = all_data[\"ExterQual\"] * all_data[\"ExterCond\"]\n",
    "# Overall kitchen score\n",
    "all_data[\"KitchenScore\"] = all_data[\"KitchenAbvGr\"] * all_data[\"KitchenQual\"]\n",
    "# Overall fireplace score\n",
    "all_data[\"FireplaceScore\"] = all_data[\"Fireplaces\"] * all_data[\"FireplaceQu\"]\n",
    "# Overall garage score\n",
    "all_data[\"GarageScore\"] = all_data[\"GarageArea\"] * all_data[\"GarageQual\"]\n",
    "# Overall pool score\n",
    "all_data[\"PoolScore\"] = all_data[\"PoolArea\"] * all_data[\"PoolQC\"]\n",
    "# Simplified overall quality of the house\n",
    "all_data[\"SimplOverallGrade\"] = all_data[\"SimplOverallQual\"] * all_data[\"SimplOverallCond\"]\n",
    "# Simplified overall quality of the exterior\n",
    "all_data[\"SimplExterGrade\"] = all_data[\"SimplExterQual\"] * all_data[\"SimplExterCond\"]\n",
    "# Simplified overall pool score\n",
    "all_data[\"SimplPoolScore\"] = all_data[\"PoolArea\"] * all_data[\"SimplPoolQC\"]\n",
    "# Simplified overall garage score\n",
    "all_data[\"SimplGarageScore\"] = all_data[\"GarageArea\"] * all_data[\"SimplGarageQual\"]\n",
    "# Simplified overall fireplace score\n",
    "all_data[\"SimplFireplaceScore\"] = all_data[\"Fireplaces\"] * all_data[\"SimplFireplaceQu\"]\n",
    "# Simplified overall kitchen score\n",
    "all_data[\"SimplKitchenScore\"] = all_data[\"KitchenAbvGr\"] * all_data[\"SimplKitchenQual\"]\n",
    "# Total number of bathrooms\n",
    "all_data[\"TotalBath\"] = all_data[\"BsmtFullBath\"] + (0.5 * all_data[\"BsmtHalfBath\"]) + \\\n",
    "all_data[\"FullBath\"] + (0.5 * all_data[\"HalfBath\"])\n",
    "# Total SF for house (incl. basement)\n",
    "all_data[\"AllSF\"] = all_data[\"GrLivArea\"] + all_data[\"TotalBsmtSF\"]\n",
    "# Total SF for 1st + 2nd floors\n",
    "all_data[\"AllFlrsSF\"] = all_data[\"1stFlrSF\"] + all_data[\"2ndFlrSF\"]\n",
    "# Total SF for porch\n",
    "all_data[\"AllPorchSF\"] = all_data[\"OpenPorchSF\"] + all_data[\"EnclosedPorch\"] + \\\n",
    "all_data[\"3SsnPorch\"] + all_data[\"ScreenPorch\"]\n",
    "# Has masonry veneer or not\n",
    "all_data[\"HasMasVnr\"] = all_data.MasVnrType.replace({\"BrkCmn\" : 1, \"BrkFace\" : 1, \"CBlock\" : 1, \n",
    "                                               \"Stone\" : 1, \"None\" : 0})\n",
    "# House completed before sale or not\n",
    "all_data[\"BoughtOffPlan\"] = all_data.SaleCondition.replace({\"Abnorml\" : 0, \"Alloca\" : 0, \"AdjLand\" : 0, \n",
    "                                                      \"Family\" : 0, \"Normal\" : 0, \"Partial\" : 1})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Skewed features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "numeric_feats = all_data.dtypes[all_data.dtypes != \"object\"].index\n",
    "\n",
    "# Check the skew of all numerical features\n",
    "skewed_feats = all_data[numeric_feats].apply(lambda x: skew(x.dropna())).sort_values(ascending=False)\n",
    "skewness = pd.DataFrame({'Skew' :skewed_feats})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "There are 87 skewed numerical features to Box Cox transform\n"
     ]
    }
   ],
   "source": [
    "skewness = skewness[abs(skewness) > 0.75]\n",
    "print(\"There are {} skewed numerical features to Box Cox transform\".format(skewness.shape[0]))\n",
    "\n",
    "from scipy.special import boxcox1p\n",
    "skewed_features = skewness.index\n",
    "skewed_features = skewed_features.drop(\"SalePrice\")\n",
    "lam = 0.15\n",
    "for feat in skewed_features:\n",
    "    #all_data[feat] += 1\n",
    "    all_data[feat] = boxcox1p(all_data[feat], lam)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2917, 279)\n"
     ]
    }
   ],
   "source": [
    "all_data = pd.get_dummies(all_data)\n",
    "print(all_data.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Feature selection."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "all_data.drop(['SalePrice'], axis=1, inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "feature_selection_train = all_data[:ntrain]\n",
    "feature_selection_test = all_data[ntrain:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "feature_selection_X = feature_selection_train\n",
    "feature_selection_Y = y_train"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use SelectKBest."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['1stFlrSF', '2ndFlrSF', 'BedroomAbvGr', 'BsmtExposure', 'BsmtFinSF1',\n",
       "       'BsmtFinType1', 'BsmtFullBath', 'BsmtQual', 'BsmtUnfSF',\n",
       "       'EnclosedPorch',\n",
       "       ...\n",
       "       'Neighborhood_Somerst', 'Neighborhood_StoneBr', 'Neighborhood_Timber',\n",
       "       'RoofMatl_WdShngl', 'RoofStyle_Gable', 'RoofStyle_Hip',\n",
       "       'SaleCondition_Abnorml', 'SaleCondition_Partial', 'SaleType_New',\n",
       "       'SaleType_WD'],\n",
       "      dtype='object', length=140)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create and fit feature_selector\n",
    "feature_selector = SelectKBest(f_regression, k=140)\n",
    "feature_selector.fit(feature_selection_X, feature_selection_Y)\n",
    "cols = feature_selector.get_support(indices=True)\n",
    "feature_selection_X_new=feature_selection_X.iloc[:,cols]\n",
    "feature_selection_X_new.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "feature_selection_col=list(feature_selection_X_new.columns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "#put feature_selection_X_new and Saleprice together\n",
    "feature_selection_X_new[\"SalePrice\"] = feature_selection_Y\n",
    "feature_selection_XY=feature_selection_X_new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SalePrice                1.000000\n",
      "AllSF                    0.819024\n",
      "OverallQual              0.808861\n",
      "AllFlrsSF                0.745397\n",
      "GrLivArea                0.738000\n",
      "SimplOverallQual         0.705830\n",
      "ExterQual                0.681381\n",
      "TotalBath                0.677743\n",
      "KitchenQual              0.664764\n",
      "GarageCars               0.650260\n",
      "SimplExterQual           0.635358\n",
      "OverallGrade             0.618629\n",
      "1stFlrSF                 0.617721\n",
      "SimplKitchenQual         0.609207\n",
      "ExterGrade               0.594875\n",
      "YearBuilt                0.585230\n",
      "FullBath                 0.584311\n",
      "SimplBsmtQual            0.577866\n",
      "YearRemodAdd             0.565975\n",
      "SimplOverallGrade        0.544306\n",
      "TotRmsAbvGrd             0.542421\n",
      "FireplaceScore           0.541544\n",
      "FireplaceQu              0.540376\n",
      "SimplKitchenScore        0.531611\n",
      "Foundation_PConc         0.531194\n",
      "SimplFireplaceScore      0.524368\n",
      "SimplFireplaceQu         0.522636\n",
      "BsmtQual                 0.520950\n",
      "SimplExterGrade          0.518441\n",
      "SimplGarageScore         0.510678\n",
      "                           ...   \n",
      "SaleCondition_Abnorml   -0.160609\n",
      "Alley_1                 -0.165372\n",
      "Electrical_FuseF        -0.166514\n",
      "Neighborhood_NAmes      -0.166737\n",
      "BsmtCond_2              -0.167545\n",
      "Exterior2nd_MetalSd     -0.167867\n",
      "Exterior1st_MetalSd     -0.173273\n",
      "Neighborhood_BrkSide    -0.175373\n",
      "HouseStyle_1.5Fin       -0.181022\n",
      "Exterior2nd_Wd Sdng     -0.183521\n",
      "Exterior1st_Wd Sdng     -0.188313\n",
      "MSZoning_C (all)        -0.188374\n",
      "RoofStyle_Gable         -0.189013\n",
      "BsmtCond_0              -0.199626\n",
      "EnclosedPorch           -0.202250\n",
      "SaleType_WD             -0.212372\n",
      "Neighborhood_Edwards    -0.214095\n",
      "Neighborhood_OldTown    -0.232232\n",
      "Neighborhood_IDOTRR     -0.233059\n",
      "Electrical_FuseA        -0.238941\n",
      "Foundation_BrkTil       -0.251691\n",
      "LotShape                -0.278987\n",
      "GarageType_No           -0.322994\n",
      "GarageFinish_No         -0.322994\n",
      "Foundation_CBlock       -0.337909\n",
      "MSZoning_RM             -0.347453\n",
      "CentralAir_N            -0.351598\n",
      "MasVnrType_None         -0.388094\n",
      "GarageType_Detchd       -0.388681\n",
      "GarageFinish_Unf        -0.432144\n",
      "Name: SalePrice, Length: 141, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "corr = feature_selection_XY.corr()\n",
    "corr.sort_values([\"SalePrice\"], ascending = False, inplace = True)\n",
    "print(corr.SalePrice)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets' look at some examples."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ALLSF is the sum of GrLivArea and TotalBsmtSF. <br>\n",
    "GrLivArea: Above grade (ground) living area square feet\n",
    "TotalBsmtSF : Total square feet of basement area"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "plt.scatter(feature_selection_XY.AllSF, y_train, c = \"blue\", marker = \"s\")\n",
    "plt.title(\"AllSF vs SalePrice\")\n",
    "plt.xlabel(\"AllSF\")\n",
    "plt.ylabel(\"SalePrice\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "OverallQual :Overall material and finish quality."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "plt.scatter(feature_selection_XY.OverallQual, y_train, c = \"blue\", marker = \"s\")\n",
    "plt.title(\"OverallQual vs SalePrice\")\n",
    "plt.xlabel(\"OverallQual\")\n",
    "plt.ylabel(\"SalePrice\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "TotalBath :Total number of bathrooms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYwAAAEWCAYAAAB1xKBvAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvOIA7rQAAHNJJREFUeJzt3XuYHVWZ7/HvzyCXA2m5pEEhCeFmgEFAbLlIRi4KhhyuKkcuMyDCZDJn0FHHUY4+I0d4GHNkRjweUIzIE0YhjAygKCAEEcPV0MEAQe4IJgFMQ4CEywgh7/mjVsO2s3f3StO1a+/dv8/z7KerVq2qevdO9n5r1apapYjAzMxsKG+rOgAzM2sPThhmZpbFCcPMzLI4YZiZWRYnDDMzy+KEYWZmWZwwrCNIWl9SSBpf0vZ3lLSqjG2XQdJUSY+UtO2TJf2sjG1ba3PCsNJIerHmtVrSKzXzxw+x7lv6wZN0qaQ/pX2tlHSnpA+sxfpPS5oy3P2PBBVOl/R4eh+LJf2whP3MlPRa2sfzkm6R9P5G9SPiBxFx2EjHYa3PCcNKExEb9b+APwCH1ZRd3IQQzkz7fgdwEXB5E/Y5kqYDHwMOSO9jL+DXJe3rorSPzYEFwGX1Kklap6T9WxtwwrDKSNpA0nmSnpK0RNLZkt4uaTPgSmDbmhbJZpL2lfSbdBT8pKRzcn7AImI1cAnwTkmbpn3vKOkmScsl9Um6SNLYtOwyih/O69O+P1MT80kp1j5J/9Tgfe0n6Q+SVFN2rKT5aXpfSb+VtCK1ZL7eIPT3A9dExO/T+3gyIi6o2ebfSnogtaAekfSpQT7rCZJ+KukZSY9JmtHgs3oV+Hdga0kbSZoh6cb07/QccFoqu6Fm27ulOs+l9/OPqXyMpH9O+3tG0sWSNm4Uo7U+Jwyr0teAXYH3AO8D9ge+GBHPAkcBj9W0SJ4FXgNOBTYD/hI4DDhlqJ2kpHIC8CDwXM2iM4B3pv1PBr4CEBFHA8uAg9O+v53qjwF6gO2BacBZkrats8ubKb5btae0jqNIWgDnAv8SEV3ADsBPGoR+B3CypM9L2kPSmAHLnwIOAbqAGcB5kv6izvsfA1wD3AZsCUwFvixpvzp11wdOBB6JiBdT8QeBhcA44N8G1N8EuAG4guKzfDcwLy3+AnBw+hzGU/z7ndPgvVo7iAi//Cr9BTwOfHhA2VLgwJr5I4AH0vRUih+twbZ5GjAnTa8PBDA+zV8KvAI8D/xXmj56kG0dA9xeM/80MKVmfse0/XE1ZfcARzbY3r8C30nTm6b9vzPNz6dITpsN8f5E8eP9K+Bl4Bngc4PU/wXwtwM/P2A/4OEBdb8GfDdNzwT+lD6rZcBcYNe0bAbw0IB1ZwA3pOmTaj+3AfV+D+xbM79Neh+q+v+jX8N7uYVhlUina94JPFFT/ASw1SDr7CzpWkl/lLQC+CrFUW8jZ0XExsAGwD7AuZIOTNvaUtJlkpambV0wxLYAXo+IZ2rmXwY2alD3EuDo1Lo5GrglIp5Oy06kaFk9lE6xfaTeBqJwUUQcAGwMfAb4Rn/LQNLhkuan02rPAwc2eA9bA5PSqbznU93PU3z+/X4YERtHxOYRcVBE3FOzbHHjj4QJwKMDC9O/7wTgmpp9/pai5bXZINuzFuaEYZWI4pDzaYofs34TKVodUBzND/R94C5guyhO55xBcRQ+5L4iYiHFkf20VHw28BKwS9rWKQO29ZaGcY6Iu4BngQ/z56ejiIj7I+ITFP0k3waukLTuENt7NSIuoTittoukDSk6ps8ENk+J8Ubqfx6LKVpuG9e8xkbEUblvZ5Bli4Ht6sQbvNmCrN3v+gOSrrURJwyr0hzg9NShvTnFaZofpWV/BDaXVHsEPxZ4ISJeTOfq/yZ3R5J2AfYG7qvZ1ovACkkTKY64a/0RqNc/sTbmAP9E0Xl9RU0sJ0jaLCJeB16g+EFe40dZ0ikqLi/eSNLbJB1O0X8yn6LV9HaKU0ir07L9G8RxS9reZ1Xcr7KOpF0l7fEW3x8U/S/bS/o7SetK6tKbl+SeD8yUNCHtf3NJvhy3jTlhWJW+CvyO4kd8IXAr8I207G7gKuCJdEpjU+BzwCmSXgTOA/5jiO3/c7rK6UXgauA7wOyafU+h+MG+kjUvuT2LolP7eUmnDvP9XUJxmujaiHihpvxQ4EFJK4GvA/8jIl6rs/5K4HRgCUVn/ZnAyRFxZzpK/wLwM4qWzJEUHdtrSNueBnyA4rRfH/BdGp9OyxYRzwEHUfQBLaNoAfV39n+DokP8xvRebwNGIklZRVS0HM3MzAbnFoaZmWVxwjAzsyxOGGZmlsUJw8zMsnTUQGLjxo2LSZMmVR2GmVnbWLBgwTMR0Z1Tt6MSxqRJk+jt7a06DDOztiHpiaFrFXxKyszMsjhhmJlZFicMMzPL4oRhZmZZnDDMzCyLE4aZmWVxwjCzUnR1gbTmq6ur6shsuJwwzKwUK1euXfnackJqvtIShqQLJS2TtKim7ExJ90haKOl6SVs2WPf1VGehpKvKitHM2lfZCcnWVGYLYzbFg+hrnR0Ru0bE7sDPKR5iU88rEbF7eh1eYoxmZpaptIQREfOA5QPKVtTMbshbfG6ymZk1T9P7MCSdJWkxcDyNWxjrS+qVdIekI4fY3vRUt7evr2/E4zUzs0LTE0ZEfCUiJgAXA42elbx1RPQAxwHfkrTdINubFRE9EdHT3Z014KKZNcHYsWtXbq2vyqukLgY+Vm9BRCxNfx8DbgLe27ywzGwkrFgBEWu+VqwYet0cTkjN19SEIWmHmtkjgAfq1NlE0nppehywL/C75kRoZu2i7IRkayrteRiS5gD7A+MkLQFOB6ZJmgysBp4AZqS6PcCMiDgF2An4nqTVFAltZkQ4YZiZVUwRnXOhUk9PT/gBSmZm+SQtSH3GQ/Kd3mZmlsUJw8zakocGaT4nDDNrSx4apPmcMMxGGR+Z23A5YZiNMj4yt+FywjAzsyxOGGZmlsUJw8zakocGab7S7vQ2MyuThwBpPrcwzCrkK5asnThhmFXIVyxZO3HCMLO25NZZ8zlhmFlbcuus+ZwwzMwsixOGmZllccIwG2V8/4INl+/DMBtlfP+CDZdbGGajTKdcXeSWUvO5hWE2ynTK1UVuKTWfWxg2qnXK0bZZMzhh2KjWKUfbZs3ghGFWIZ+Ht3biPgyzCvk8vLWTUlsYki6UtEzSopqyMyXdI2mhpOslbdlg3RMlPZxeJ5YZp5mZDa3sU1KzgakDys6OiF0jYnfg58BXB64kaVPgdGAvYE/gdEmblByrWdO5093aSakJIyLmAcsHlNU2wjcEos6qHwHmRsTyiHgOmMuaicfsLau6D6GTO92dDDtPJX0Yks4CTgBeAA6oU2UrYHHN/JJUVm9b04HpABMnThzZQM1s2Do5GY5WlVwlFRFfiYgJwMXAqW9xW7Mioicierq7u0cmQBs1/KNmlq/qy2ovBj5Wp3wpMKFmfnwqMzOzijQ9YUjaoWb2COCBOtWuAw6WtEnq7D44lZmZWUVK7cOQNAfYHxgnaQnFlU/TJE0GVgNPADNS3R5gRkScEhHLJZ0J3Jk2dUZELF9jB9Z2urrqn+4ZO9b3JJi1OkXUu0ipPfX09ERvb2/VYdggpMbLqvivWHU8Vey/Wfus+rO1PJIWRERPTt2q+zDMrENVfcmyjTwPDWJmpfApxs7jFoaZlcI37nUeJwwzK4Xvcek8ThhmZpbFCcPMzLI4YZiZWRYnDGsqX2pp1r58Wa01lS+1NGtfbmGYmVkWJwwzM8vihGFmZlnch2FN5QHpzNqXWxhmZpbFCcPMzLI4YZiZWRYnDDMzy+KEYWZmWZwwzMwsixOGmZllccIwM7MsThhmZpbFCaND+PnJ1mo8lH3nKW1oEEkXAocCyyJil1R2NnAY8CrwKHBSRDxfZ93HgZXA68CqiOgpK85O4ecnW6vxUPadp8wWxmxg6oCyucAuEbEr8BDwvwZZ/4CI2N3JwsysNZSWMCJiHrB8QNn1EbEqzd4BjC9r/2ZmNrKq7MP4FHBtg2UBXC9pgaTpg21E0nRJvZJ6+/r6RjxIMzMrVJIwJH0FWAVc3KDKlIjYAzgE+HtJH2y0rYiYFRE9EdHT3d1dQrRmZgYVJAxJn6ToDD8+ov4TECJiafq7DLgS2LNpAZpZW/CVgc3X1IQhaSrwReDwiHi5QZ0NJY3tnwYOBhY1L0ozawe+MrD5SksYkuYAtwOTJS2RdDJwLjAWmCtpoaTzU90tJV2TVt0CuEXS3cB84OqI+EVZcZqZWZ7S7sOIiGPrFP+gQd0ngWlp+jFgt7LiMjOz4fGd3mZmlsUJg/odZ/0vMxsed0p3HicMMytF2Z3SHquq+UrrwzAzK5PHqmo+tzDMzCyLE4aZmWXJThiSpkg6KU13S9qmvLDMzKzVZCUMSacDX+LN4cjfDvyorKDMzKz15LYwjgIOB16CN26065hrESIav8zMrJCbMF5NAwUGvDHGk5mZjSK5CePHkr4HbCzpb4AbgO+XF5aZ2eB8Y2DzZd2HERH/KukgYAUwGfhqRMwtNTIzs0F4tNrmy0oY6Yqom/uThKQNJE2KiMfLDM7MzFpH7impy4DVNfOvpzIzMxslchPGOhHxav9Mml63nJDMzKwV5SaMPkmH989IOgJ4ppyQzMysFeUOPjgDuFjSuYCAxcAJpUXVZF1d9TvKxo71AGdmrWrs2MbfWytH7lVSjwJ7S9oozb9YalRN5qstzNrPaD2Yq/IAd9CEIemvIuJHkj4/oByAiPhmibGZmdkAVR7gDtXC6L+j2408M7NRbtCEERHfkzQGWBER5zQpJjPrAO5j6DxDXiUVEa8DxzYhFjPrICtW1B/Qc7T2PXSC3Kukbk1XSP0HacRagIi4q5SozMys5eQmjN3T3zNqygI4sNEKki4EDgWWRcQuqexs4DDgVeBR4KSIeL7OulOB/wuMAS6IiJmZcZqZdbQqT/Vl3bgXEQfUeTVMFslsYOqAsrnALhGxK/AQbz6Q6Q2pz+Q84BBgZ+BYSTvnxGlm1umqPNU3aMKQtJekuyW9KOl2STvlbjgi5gHLB5RdHxGr0uwdwPg6q+4JPBIRj6UhSC4Fjsjdr5mZlWOoFsZ5wBeAzYBvAt8awX1/Cri2TvlWFHeS91uSyuqSNF1Sr6Tevr6+EQzPzMxqDZUw3hYRcyPiTxFxGdA9EjuV9BVgFXDxW91WRMyKiJ6I6OnuHpHwzMysjqE6vTeW9NFG8xFxxdruUNInKTrDP5Qe+zrQUmBCzfz4VGZmbcRjtHWeoRLGrymuaqo3H8BaJYx09dMXgf0i4uUG1e4EdkgPbVoKHAMctzb7MbPqeYy2zjPUnd4nDXfDkuYA+wPjJC0BTqe4Kmo9YG4aj+qOiJghaUuKy2enRcQqSacC11FcVnthRNw33DjMzNaGW0aNqf5ZoQGVpC2AfwG2jIhD0mWu+0TED8oOcG309PREb2/vWq+XxlKsK+PjaQnt8h5aLc6q46li/83aZ9Wf7XC1a9zDJWlBRPTk1M19gNJsiiP+LdP8Q8Bn1z40MzNrV7kJY1xE/Jj0XO90L8XrpUVlZmYtJzdhvCRpM4qObiTtDbxQWlRm1vYaDVXh0WrbV+5YUp8HrgK2k3Qrxf0YHy8tKjMrTbPOw4/2DuJOlPuI1rsk7QdMpnim94MR8VqpkZmZVcDP8WhsqEe0frTBondLGtaNe2Zmrcwto8aGamEcNsiytb5xz8zM2ldpN+6ZmVlnye30RtJ/B/4CWL+/LCLOaLyGmZl1kqzLaiWdD3wC+DRFp/fRwNYlxmVmZi0m9z6MD0TECcBzEfE1YB/g3eWFZWZmrSY3YbyS/r6cBgpcBbyrnJDMzKwV5fZh/FzSxsA3gAWp7IJyQjIzs1Y01H0Y7wcWR8SZaX4j4F7gAeCc8sMzM7NWMdQpqe8BrwJI+iAwM5W9AMwqNzSzzufxlqydDHVKakxELE/TnwBmRcTlwOWSFpYbmlnn813F1k6GamGMkdSfVD4E3FizLPseDjOrT2r8Mms1Q/3ozwF+LekZiiulbgaQtD0e3tzMbFQZamiQsyT9kuIS2uvjzee5vo3iJj4zMxslhjytFBF31Cl7qJxwzMysVeXeuGdmZqOcE4aZmWVxwjAzsyylJQxJF0paJmlRTdnRku6TtFpSzyDrPi7pXkkLJfWWFaOZmeUrs4UxG5g6oGwR8FFgXsb6B0TE7hHRMLGYmVnzlHbzXUTMkzRpQNn9APJdSWZmbadV+zACuF7SAknTB6soabqkXkm9fX19TQrPzGz0adWEMSUi9gAOAf4+DXxYV0TMioieiOjp7u5uXoRmZqNMSyaMiFia/i4DrgT2rDYiMzNruYQhaUNJY/ungYMpOsvNzKxCZV5WOwe4HZgsaYmkkyUdJWkJxTPBr5Z0Xaq7paRr0qpbALdIuhuYD1wdEb8oK04zM8tT5lVSxzZYdGWduk8C09L0Y8BuZcVlZmbD03KnpMzMrDU5YZiZWRYnDBvV/Exts3x+zKqNan6mtlk+tzDMzCyLE4ZZhXxKzNqJT0mZVcinxKyduIVhZmZZnDDMzCyLE4aZmWVxwjAzsyxOGGZmlsUJw8zMsjhhmJlZFieMDtEuN4C1S5xmtibfuNchfAOYmZXNLYwO0dUF0pqvrq6qI/tzK1euXbmZtQ4njA7hH2IzK5sThpmZZXHCMDOzLE4YZmaWxQnDzMyylJYwJF0oaZmkRTVlR0u6T9JqST2DrDtV0oOSHpF0WlkxmplZvjJbGLOBqQPKFgEfBeY1WknSGOA84BBgZ+BYSTuXFKOZmWUqLWFExDxg+YCy+yPiwSFW3RN4JCIei4hXgUuBI0oK08zMMrViH8ZWwOKa+SWpzMzMKtSKCWOtSJouqVdSb19fX9XhmJl1rFZMGEuBCTXz41NZXRExKyJ6IqKnu7u79OBalQf1M7OyteLgg3cCO0jahiJRHAMcV21Irc+DD5pZ2cq8rHYOcDswWdISSSdLOkrSEmAf4GpJ16W6W0q6BiAiVgGnAtcB9wM/joj7yorTzMzylNbCiIhjGyy6sk7dJ4FpNfPXANeUFJqZmQ1DK/ZhmJlZC3LCMDOzLE4YZmaWxQnDmsqX/5q1r1a8rNY6mC//NWtfbmGYmVkWJwwzM8vihIHPq5uZ5XAfBj6vbmaWwy0MMzPL4oRhZmZZnDDMzCyLE4aZmWVxwjAzsyxOGGZmlsUJw8zMsjhhmJlZFicMoKsLpDVfXV1VR2Zm1jqcMICVK9eu3MxsNHLCMDOzLE4YZmaWxQnDzMyyOGGYmVmW0hKGpAslLZO0qKZsU0lzJT2c/m7SYN3XJS1Mr6vKitHMzPKV2cKYDUwdUHYa8MuI2AH4ZZqv55WI2D29Di8xRjMzy1RawoiIecDyAcVHABel6YuAI8vav5mZjaxm92FsERFPpemngS0a1FtfUq+kOyQ5qZiZtYDKHtEaESEpGizeOiKWStoWuFHSvRHxaL2KkqYD0wEmTpxYUrRmZtbsFsYfJb0LIP1dVq9SRCxNfx8DbgLe22iDETErInoioqe7u3vkIzYzM6D5CeMq4MQ0fSLw04EVJG0iab00PQ7YF/hd0yI0M7O6yrysdg5wOzBZ0hJJJwMzgYMkPQx8OM0jqUfSBWnVnYBeSXcDvwJmRoQThplZxUrrw4iIYxss+lCdur3AKWn6NuA9ZcVlZmbD4zu9gbFj167czGw0quwqqVayYkXVEZiZtT63MMzMLIsThpmZZXHCMDOzLE4YZmaWxQnDzMyyOGGYmVkWRTQa/6/9SOoDnqhg1+OAZyrYb65Wjs+xDV8rx+fYhq/Z8W0dEVkD8XVUwqiKpN6I6Kk6jkZaOT7HNnytHJ9jG75Wjs+npMzMLIsThpmZZXHCGBmzqg5gCK0cn2MbvlaOz7ENX8vG5z4MMzPL4haGmZllccIwM7MsThhrQdJUSQ9KekTSaXWWT5T0K0m/lXSPpGlNjO1CScskLWqwXJK+nWK/R9IeLRTb8SmmeyXdJmm3Vomtpt77Ja2S9PFmxZb2O2R8kvaXtFDSfZJ+3SqxSXqHpJ9JujvFdlITY5uQvou/S/v+hzp1KvlOZMZW2XdiUBHhV8YLGAM8CmwLrAvcDew8oM4s4O/S9M7A402M74PAHsCiBsunAdcCAvYGftNCsX0A2CRNH9JKsdX8298IXAN8vMn/74b67DameOb9xDS/eQvF9mXg/6TpbmA5sG6TYnsXsEeaHgs8VOf7Wsl3IjO2yr4Tg73cwsi3J/BIRDwWEa8ClwJHDKgTQFeafgfwZLOCi4h5FF/IRo4A/j0KdwAbS3pXK8QWEbdFxHNp9g5gfDPiSvse6nMD+DRwObCs/Ij+XEZ8xwFXRMQfUv2mxZgRWwBjJQnYKNVd1aTYnoqIu9L0SuB+YKsB1Sr5TuTEVuV3YjBOGPm2AhbXzC9hzf+A/xv4K0lLKI5GP92c0LLkxN8KTqY46msJkrYCjgK+W3UsDbwb2ETSTZIWSDqh6oBqnAvsRHHgdC/wDxGxutlBSJoEvBf4zYBFlX8nBomtVst8J/yI1pF1LDA7Iv5N0j7ADyXtUsWXpB1JOoDiyzGl6lhqfAv4UkSsLg6UW846wPuADwEbALdLuiMiHqo2LAA+AiwEDgS2A+ZKujkimvZQZEkbUbQOP9vM/ebIia3VvhNOGPmWAhNq5senslonA1MBIuJ2SetTDCTW9FMZdeTEXxlJuwIXAIdExLNVx1OjB7g0JYtxwDRJqyLiJ9WG9YYlwLMR8RLwkqR5wG4U58WrdhIwM4oT8Y9I+j2wIzC/GTuX9HaKH+SLI+KKOlUq+05kxNaS3wmfksp3J7CDpG0krQscA1w1oM4fKI70kLQTsD7Q19QoG7sKOCFdGbI38EJEPFV1UFBcXQZcAfx1ixwZvyEitomISRExCfhP4H+2ULIA+CkwRdI6kv4bsBfFOfFWUPt92AKYDDzWjB2nfpMfAPdHxDcbVKvkO5ETW6t+J9zCyBQRqySdClxHcdXMhRFxn6QzgN6IuAr4R+D7kj5H0eH3yXR0VTpJc4D9gXGpD+V04O0p9vMp+lSmAY8AL1Mc/TVFRmxfBTYDvpOO5FdFk0brzIitUkPFFxH3S/oFcA+wGrggIga9RLhZsQFnArMl3UtxJdKXIqJZw3bvC/w1cK+khansy8DEmviq+k7kxFbZd2IwHhrEzMyy+JSUmZllccIwM7MsThhmZpbFCcPMzLI4YZiZWRYnDDNA0mZpxNeFkp6WtLRmft069TeVNCNju+tIej5Nby/plbTNuyXdKmmHIdbfVtIxNfOnSPrWcN6j2VvlhGEGRMSzEbF7ROwOnA+c0z+fBpscaFNgyIRRx4Npm7sBlwBrDJM/wLYUN4maVc4Jw2wIkr4oaVF69Q8oOROYnFoLMyV1SbpR0l3pOQaHZmy6C3gu7WM7STereJbKAkl71ezngLSfz6Sy8ZKuk/SwpK+P6Js1G4Tv9DYbRPrhPh54P8X3Zb6kmyhaBtunFkn/2EBHRsQKSZsDtwI/r7PJyenu3i5gPYqhPACeAg6KiP+StCNwUVp2GnBqRByZ9nMKxVhR7wNeAx6S9P8iomlD6dvo5YRhNrgpwOUR8QqApJ8AfwlcP6CegJmSplAM0TFB0jjg+QH1HqxJMsdTnP46lCJ5nJuerLaKYnTXRm7oH91U0gMUQ0o4YVjpfErKbGScQPHQrD1SQniGYvDJwVxF8dQ6KMYhWwy8h+JhXesNst6faqZfxwd+1iROGGaDuxk4StIG6fkFR6SylRSP1+z3DmBZGqTyIPIexDOF4rG//es/lQarPJGixUKd/ZhVxkcmZoOIiPlpVNY7U9F3I+JegNQ5fS9wNfBN4Gdpfj7wcINN9vdhiKKlMD2Vnwv8p6RPpe31tyJ+C4yRdDfFkNgvj+gbNFsLHq3WzMyy+JSUmZllccIwM7MsThhmZpbFCcPMzLI4YZiZWRYnDDMzy+KEYWZmWf4/BtINFY5AW9UAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(feature_selection_XY.TotalBath, y_train, c = \"blue\", marker = \"s\")\n",
    "plt.title(\"TotalBath vs SalePrice\")\n",
    "plt.xlabel(\"TotalBath\")\n",
    "plt.ylabel(\"SalePrice\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look deep into these features:<br>\n",
    "AllSF                = all_data[\"GrLivArea\"] + all_data[\"TotalBsmtSF\"]<br>\n",
    "OverallQual          :Overall material and finish quality<br>\n",
    "AllFlrsSF            = all_data[\"1stFlrSF\"] + all_data[\"2ndFlrSF\"]<br>\n",
    "GrLivArea            = Above grade (ground) living area square feet<br>\n",
    "SimplOverallQual     <br>\n",
    "ExterQual            :Exterior material quality<br>\n",
    "TotalBath            :Total number of bathrooms<br>\n",
    "KitchenQual          :Kitchen quality<br>\n",
    "GarageCars           :Size of garage in car capacity<br>\n",
    "SimplExterQual       <br>\n",
    "OverallGrade         = all_data[\"OverallQual\"] * all_data[\"OverallCond\"]<br>\n",
    "1stFlrSF            <br>\n",
    "SimplKitchenQual    <br>\n",
    "ExterGrade          <br>\n",
    "YearBuilt            :Original construction date<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We rule out some features with high correlations. And use the rest as the final features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "train = all_data[:ntrain][feature_selection_col]\n",
    "test = all_data[ntrain:][feature_selection_col]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model Evaluation:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use the cross_val_score function of Sklearn. However this function has not a shuffle attribut, we add then one line of code, in order to shuffle the dataset prior to cross-validation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_folds = 5\n",
    "\n",
    "def rmsle_cv(model):\n",
    "    kf = KFold(n_folds, shuffle=True, random_state=42).get_n_splits(train.values)\n",
    "    rmse= np.sqrt(-cross_val_score(model, train.values, y_train, scoring=\"neg_mean_squared_error\", cv = kf))\n",
    "    return(rmse)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "LASSO Regression :\n",
    "This model may be very sensitive to outliers. So we need to made it more robust on them. For that we use the sklearn's Robustscaler() method on pipeline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "lasso = make_pipeline(RobustScaler(), Lasso(alpha =0.0005, random_state=1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Elastic Net Regression :\n",
    "again made robust to outliers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "ENet = make_pipeline(RobustScaler(), ElasticNet(alpha=0.0005, l1_ratio=.9, random_state=3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Kernel Ridge Regression :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "KRR = KernelRidge(alpha=0.6, kernel='polynomial', degree=2, coef0=2.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Gradient Boosting Regression :\n",
    "With huber loss that makes it robust to outliers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "GBoost = GradientBoostingRegressor(n_estimators=3000, learning_rate=0.05,\n",
    "                                   max_depth=4, max_features='sqrt',\n",
    "                                   min_samples_leaf=15, min_samples_split=10, \n",
    "                                   loss='huber', random_state =5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "XGBoost:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "model_xgb = xgb.XGBRegressor(colsample_bytree=0.4603, gamma=0.0468, \n",
    "                             learning_rate=0.05, max_depth=3, \n",
    "                             min_child_weight=1.7817, n_estimators=2200,\n",
    "                             reg_alpha=0.4640, reg_lambda=0.8571,\n",
    "                             subsample=0.5213, silent=1,\n",
    "                             random_state =7, nthread = -1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "LightGBM :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "model_lgb = lgb.LGBMRegressor(objective='regression',num_leaves=5,\n",
    "                              learning_rate=0.05, n_estimators=720,\n",
    "                              max_bin = 55, bagging_fraction = 0.8,\n",
    "                              bagging_freq = 5, feature_fraction = 0.2319,\n",
    "                              feature_fraction_seed=9, bagging_seed=9,\n",
    "                              min_data_in_leaf =6, min_sum_hessian_in_leaf = 11)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see how these base models perform on the data by evaluating the cross-validation rmsle error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Lasso score: 0.1140 (0.0054)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "score = rmsle_cv(lasso)\n",
    "print(\"\\nLasso score: {:.4f} ({:.4f})\\n\".format(score.mean(), score.std()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ElasticNet score: 0.1141 (0.0053)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "score = rmsle_cv(ENet)\n",
    "print(\"ElasticNet score: {:.4f} ({:.4f})\\n\".format(score.mean(), score.std()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Kernel Ridge score: 0.1156 (0.0051)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "score = rmsle_cv(KRR)\n",
    "print(\"Kernel Ridge score: {:.4f} ({:.4f})\\n\".format(score.mean(), score.std()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gradient Boosting score: 0.1167 (0.0075)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "score = rmsle_cv(GBoost)\n",
    "print(\"Gradient Boosting score: {:.4f} ({:.4f})\\n\".format(score.mean(), score.std()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Xgboost score: 0.1143 (0.0058)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "score = rmsle_cv(model_xgb)\n",
    "print(\"Xgboost score: {:.4f} ({:.4f})\\n\".format(score.mean(), score.std()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LGBM score: 0.1163 (0.0067)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "score = rmsle_cv(model_lgb)\n",
    "print(\"LGBM score: {:.4f} ({:.4f})\\n\" .format(score.mean(), score.std()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model Ensembling:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Simplest Stacking approach : Averaging base models\n",
    "We begin with this simple approach of averaging base models. We build a new class to extend scikit-learn with our model and also to laverage encapsulation and code reuse (inheritance)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "class AveragingModels(BaseEstimator, RegressorMixin, TransformerMixin):\n",
    "    def __init__(self, models):\n",
    "        self.models = models\n",
    "        \n",
    "    # we define clones of the original models to fit the data in\n",
    "    def fit(self, X, y):\n",
    "        self.models_ = [clone(x) for x in self.models]\n",
    "        \n",
    "        # Train cloned base models\n",
    "        for model in self.models_:\n",
    "            model.fit(X, y)\n",
    "\n",
    "        return self\n",
    "    \n",
    "    #Now we do the predictions for cloned models and average them\n",
    "    def predict(self, X):\n",
    "        predictions = np.column_stack([\n",
    "            model.predict(X) for model in self.models_\n",
    "        ])\n",
    "        return np.mean(predictions, axis=1)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We just average four models here ENet, GBoost, KRR and lasso. Of course we could easily add more models in the mix."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "averaged_models = AveragingModels(models = (ENet, GBoost, KRR, lasso))\n",
    "\n",
    "score = rmsle_cv(averaged_models)\n",
    "print(\" Averaged base models score: {:.4f} ({:.4f})\\n\".format(score.mean(), score.std()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Less simple Stacking : Adding a Meta-model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this approach, we add a meta-model on averaged base models and use the out-of-folds predictions of these base models to train our meta-model.\n",
    "\n",
    "The procedure, for the training part, may be described as follows:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1.Split the total training set into two disjoint sets (here train and .holdout )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2.Train several base models on the first part (train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3.Test these base models on the second part (holdout)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "4.Use the predictions from 3) (called out-of-folds predictions) as the inputs, and the correct responses (target variable) as the outputs to train a higher level learner called meta-model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first three steps are done iteratively . If we take for example a 5-fold stacking , we first split the training data into 5 folds. Then we will do 5 iterations. In each iteration, we train every base model on 4 folds and predict on the remaining fold (holdout fold)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, we will be sure, after 5 iterations , that the entire data is used to get out-of-folds predictions that we will then use as new feature to train our meta-model in the step 4."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the prediction part , We average the predictions of all base models on the test data and used them as meta-features on which, the final prediction is done with the meta-model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "class StackingAveragedModels(BaseEstimator, RegressorMixin, TransformerMixin):\n",
    "    def __init__(self, base_models, meta_model, n_folds=5):\n",
    "        self.base_models = base_models\n",
    "        self.meta_model = meta_model\n",
    "        self.n_folds = n_folds\n",
    "   \n",
    "    # We again fit the data on clones of the original models\n",
    "    def fit(self, X, y):\n",
    "        self.base_models_ = [list() for x in self.base_models]\n",
    "        self.meta_model_ = clone(self.meta_model)\n",
    "        kfold = KFold(n_splits=self.n_folds, shuffle=True, random_state=156)\n",
    "        \n",
    "        # Train cloned base models then create out-of-fold predictions\n",
    "        # that are needed to train the cloned meta-model\n",
    "        out_of_fold_predictions = np.zeros((X.shape[0], len(self.base_models)))\n",
    "        for i, model in enumerate(self.base_models):\n",
    "            for train_index, holdout_index in kfold.split(X, y):\n",
    "                instance = clone(model)\n",
    "                self.base_models_[i].append(instance)\n",
    "                instance.fit(X[train_index], y[train_index])\n",
    "                y_pred = instance.predict(X[holdout_index])\n",
    "                out_of_fold_predictions[holdout_index, i] = y_pred\n",
    "                \n",
    "        # Now train the cloned  meta-model using the out-of-fold predictions as new feature\n",
    "        self.meta_model_.fit(out_of_fold_predictions, y)\n",
    "        return self\n",
    "   \n",
    "    #Do the predictions of all base models on the test data and use the averaged predictions as \n",
    "    #meta-features for the final prediction which is done by the meta-model\n",
    "    def predict(self, X):\n",
    "        meta_features = np.column_stack([\n",
    "            np.column_stack([model.predict(X) for model in base_models]).mean(axis=1)\n",
    "            for base_models in self.base_models_ ])\n",
    "        return self.meta_model_.predict(meta_features)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To make the two approaches comparable (by using the same number of models) , we just average Enet KRR and Gboost, then we add lasso as meta-model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Stacking Averaged models score: 0.1088 (0.0056)\n"
     ]
    }
   ],
   "source": [
    "stacked_averaged_models = StackingAveragedModels(base_models = (ENet, GBoost, KRR),\n",
    "                                                 meta_model = lasso)\n",
    "\n",
    "score = rmsle_cv(stacked_averaged_models)\n",
    "print(\"Stacking Averaged models score: {:.4f} ({:.4f})\".format(score.mean(), score.std()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ensembling StackedRegressor, XGBoost and LightGBM"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We add XGBoost and LightGBM to the StackedRegressor defined previously."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We first define a rmsle evaluation function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rmsle(y, y_pred):\n",
    "    return np.sqrt(mean_squared_error(y, y_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "StackedRegressor:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.07668436230748962\n"
     ]
    }
   ],
   "source": [
    "stacked_averaged_models.fit(train.values, y_train)\n",
    "stacked_train_pred = stacked_averaged_models.predict(train.values)\n",
    "stacked_pred = np.expm1(stacked_averaged_models.predict(test.values))\n",
    "print(rmsle(y_train, stacked_train_pred))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.07971281394832326\n"
     ]
    }
   ],
   "source": [
    "model_xgb.fit(train, y_train)\n",
    "xgb_train_pred = model_xgb.predict(train)\n",
    "xgb_pred = np.expm1(model_xgb.predict(test))\n",
    "print(rmsle(y_train, xgb_train_pred))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.07320429803422897\n"
     ]
    }
   ],
   "source": [
    "model_lgb.fit(train, y_train)\n",
    "lgb_train_pred = model_lgb.predict(train)\n",
    "lgb_pred = np.expm1(model_lgb.predict(test.values))\n",
    "print(rmsle(y_train, lgb_train_pred))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSLE score on train data:\n",
      "0.07262034999905438\n"
     ]
    }
   ],
   "source": [
    "print('RMSLE score on train data:')\n",
    "print(rmsle(y_train,stacked_train_pred*0.2 + xgb_train_pred*0.1 + lgb_train_pred*0.7 ))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "ensemble = stacked_pred*0.2 + xgb_pred*0.1 + lgb_pred*0.7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "    .dataframe tbody tr th {\n",
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       "    .dataframe thead th {\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>Id</th>\n",
       "      <th>SalePrice</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1461</td>\n",
       "      <td>124404.511712</td>\n",
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       "      <th>2</th>\n",
       "      <td>1463</td>\n",
       "      <td>186004.429185</td>\n",
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       "      <th>3</th>\n",
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       "      <th>4</th>\n",
       "      <td>1465</td>\n",
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       "    </tr>\n",
       "  </tbody>\n",
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      "text/plain": [
       "     Id      SalePrice\n",
       "0  1461  124404.511712\n",
       "1  1462  160040.347525\n",
       "2  1463  186004.429185\n",
       "3  1464  186637.733045\n",
       "4  1465  187699.591124"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sub = pd.DataFrame()\n",
    "sub['Id'] = sample[\"Id\"]\n",
    "sub['SalePrice'] = ensemble\n",
    "sub.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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