House_Prices_Study.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# House Prices Study (In Python)\n",
    "\n",
    "# Introduction: \n",
    "Here, we look at the dataset provided by Kaggle on house prices and house price predictors and follow the following main steps:\n",
    "\n",
    "- Descriptive Statistics\n",
    "- Feature Engineering\n",
    "- Make Predictions\n",
    "\n",
    "# 1.1: Load Modules/Packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "#from pandas.plotting import scatter_matrix\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import os #for loading path\n",
    "\n",
    "# initial variable analysis tools\n",
    "from statsmodels.formula.api import ols\n",
    "from statsmodels.stats.outliers_influence import variance_inflation_factor\n",
    "import statsmodels.api as sm\n",
    "from sklearn.decomposition import PCA\n",
    "from patsy import dmatrices\n",
    "import itertools\n",
    "\n",
    "# data cleaning tools\n",
    "from sklearn.preprocessing import StandardScaler, LabelEncoder, Imputer\n",
    "\n",
    "# model evaluation tools\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.metrics import accuracy_score, mean_squared_error\n",
    "from statsmodels.tools.eval_measures import mse\n",
    "\n",
    "# machine learning modules\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.ensemble import RandomForestRegressor, AdaBoostRegressor, IsolationForest\n",
    "from sklearn.neighbors import KNeighborsRegressor, KNeighborsClassifier\n",
    "from sklearn.naive_bayes import GaussianNB\n",
    "from sklearn.neural_network import MLPRegressor\n",
    "from sklearn.svm import SVR\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1.2 Load and look at data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "house_train = pd.read_csv(\"//home/rxu17/Documents/house_train.csv\")\n",
    "house_test = pd.read_csv(\"//home/rxu17/Documents/house_test.csv\")\n",
    "\n",
    "# rename some columns to use for dmatrices\n",
    "house_train = house_train.rename(columns = {'1stFlrSF': 'FirstFlrSF', '2ndFlrSF':'SecFlrSF', '3SsnPorch':'ThreeSsnPorch'}) \n",
    "house_test = house_test.rename(columns = {'1stFlrSF': 'FirstFlrSF', '2ndFlrSF':'SecFlrSF', '3SsnPorch':'ThreeSsnPorch'})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Id</th>\n",
       "      <th>MSSubClass</th>\n",
       "      <th>MSZoning</th>\n",
       "      <th>LotFrontage</th>\n",
       "      <th>LotArea</th>\n",
       "      <th>Street</th>\n",
       "      <th>Alley</th>\n",
       "      <th>LotShape</th>\n",
       "      <th>LandContour</th>\n",
       "      <th>Utilities</th>\n",
       "      <th>...</th>\n",
       "      <th>PoolArea</th>\n",
       "      <th>PoolQC</th>\n",
       "      <th>Fence</th>\n",
       "      <th>MiscFeature</th>\n",
       "      <th>MiscVal</th>\n",
       "      <th>MoSold</th>\n",
       "      <th>YrSold</th>\n",
       "      <th>SaleType</th>\n",
       "      <th>SaleCondition</th>\n",
       "      <th>SalePrice</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>60</td>\n",
       "      <td>RL</td>\n",
       "      <td>65.0</td>\n",
       "      <td>8450</td>\n",
       "      <td>Pave</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Reg</td>\n",
       "      <td>Lvl</td>\n",
       "      <td>AllPub</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>2008</td>\n",
       "      <td>WD</td>\n",
       "      <td>Normal</td>\n",
       "      <td>208500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>20</td>\n",
       "      <td>RL</td>\n",
       "      <td>80.0</td>\n",
       "      <td>9600</td>\n",
       "      <td>Pave</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Reg</td>\n",
       "      <td>Lvl</td>\n",
       "      <td>AllPub</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>2007</td>\n",
       "      <td>WD</td>\n",
       "      <td>Normal</td>\n",
       "      <td>181500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>60</td>\n",
       "      <td>RL</td>\n",
       "      <td>68.0</td>\n",
       "      <td>11250</td>\n",
       "      <td>Pave</td>\n",
       "      <td>NaN</td>\n",
       "      <td>IR1</td>\n",
       "      <td>Lvl</td>\n",
       "      <td>AllPub</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0</td>\n",
       "      <td>9</td>\n",
       "      <td>2008</td>\n",
       "      <td>WD</td>\n",
       "      <td>Normal</td>\n",
       "      <td>223500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>70</td>\n",
       "      <td>RL</td>\n",
       "      <td>60.0</td>\n",
       "      <td>9550</td>\n",
       "      <td>Pave</td>\n",
       "      <td>NaN</td>\n",
       "      <td>IR1</td>\n",
       "      <td>Lvl</td>\n",
       "      <td>AllPub</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>2006</td>\n",
       "      <td>WD</td>\n",
       "      <td>Abnorml</td>\n",
       "      <td>140000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>60</td>\n",
       "      <td>RL</td>\n",
       "      <td>84.0</td>\n",
       "      <td>14260</td>\n",
       "      <td>Pave</td>\n",
       "      <td>NaN</td>\n",
       "      <td>IR1</td>\n",
       "      <td>Lvl</td>\n",
       "      <td>AllPub</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0</td>\n",
       "      <td>12</td>\n",
       "      <td>2008</td>\n",
       "      <td>WD</td>\n",
       "      <td>Normal</td>\n",
       "      <td>250000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 81 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   Id  MSSubClass MSZoning  LotFrontage  LotArea Street Alley LotShape  \\\n",
       "0   1          60       RL         65.0     8450   Pave   NaN      Reg   \n",
       "1   2          20       RL         80.0     9600   Pave   NaN      Reg   \n",
       "2   3          60       RL         68.0    11250   Pave   NaN      IR1   \n",
       "3   4          70       RL         60.0     9550   Pave   NaN      IR1   \n",
       "4   5          60       RL         84.0    14260   Pave   NaN      IR1   \n",
       "\n",
       "  LandContour Utilities    ...     PoolArea PoolQC Fence MiscFeature MiscVal  \\\n",
       "0         Lvl    AllPub    ...            0    NaN   NaN         NaN       0   \n",
       "1         Lvl    AllPub    ...            0    NaN   NaN         NaN       0   \n",
       "2         Lvl    AllPub    ...            0    NaN   NaN         NaN       0   \n",
       "3         Lvl    AllPub    ...            0    NaN   NaN         NaN       0   \n",
       "4         Lvl    AllPub    ...            0    NaN   NaN         NaN       0   \n",
       "\n",
       "  MoSold YrSold  SaleType  SaleCondition  SalePrice  \n",
       "0      2   2008        WD         Normal     208500  \n",
       "1      5   2007        WD         Normal     181500  \n",
       "2      9   2008        WD         Normal     223500  \n",
       "3      2   2006        WD        Abnorml     140000  \n",
       "4     12   2008        WD         Normal     250000  \n",
       "\n",
       "[5 rows x 81 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "house_train.head() # peeking at data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looks like our training set has some NaN values we'll need to fix later"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Id</th>\n",
       "      <th>MSSubClass</th>\n",
       "      <th>LotFrontage</th>\n",
       "      <th>LotArea</th>\n",
       "      <th>OverallQual</th>\n",
       "      <th>OverallCond</th>\n",
       "      <th>YearBuilt</th>\n",
       "      <th>YearRemodAdd</th>\n",
       "      <th>MasVnrArea</th>\n",
       "      <th>BsmtFinSF1</th>\n",
       "      <th>...</th>\n",
       "      <th>WoodDeckSF</th>\n",
       "      <th>OpenPorchSF</th>\n",
       "      <th>EnclosedPorch</th>\n",
       "      <th>ThreeSsnPorch</th>\n",
       "      <th>ScreenPorch</th>\n",
       "      <th>PoolArea</th>\n",
       "      <th>MiscVal</th>\n",
       "      <th>MoSold</th>\n",
       "      <th>YrSold</th>\n",
       "      <th>SalePrice</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1460.000000</td>\n",
       "      <td>1460.000000</td>\n",
       "      <td>1201.000000</td>\n",
       "      <td>1460.000000</td>\n",
       "      <td>1460.000000</td>\n",
       "      <td>1460.000000</td>\n",
       "      <td>1460.000000</td>\n",
       "      <td>1460.000000</td>\n",
       "      <td>1452.000000</td>\n",
       "      <td>1460.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>1460.000000</td>\n",
       "      <td>1460.000000</td>\n",
       "      <td>1460.000000</td>\n",
       "      <td>1460.000000</td>\n",
       "      <td>1460.000000</td>\n",
       "      <td>1460.000000</td>\n",
       "      <td>1460.000000</td>\n",
       "      <td>1460.000000</td>\n",
       "      <td>1460.000000</td>\n",
       "      <td>1460.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>730.500000</td>\n",
       "      <td>56.897260</td>\n",
       "      <td>70.049958</td>\n",
       "      <td>10516.828082</td>\n",
       "      <td>6.099315</td>\n",
       "      <td>5.575342</td>\n",
       "      <td>1971.267808</td>\n",
       "      <td>1984.865753</td>\n",
       "      <td>103.685262</td>\n",
       "      <td>443.639726</td>\n",
       "      <td>...</td>\n",
       "      <td>94.244521</td>\n",
       "      <td>46.660274</td>\n",
       "      <td>21.954110</td>\n",
       "      <td>3.409589</td>\n",
       "      <td>15.060959</td>\n",
       "      <td>2.758904</td>\n",
       "      <td>43.489041</td>\n",
       "      <td>6.321918</td>\n",
       "      <td>2007.815753</td>\n",
       "      <td>180921.195890</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>421.610009</td>\n",
       "      <td>42.300571</td>\n",
       "      <td>24.284752</td>\n",
       "      <td>9981.264932</td>\n",
       "      <td>1.382997</td>\n",
       "      <td>1.112799</td>\n",
       "      <td>30.202904</td>\n",
       "      <td>20.645407</td>\n",
       "      <td>181.066207</td>\n",
       "      <td>456.098091</td>\n",
       "      <td>...</td>\n",
       "      <td>125.338794</td>\n",
       "      <td>66.256028</td>\n",
       "      <td>61.119149</td>\n",
       "      <td>29.317331</td>\n",
       "      <td>55.757415</td>\n",
       "      <td>40.177307</td>\n",
       "      <td>496.123024</td>\n",
       "      <td>2.703626</td>\n",
       "      <td>1.328095</td>\n",
       "      <td>79442.502883</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>20.000000</td>\n",
       "      <td>21.000000</td>\n",
       "      <td>1300.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1872.000000</td>\n",
       "      <td>1950.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>2006.000000</td>\n",
       "      <td>34900.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>365.750000</td>\n",
       "      <td>20.000000</td>\n",
       "      <td>59.000000</td>\n",
       "      <td>7553.500000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>1954.000000</td>\n",
       "      <td>1967.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>2007.000000</td>\n",
       "      <td>129975.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>730.500000</td>\n",
       "      <td>50.000000</td>\n",
       "      <td>69.000000</td>\n",
       "      <td>9478.500000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>1973.000000</td>\n",
       "      <td>1994.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>383.500000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>25.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>2008.000000</td>\n",
       "      <td>163000.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>1095.250000</td>\n",
       "      <td>70.000000</td>\n",
       "      <td>80.000000</td>\n",
       "      <td>11601.500000</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>2000.000000</td>\n",
       "      <td>2004.000000</td>\n",
       "      <td>166.000000</td>\n",
       "      <td>712.250000</td>\n",
       "      <td>...</td>\n",
       "      <td>168.000000</td>\n",
       "      <td>68.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>2009.000000</td>\n",
       "      <td>214000.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1460.000000</td>\n",
       "      <td>190.000000</td>\n",
       "      <td>313.000000</td>\n",
       "      <td>215245.000000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>9.000000</td>\n",
       "      <td>2010.000000</td>\n",
       "      <td>2010.000000</td>\n",
       "      <td>1600.000000</td>\n",
       "      <td>5644.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>857.000000</td>\n",
       "      <td>547.000000</td>\n",
       "      <td>552.000000</td>\n",
       "      <td>508.000000</td>\n",
       "      <td>480.000000</td>\n",
       "      <td>738.000000</td>\n",
       "      <td>15500.000000</td>\n",
       "      <td>12.000000</td>\n",
       "      <td>2010.000000</td>\n",
       "      <td>755000.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8 rows × 38 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                Id   MSSubClass  LotFrontage        LotArea  OverallQual  \\\n",
       "count  1460.000000  1460.000000  1201.000000    1460.000000  1460.000000   \n",
       "mean    730.500000    56.897260    70.049958   10516.828082     6.099315   \n",
       "std     421.610009    42.300571    24.284752    9981.264932     1.382997   \n",
       "min       1.000000    20.000000    21.000000    1300.000000     1.000000   \n",
       "25%     365.750000    20.000000    59.000000    7553.500000     5.000000   \n",
       "50%     730.500000    50.000000    69.000000    9478.500000     6.000000   \n",
       "75%    1095.250000    70.000000    80.000000   11601.500000     7.000000   \n",
       "max    1460.000000   190.000000   313.000000  215245.000000    10.000000   \n",
       "\n",
       "       OverallCond    YearBuilt  YearRemodAdd   MasVnrArea   BsmtFinSF1  \\\n",
       "count  1460.000000  1460.000000   1460.000000  1452.000000  1460.000000   \n",
       "mean      5.575342  1971.267808   1984.865753   103.685262   443.639726   \n",
       "std       1.112799    30.202904     20.645407   181.066207   456.098091   \n",
       "min       1.000000  1872.000000   1950.000000     0.000000     0.000000   \n",
       "25%       5.000000  1954.000000   1967.000000     0.000000     0.000000   \n",
       "50%       5.000000  1973.000000   1994.000000     0.000000   383.500000   \n",
       "75%       6.000000  2000.000000   2004.000000   166.000000   712.250000   \n",
       "max       9.000000  2010.000000   2010.000000  1600.000000  5644.000000   \n",
       "\n",
       "           ...         WoodDeckSF  OpenPorchSF  EnclosedPorch  ThreeSsnPorch  \\\n",
       "count      ...        1460.000000  1460.000000    1460.000000    1460.000000   \n",
       "mean       ...          94.244521    46.660274      21.954110       3.409589   \n",
       "std        ...         125.338794    66.256028      61.119149      29.317331   \n",
       "min        ...           0.000000     0.000000       0.000000       0.000000   \n",
       "25%        ...           0.000000     0.000000       0.000000       0.000000   \n",
       "50%        ...           0.000000    25.000000       0.000000       0.000000   \n",
       "75%        ...         168.000000    68.000000       0.000000       0.000000   \n",
       "max        ...         857.000000   547.000000     552.000000     508.000000   \n",
       "\n",
       "       ScreenPorch     PoolArea       MiscVal       MoSold       YrSold  \\\n",
       "count  1460.000000  1460.000000   1460.000000  1460.000000  1460.000000   \n",
       "mean     15.060959     2.758904     43.489041     6.321918  2007.815753   \n",
       "std      55.757415    40.177307    496.123024     2.703626     1.328095   \n",
       "min       0.000000     0.000000      0.000000     1.000000  2006.000000   \n",
       "25%       0.000000     0.000000      0.000000     5.000000  2007.000000   \n",
       "50%       0.000000     0.000000      0.000000     6.000000  2008.000000   \n",
       "75%       0.000000     0.000000      0.000000     8.000000  2009.000000   \n",
       "max     480.000000   738.000000  15500.000000    12.000000  2010.000000   \n",
       "\n",
       "           SalePrice  \n",
       "count    1460.000000  \n",
       "mean   180921.195890  \n",
       "std     79442.502883  \n",
       "min     34900.000000  \n",
       "25%    129975.000000  \n",
       "50%    163000.000000  \n",
       "75%    214000.000000  \n",
       "max    755000.000000  \n",
       "\n",
       "[8 rows x 38 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "house_train.describe() # some descriptive statistics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "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",
      "FirstFlrSF       1460 non-null int64\n",
      "SecFlrSF         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",
      "ThreeSsnPorch    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: 678.7+ KB\n"
     ]
    }
   ],
   "source": [
    "house_train.info() # getting a sense of object types "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1.3 Data Visualization\n",
    "Now we will visualize the data with boxplots, histograms and scatterplots when applicable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeQAAAFZCAYAAABJ+lxSAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa9327b8c>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAfIAAAFYCAYAAACoFn5YAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nvRLwdeG1AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa78548ac>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAfUAAAFZCAYAAACBlraEAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n/B/NvbCwyq9NCQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa75bfc8c>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAfgAAAFYCAYAAAC/NO6RAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nMILOoKDvAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa94b6b4c>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAd8AAAFZCAYAAADZ6SWdAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAFBMfAGgmPgCQDHxBYBi/wNeDO0noXr9DwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa9327a8c>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAfIAAAFYCAYAAACoFn5YAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAb7f9yWdQf93fzWAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa785a3ec>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAdkAAAFZCAYAAADU91XaAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\noBCRBYBC/i9dyfNGJheQ4QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa76b7dec>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAfIAAAFYCAYAAACoFn5YAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAACD/R8BM9mDIPBVxAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa7613f2c>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeoAAAFZCAYAAABXM2zhAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa76ac5ec>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAfIAAAFYCAYAAACoFn5YAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa7327f6c>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeoAAAFZCAYAAABXM2zhAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa6fe0ccc>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAfIAAAFYCAYAAACoFn5YAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa7150d2c>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeoAAAFZCAYAAABXM2zhAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nI9QAABhGqAEAMIxQAwBgGKEGAMCw/wPBZJA7EY+/fwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa718548c>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAfIAAAFYCAYAAACoFn5YAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nhBwAAIMRcgAADPb/JsXtw/I9e4YAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa6f0340c>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeoAAAFZCAYAAABXM2zhAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\njFADAGAwQg0AgMEINQAABvs/zjkmGpOqIiQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa711168c>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAfgAAAFYCAYAAAC/NO6RAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAICBCHgAAAz0/wvDVu1AmsV9AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa70e9eec>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeoAAAFZCAYAAABXM2zhAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa935d74c>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAfIAAAFYCAYAAACoFn5YAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\njCAHAMBg/w/F2pX6+tVSEwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa736170c>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plots the boxplot and histogram of integer valued variables only\n",
    "for v in house_train.select_dtypes(include = ['int64']).columns.values[1:10]:\n",
    "    plt.boxplot(house_train[v])\n",
    "    plt.title(v)\n",
    "    plt.show()\n",
    "    plt.hist(house_train[v])\n",
    "    plt.xlabel(v)\n",
    "    plt.ylabel(\"Frequency\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAfgAAAFnCAYAAABKGFvpAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa934ceac>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAe0AAAFnCAYAAACLnxFFAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa77d706c>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAfIAAAFnCAYAAABdOssgAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzt3XtYlHX+//HXcApIUiDI7LSWqx1EDMm2Axp4AEsLS11T\nsTZ2qyvzsOsBM79Zq2lp6zG3uirTzJQrTBeLwuy3WW3KbuCiZR46GWgKI0cFRPHz+6Nv89VKHK27\n4YPPx3V1Xcw9M/e8Z27tyX3f44zLGGMEAACs5OfrAQAAwOkj5AAAWIyQAwBgMUIOAIDFCDkAABYj\n5AAAWCzA1wMAturQoYMuvvhi+fv7e5ZdcMEFevHFF3041a+vurpaw4YNU21trTIzMxUeHu65bsGC\nBdq7d68ef/xxr9dXX1+vnJwcpaamSpK++eYbTZ8+XV999ZUkKSQkRA8++KB69uyp4uJi9e7dW1u3\nbv1lnxRgEUIO/AxLly5V69atfT2GT23fvl0VFRVav379L7K+rVu3avXq1Z6Qjxs3TrfddpueffZZ\nSVJhYaHuuusuvfXWW7/I4wG249A64IC0tDTNmTNHffr0UUFBgaqqqjR+/HglJyerR48eWrlypee2\nr732mhITE9WvXz8tXrxYHTp0kPTd3uzDDz/sud2xl/fu3av7779fycnJSk5O9kS0uLhYN954o15+\n+WX169dPCQkJysnJkSQZYzRjxgwlJSUpOTlZL7zwgiorKxUbGyu32+15nCeffPIn96Dz8vLUv39/\npaSkaODAgdqyZYv27NmjcePGaf/+/UpJSVFZWZnXr9FPrc/tduvBBx/Uf//7Xw0ZMkSStGPHDsXG\nxnruFxsbq9zc3ON+gcrKylK/fv3UvXt3vfHGG5Kko0eP6rHHHlNycrKSkpI0fvx4HT582LN9FixY\noEGDBun666/X5MmT1dDQIEnKz8/XHXfcoV69emnQoEEqKiry+jkBPmEAnJb27dubb7/99ievGzZs\nmLnnnntMQ0ODMcaYhx56yEyYMME0NDSY/fv3m+7du5vt27eb8vJy06lTJ7Nz505jjDGPPfaYad++\nvTHGmPnz55tJkyZ51nns5eHDh5s5c+YYY4z5+uuvTdeuXU1ZWZkpKioyV155pVm6dKkxxpicnBzT\nq1cvY4wxq1evNoMHDzb19fWmurradO/e3RQWFpr77rvPLFmyxPM4PXr0MJs2bTru+Rw4cMBce+21\n5uOPPzbGGPP222+b3r17m4aGBrNx40bTs2fPn3wdfvgcvFnfypUrzV133eW57ciRI01iYqJZsmSJ\n+fzzz49bT1FRkenQoYN59dVXjTHGvPXWW6ZHjx6edfbt29fU19eburo606dPH7N69WrP9hkwYICp\nqakxNTU1pnfv3uadd94x1dXV5pprrjEffvihMcaYNWvWmP79+//kcwOaCvbIgZ8hLS1NKSkpnv8m\nT57sua579+7y8/vur9g///lPDR8+XH5+foqIiFCvXr20du1abd68Wb/5zW/Url07SfIcTm5MTU2N\n8vLydPfdd0uSLrnkEnXp0sWzV37kyBHdfvvtkqSrrrpKe/bskSS9//77Sk5OVmBgoFq0aKGcnBzF\nxMSob9++evPNNyVJ27Zt09GjR9W5c+fjHnPz5s1q3bq1unTpIklKTk5WeXm5du/efVqv26msb9as\nWRo6dKjWrFmjvn37KikpScuXL/dcb4zxvG5XXnml9u7d61nnypUrFRgYqLPOOksxMTHH7V3fcsst\nCgkJUUhIiBISErRp0ybl5+frvPPO0w033CBJ6tu3r7755hvPawg0RZwjB36Gxs6Rt2zZ0vNzdXW1\nxowZ43lj3KFDh5SSkqLKykqdc845nttFRESc9DGrq6tljNHgwYM9y2pqavS73/1OkuTv76/Q0FBJ\nkp+fn44ePSpJKi8vP+6xvr9NUlKS/ud//kdFRUVat26dUlJSfvSYZWVlx91XksLCwrR///6TzvtT\nTmV9Z511ltLT05Wenq6qqiq9/fbbmj59ui688EK1bdtW/v7+CgkJ+dHzLSsr09SpU7V161a5XC65\n3W7dddddnvUeu31atmypkpISVVVVqaio6LjXICgoSGVlZWrTps1pPVfAaYQc+BVER0dr4cKFat++\n/XHL169fr+rqas/lY88xHxslSaqsrJQkRUZGyt/fXytXrtTZZ5993PqKi4tPOEN4eLjKy8s9l91u\nt4KDg9WiRQslJibq7bffVm5urmbMmPGj+0ZGRqqiosJz2RijyspKRUZGntbeamPr+/LLLz3Ly8rK\n9Nlnn3n2kM855xwNGjRIH3zwgXbs2KG2bdue8DHmzJmjgIAArVmzRkFBQRo7duxx1x/7WlRWVqpl\ny5aKjo7WpZdeqtdff/2UnxPgKxxaB34FSUlJWrFihaTvDn1Pnz5dn376qTp27Kgvv/xSX3/9taTv\n3rT1vejoaO3YsUNHjx5VWVmZ3n//fUlSQECAunfv7llfbW2tHnroIX377bcnneHNN99UfX29ampq\nNGTIEO3YsUPSd4eQly9frrq6OnXs2PFH9+3UqZPcbrc2bdokSXrzzTfVunVrXXjhhaf1ejS2voCA\nAB04cEDGGNXV1WnUqFH64IMPPPfdtWuXCgsLFR8f3+hj7N+/X+3bt1dQUJC2bdumTZs2qaamxnP9\nO++843kt3n//fcXHxys2NlalpaUqLCyUJBUVFWn8+PEyfEkkmjD2yIFfwZgxYzzvoJakhIQEdejQ\nQQEBAZowYYLuvvtuhYWFHXeOPCUlRdnZ2erZs6cuvfRSpaSkeA49P/roo5oyZYpee+01SdKtt96q\n888/v9E98ptvvlnbt29X7969ddZZZ2nAgAGKi4uTJN144406cOCA7rzzzp+8b2hoqObOnaupU6eq\npqZGERERmj17tlwu10mfe25urvLz8z2Xr7jiCs2ZM+eE6+vSpYueeuopJSQkaP369XrmmWc0f/58\nTZs2TcYYtWjRQg899JBiY2Mbfb733HOPMjIy9Prrrys+Pl4ZGRl6+OGH1alTJ0nS1VdfreHDh+vr\nr79Wr1691K1bN/n5+Wn+/PmaOnWqDh48qMDAQI0ePdqr5wn4isvwqybQZOzdu1fdu3fX9u3bf/XH\nvuWWWzRv3jzPG++as7S0NA0YMEC33Xabr0cBfjYOrQPQm2++qaioqDMi4kBzw6F14Az3hz/8QeXl\n5Zo/f76vRwFwGji0DgCAxTi0DgCAxQg5AAAWs/IceWlp9clvBABAMxEVFXbC69gjBwDAYoQcAACL\nEXIAACxGyAEAsBghBwDAYoQcAACLEXIAACxGyAEAsBghBwDAYoQcAACLEXIAACxGyAEAsBghBwDA\nYlZ++9mpSB3d39cjnBFWz1vl6xEA4IzEHjkAABYj5AAAWIyQAwBgMUIOAIDFCDkAABYj5AAAWIyQ\nAwBgMUIOAIDFCDkAABYj5AAAWIyQAwBgMUIOAIDFCDkAABYj5AAAWIyQAwBgMUIOAIDFCDkAABYj\n5AAAWIyQAwBgMUIOAIDFCDkAABYj5AAAWIyQAwBgMUIOAIDFCDkAABYj5AAAWIyQAwBgMUIOAIDF\nCDkAABYj5AAAWIyQAwBgMUIOAIDFCDkAABYj5AAAWCzAqRUfPHhQGRkZqqys1OHDhzVixAi1a9dO\nEyZMUENDg6KiojRr1iwFBQUpOztbS5YskZ+fnwYNGqSBAwc6NRYAAM2KYyFftWqV2rZtq7Fjx2rf\nvn266667dPXVV2vIkCHq06ePZs+eraysLKWmpmrhwoXKyspSYGCgBgwYoF69eqlVq1ZOjQYAQLPh\n2KH18PBwVVRUSJKqqqoUHh6uvLw89ejRQ5KUmJioDRs2qLCwUDExMQoLC1NwcLDi4uJUUFDg1FgA\nADQrjoX8lltu0Z49e9SrVy8NGzZMGRkZqq2tVVBQkCQpMjJSpaWlcrvdioiI8NwvIiJCpaWlTo0F\nAECz4tih9X/84x9q06aNXnzxRW3btk2TJk067npjzE/e70TLjxUeHqqAAP9fZE78MqKiwnw9AgCc\nkRwLeUFBgW688UZJ0uWXX66SkhKFhISorq5OwcHB2rdvn6KjoxUdHS232+25X0lJiTp37tzousvL\na5waG6eptLTa1yMAQLPV2M6SY4fWL7nkEhUWFkqSdu/erbPPPls33HCDcnNzJUlr165VQkKCYmNj\ntWXLFlVVVengwYMqKChQfHy8U2MBANCsOLZH/vvf/16TJk3SsGHDdOTIET366KO67LLLlJGRoczM\nTLVp00apqakKDAzU2LFjlZ6eLpfLpREjRigsjMO0AAB4w2W8OSndxJzKYdzU0f0dnATfWz1vla9H\nAIBmyyeH1gEAgPMIOQAAFiPkAABYjJADAGAxQg4AgMUIOQAAFiPkAABYjJADAGAxQg4AgMUIOQAA\nFiPkAABYjJADAGAxQg4AgMUIOQAAFiPkAABYjJADAGAxQg4AgMUIOQAAFiPkAABYjJADAGAxQg4A\ngMUIOQAAFiPkAABYjJADAGAxQg4AgMUIOQAAFiPkAABYjJADAGAxQg4AgMUIOQAAFiPkAABYjJAD\nAGAxQg4AgMUIOQAAFiPkAABYjJADAGAxQg4AgMUIOQAAFiPkAABYjJADAGAxQg4AgMUIOQAAFiPk\nAABYjJADAGAxQg4AgMUIOQAAFiPkAABYjJADAGAxQg4AgMUIOQAAFiPkAABYjJADAGCxACdXnp2d\nrRdeeEEBAQEaNWqUOnTooAkTJqihoUFRUVGaNWuWgoKClJ2drSVLlsjPz0+DBg3SwIEDnRwLAIBm\nw7GQl5eXa+HChVq5cqVqamq0YMEC5ebmasiQIerTp49mz56trKwspaamauHChcrKylJgYKAGDBig\nXr16qVWrVk6NBgBAs+HYofUNGzbouuuuU4sWLRQdHa2pU6cqLy9PPXr0kCQlJiZqw4YNKiwsVExM\njMLCwhQcHKy4uDgVFBQ4NRYAAM2KY3vkxcXFqqur0/3336+qqiqNHDlStbW1CgoKkiRFRkaqtLRU\nbrdbERERnvtFRESotLTUqbEAAGhWHD1HXlFRoaefflp79uzR8OHDZYzxXHfsz8c60fJjhYeHKiDA\n/xebEz9fVFSYr0cAgDOSYyGPjIzU1VdfrYCAAF188cU6++yz5e/vr7q6OgUHB2vfvn2Kjo5WdHS0\n3G63534lJSXq3Llzo+suL69xamycptLSal+PAADNVmM7S46dI7/xxhu1ceNGHT16VOXl5aqpqdH1\n11+v3NxcSdLatWuVkJCg2NhYbdmyRVVVVTp48KAKCgoUHx/v1FgAADQrju2Rn3feeUpOTtagQYMk\nSZMnT1ZMTIwyMjKUmZmpNm3aKDU1VYGBgRo7dqzS09Plcrk0YsQIhYVxmBYAAG+4jDcnpZuYUzmM\nmzq6v4OT4Hur563y9QgA0Gz55NA6AABwHiEHAMBihBwAAIsRcgAALEbIAQCwGCEHAMBihBwAAIsR\ncgAALEbIAQCwGCEHAMBihBwAAIsRcgAALEbIAQCwGCEHAMBihBwAAIsRcgAALEbIAQCwGCEHAMBi\nhBwAAIt5FfKJEyf+aFl6evovPgwAADg1AY1dmZ2drRUrVmjnzp0aOnSoZ/nhw4fldrsdHw4AADSu\n0ZDfeuutuvbaazVu3DiNHDnSs9zPz0/t2rVzfDgAANC4RkMuSeedd56WLl2q6upqVVRUeJZXV1er\nVatWjg4HAAAad9KQS9K0adO0cuVKRUREyBgjSXK5XHr33XcdHQ4AADTOq5Dn5eVp48aNOuuss5ye\nBwAAnAKv3rV+ySWXEHEAAJogr/bIW7duraFDh6pLly7y9/f3LB89erRjgwEAgJPzKuStWrXSdddd\n5/QsAADgFHkV8gceeMDpOQAAwGnwKuRXXnmlXC6X57LL5VJYWJjy8vIcGwwAAJycVyHftm2b5+f6\n+npt2LBB27dvd2woAADgHa9CfqygoCB1795dixYt0r333uvETIDH7//+B1+P0OxlPvCSr0cA8DN4\nFfKsrKzjLu/du1f79u1zZCAAAOA9r0Ken59/3OUWLVpo7ty5jgwEAAC851XIZ8yYIUmqqKiQy+VS\ny5YtHR0KAAB4x6uQFxQUaMKECTp48KCMMWrVqpVmzZqlmJgYp+cDAACN8Crkf/vb3/T3v/9d7du3\nlyRt3bpVjz/+uJYtW+bocAAAoHFefda6n5+fJ+LSd/+u/NiPagUAAL7hdchzc3N14MABHThwQDk5\nOYQcAIAmwKtD64899pimTp2qyZMny8/PT5dffrmmTZvm9GwAAOAkvNoj/9e//qWgoCD95z//UV5e\nno4ePar169c7PRsAADgJr0KenZ2tp59+2nN50aJFWrNmjWNDAQAA73gV8oaGhuPOifv5eXU3AADg\nMK/OkSclJWnw4MHq0qWLjh49qo0bN6p3795OzwYAAE7C6+8j79q1qzZv3iyXy6UpU6aoc+fOTs8G\nAABOwutvP4uPj1d8fLyTswAAgFPEyW4AACxGyAEAsBghBwDAYoQcAACLEXIAACxGyAEAsBghBwDA\nYo6GvK6uTj179tTrr7+ub7/9VmlpaRoyZIhGjx6t+vp6Sd99jvsdd9yhgQMH6rXXXnNyHAAAmh1H\nQ/7MM8+oZcuWkqT58+dryJAhevXVV3XJJZcoKytLNTU1WrhwoRYvXqylS5dqyZIlqqiocHIkAACa\nFcdC/sUXX+jzzz/XTTfdJEnKy8tTjx49JEmJiYnasGGDCgsLFRMTo7CwMAUHBysuLk4FBQVOjQQA\nQLPjWMiffPJJTZw40XO5trZWQUFBkqTIyEiVlpbK7XYrIiLCc5uIiAiVlpY6NRIAAM2O15+1fipW\nr16tzp0766KLLvrJ640xp7T8h8LDQxUQ4H/yG+JXExUV5usRcJrYdoDdHAn5e++9p6KiIr333nva\nu3evgoKCFBoaqrq6OgUHB2vfvn2Kjo5WdHS03G63534lJSVefataeXmNE2PjZygtrfb1CDhNbDug\n6WvsF25HQj537lzPzwsWLNAFF1ygTZs2KTc3V7fddpvWrl2rhIQExcbGavLkyaqqqpK/v78KCgo0\nadIkJ0YCAKBZciTkP2XkyJHKyMhQZmam2rRpo9TUVAUGBmrs2LFKT0+Xy+XSiBEjFBbGYT4AALzl\neMhHjhzp+fmll1760fUpKSlKSUlxegwAAJolPtkNAACLEXIAACxGyAEAsBghBwDAYoQcAACLEXIA\nACxGyAEAsBghBwDAYoQcAACLEXIAACxGyAEAsBghBwDAYoQcAACLEXIAACxGyAEAsBghBwDAYoQc\nAACLEXIAACxGyAEAsBghBwDAYoQcAACLEXIAACxGyAEAsBghBwDAYoQcAACLEXIAACxGyAEAsBgh\nBwDAYoQcAACLEXIAACxGyAEAsBghBwDAYoQcAACLEXIAACxGyAEAsBghBwDAYoQcAACLEXIAACxG\nyAEAsBghBwDAYoQcAACLEXIAACxGyAEAsBghBwDAYoQcAACLEXIAACxGyAEAsBghBwDAYoQcAACL\nEXIAACxGyAEAsBghBwDAYoQcAACLBTi58pkzZyo/P19HjhzRfffdp5iYGE2YMEENDQ2KiorSrFmz\nFBQUpOzsbC1ZskR+fn4aNGiQBg4c6ORYAAA0G46FfOPGjdq5c6cyMzNVXl6u/v3767rrrtOQIUPU\np08fzZ49W1lZWUpNTdXChQuVlZWlwMBADRgwQL169VKrVq2cGg0AgGbDsUPr11xzjebNmydJOuec\nc1RbW6u8vDz16NFDkpSYmKgNGzaosLBQMTExCgsLU3BwsOLi4lRQUODUWAAANCuO7ZH7+/srNDRU\nkpSVlaVu3brpww8/VFBQkCQpMjJSpaWlcrvdioiI8NwvIiJCpaWlja47PDxUAQH+To2O0xAVFebr\nEXCa2HaA3Rw9Ry5J69atU1ZWlhYtWqTevXt7lhtjfvL2J1p+rPLyml9sPvwySkurfT0CThPbDmj6\nGvuF29F3rX/wwQd69tln9fzzzyssLEyhoaGqq6uTJO3bt0/R0dGKjo6W2+323KekpETR0dFOjgUA\nQLPhWMirq6s1c+ZMPffcc543rl1//fXKzc2VJK1du1YJCQmKjY3Vli1bVFVVpYMHD6qgoEDx8fFO\njQUAQLPi2KH1nJwclZeXa8yYMZ5lTzzxhCZPnqzMzEy1adNGqampCgwM1NixY5Weni6Xy6URI0Yo\nLIxzdgAAeMNlvDkp3cScyjm91NH9HZwE31s9b5Uj6/393//gyHrxfzIfeMnXIwA4CZ+dIwcAAM4i\n5AAAWIyQAwBgMUIOAIDFCDkAABYj5AAAWIyQAwBgMUIOAIDFCDkAABYj5AAAWIyQAwBgMUIOAIDF\nCDkAABYj5AAAWIyQAwBgMUIOAIDFCDkAABYj5AAAWIyQAwBgMUIOAIDFCDkAABYj5AAAWIyQAwBg\nMUIOAIDFCDkAABYj5AAAWIyQAwBgMUIOAIDFCDkAABYj5AAAWIyQAwBgMUIOAIDFCDkAABYj5AAA\nWIyQAwBgMUIOAIDFCDkAABYj5AAAWIyQAwBgMUIOAIDFCDkAABYj5AAAWIyQAwBgsQBfDwCgeRrz\n1iRfj3BGmNtnuq9HgI+xRw4AgMUIOQAAFiPkAABYjJADAGAxQg4AgMUIOQAAFiPkAABYjJADAGCx\nJvOBMNOnT1dhYaFcLpcmTZqkTp06+XokAACavCYR8n//+9/atWuXMjMz9cUXX2jSpEnKzMz09VgA\ncMZ6ccvzvh6h2UuP+dMvsp4mcWh9w4YN6tmzpyTpsssuU2VlpQ4cOODjqQAAaPqaRMjdbrfCw8M9\nlyMiIlRaWurDiQAAsEOTOLT+Q8aYRq+Pigrzel3/enXdzx0HPvT/pmT5egScpmXDF/h6BPwME5P+\n4usR4KUmsUceHR0tt9vtuVxSUqKoqCgfTgQAgB2aRMhvuOEG5ebmSpI+/fRTRUdHq0WLFj6eCgCA\npq9JHFqPi4vTVVddpcGDB8vlcmnKlCm+HgkAACu4zMlOSAMAgCarSRxaBwAAp4eQAwBgsSZxjvxM\nU1xcrH79+qljx46SpPr6erVv316PPvqo/P39fTwdvFFcXKxRo0Zp2LBhmjdvni6++GJJUk1NjQYM\nGKA777xTkrRjxw498MADuvvuuzVs2DBfjoz/5e22mzlzpvLz83XkyBHdd9996t27ty/Hxv/yZvvV\n1tZq4sSJ2r9/vw4dOqQHHnhAiYmJPp7cOYTcR9q2baulS5d6Lk+cOFFr1qxRamqqD6fC6bj55puV\nkZEh6btfylJTU5WQkKCIiAhNnTpV1113nY8nxImcaNsVFxdr586dyszMVHl5ufr370/Im6ATbb/N\nmzerY8eO+tOf/qTdu3frnnvuIeRwXqdOnbRr1y4tW7ZMa9askZ+fn3r27Kl77rlHe/fu1ejRoxUY\nGKj4+Hjl5+cf90sAmo6goCC1b99eRUVFat26tZ5//nk9/zyfWW2DY7dd165dPV/cdM4556i2tlYN\nDQ0cMWvCjt1+N998s2f5t99+q/POO8+HkzmPc+RNwOHDh/Xuu++qZcuWevvtt7V8+XItW7ZMa9eu\n1Z49e7R48WL16dNHr7zyiurr6309Lhrhdru1efNmtW/fXgEBAQoODvb1SPDSsdvO399foaGhkqSs\nrCx169aNiDdxx26/7w0ePFjjxo3TpEmTfDiZ89gj95GvvvpKaWlpkqTt27frj3/8o6Kjo7Vr1y4N\nHz5cknTw4EHt3r1bX3zxhec3zKSkJG3ZssVnc+PHcnJy9Mknn+jQoUNyu92aPHmyIiMjfT0WvHCy\nbbdu3TplZWVp0aJFPpwSJ3Ky7bdixQp99tlnGj9+vLKzs+VyuXw4rXMIuY8ce4581KhRatu2rSTp\npptu0l//+tfjbvvcc895/gA21z+INvv+PF1tba1uv/12XXnllb4eCV5qbNt98MEHevbZZ/XCCy8o\nLMz773fAr+dE2++TTz5RZGSkzj//fF1xxRVqaGhQWVlZs/0Fm0PrTcD48eP11FNP6aqrrlJeXp5q\na2tljNG0adNUV1eniy++WJ988okk6f333/fxtDiRkJAQjRgxQtOnT/f1KDhFP9x21dXVmjlzpp57\n7jm1atXKx9PhZH64/T7++GPPURS3262amprjvmGzuSHkTcBFF12k5ORkrVixQsOHD9fQoUM1aNAg\nRUVFKTg4WMOHD1dmZqbuvvtuSZKfH5utqerbt69KSkr04Ycf6pNPPlFaWppWrVqll19+WWlpaaqo\nqPD1iDiBY7ddTk6OysvLNWbMGKWlpSktLU179uzx9YhoxLHbb/DgwSorK9OQIUN077336pFHHmnW\n/9/kI1otsHPnTlVVValLly564403lJeXp6lTp/p6LABAE8A5cgucffbZeuSRR+RyueTn56cZM2b4\neiQAQBPBHjkAABZrvicNAAA4AxByAAAsRsgBALAYIQeaoeLiYnXr1s3r269fv97zT+PKyso0atQo\nDR06VMOGDdPAgQO1YcMGSdKCBQs0Z84cR2YGcHoIOQAtXrxYlZWVkqTZs2crLi5Oy5Yt0yuvvKIp\nU6Zo7ty54n2xQNPEPz8DziBZWVlasWKFQkJCFBkZqWnTpik7O1sff/yxxo0bpxkzZqiyslIHDhzw\n3Kdjx47KzMz0XN63b59GjRqlL7/8Ul27dtUjjzyimpoaZWRkqKKiQgcPHlRKSoruvfde5eXlae7c\nuWrTpo12796tsLAwzZkzRy1atFBOTo5eeeUVGWMUERGhadOmNetP3wIcYwA0O0VFRSYhIeG4Zbt3\n7zbdunUz1dXVxhhjnnjiCbNgwQJjjDGJiYnm66+/NsYYs3XrVnPTTTeZlJQU89hjj5n33nvPNDQ0\nGGOMmT9/vhk8eLA5fPiwqaurM507dzZlZWXmm2++MatWrTLGGHPo0CETFxdnqqurzcaNG01MTIzZ\nu3evMcaYcePGmSVLlpg9e/aYfv36mUOHDhljjFm8eLGZMWOG8y8M0AyxRw6cIbZu3aqrrrpKLVq0\nkCR17doZ/zR2AAACMUlEQVRVK1as+NHtrrjiCq1bt075+fnKy8vTzJkz9eyzz+qVV16RJHXp0kUB\nAQEKCAhQeHi4qqurde655yo/P18rVqxQYGCgDh065Dnn3q5dO8/3QcfFxemzzz7Tueeeq9LSUqWn\np0uS6uvrdeGFF/4aLwPQ7BBy4AxljPnJb9Orra1VSEiIunbtqq5du+r+++9XcnKytm3bJkk/+l5u\nY4yWLFmi+vp6LV++XC6XS9dee+1x1//wMYOCgtSpUyc999xzDj074MzBm92AM0THjh316aefes5/\nf/TRR4qNjZX03dfjHjlyRA0NDerTp4/y8vI89ysvL1d9fb1at259wnXv379fl112mVwul959913V\n1dWpvr5ekvTll1+qpKREkpSfn68OHTooJiZGmzdvVmlpqSTprbfe0rp16xx53kBzx0e0As1QcXGx\nUlJSdPXVV3uWxcTEqF27dlq+fLmCgoLUunVrTZ06VaGhoZoyZYo++ugjPfnkkwoODtbMmTNVX1+v\nwMBA1dfX67777tNNN92kBQsW6MiRI/rzn/8sSUpKStJLL72kmpoa/eUvf1FUVJR69OihnTt3auvW\nrcrIyNDMmTP129/+Vrt27VLLli01e/ZshYaG6o033tCiRYsUEhKi4OBgPfnkkzr33HN99ZIB1iLk\nABzz/bvWly9f7utRgGaLQ+sAAFiMPXIAACzGHjkAABYj5AAAWIyQAwBgMUIOAIDFCDkAABYj5AAA\nWOz/AyXjUzDTv8PjAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa75e3f4c>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAfgAAAFnCAYAAABKGFvpAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAGAgCh4AAAP9P+gTWi3SoDW5AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa76dd8ac>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# grabbing the boxplots of the categorical variables\n",
    "for v in house_train.select_dtypes(include = ['object']).columns.values[1:5]:\n",
    "    sns.countplot(x=v, data=house_train, palette=\"Greens_d\")\n",
    "    plt.title(\"Frequency of \" + v)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "max must be larger than min in range parameter.",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-8-a3d417e599b3>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m# plotting the scatterplot of the float variables\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0;31m#for v in house_train.select_dtypes(include = ['float64']).columns.values[1:(house_train.shape[0]-1)]:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0msns\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpairplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mhouse_train\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mselect_dtypes\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0minclude\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m'float64'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshow\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/home/rxu17/anaconda2/lib/python2.7/site-packages/seaborn/linearmodels.pyc\u001b[0m in \u001b[0;36mpairplot\u001b[0;34m(data, hue, hue_order, palette, vars, x_vars, y_vars, kind, diag_kind, markers, size, aspect, dropna, plot_kws, diag_kws, grid_kws)\u001b[0m\n\u001b[1;32m   1607\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mgrid\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msquare_grid\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1608\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mdiag_kind\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m\"hist\"\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1609\u001b[0;31m             \u001b[0mgrid\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmap_diag\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhist\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mdiag_kws\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1610\u001b[0m         \u001b[0;32melif\u001b[0m \u001b[0mdiag_kind\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m\"kde\"\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1611\u001b[0m             \u001b[0mdiag_kws\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m\"legend\"\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mFalse\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/home/rxu17/anaconda2/lib/python2.7/site-packages/seaborn/axisgrid.pyc\u001b[0m in \u001b[0;36mmap_diag\u001b[0;34m(self, func, **kwargs)\u001b[0m\n\u001b[1;32m   1346\u001b[0m                 \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1347\u001b[0m                     func(vals, color=self.palette, histtype=\"barstacked\",\n\u001b[0;32m-> 1348\u001b[0;31m                          **kwargs)\n\u001b[0m\u001b[1;32m   1349\u001b[0m             \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1350\u001b[0m                 \u001b[0;32mfor\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlabel_k\u001b[0m \u001b[0;32min\u001b[0m \u001b[0menumerate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhue_names\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/home/rxu17/anaconda2/lib/python2.7/site-packages/matplotlib/pyplot.pyc\u001b[0m in \u001b[0;36mhist\u001b[0;34m(x, bins, range, normed, weights, cumulative, bottom, histtype, align, orientation, rwidth, log, color, label, stacked, hold, data, **kwargs)\u001b[0m\n\u001b[1;32m   3080\u001b[0m                       \u001b[0mhisttype\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mhisttype\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0malign\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0malign\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0morientation\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0morientation\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3081\u001b[0m                       \u001b[0mrwidth\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mrwidth\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlog\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mlog\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcolor\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcolor\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlabel\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mlabel\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 3082\u001b[0;31m                       stacked=stacked, data=data, **kwargs)\n\u001b[0m\u001b[1;32m   3083\u001b[0m     \u001b[0;32mfinally\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3084\u001b[0m         \u001b[0max\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_hold\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mwashold\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/home/rxu17/anaconda2/lib/python2.7/site-packages/matplotlib/__init__.pyc\u001b[0m in \u001b[0;36minner\u001b[0;34m(ax, *args, **kwargs)\u001b[0m\n\u001b[1;32m   1890\u001b[0m                     warnings.warn(msg % (label_namer, func.__name__),\n\u001b[1;32m   1891\u001b[0m                                   RuntimeWarning, stacklevel=2)\n\u001b[0;32m-> 1892\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mfunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0max\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1893\u001b[0m         \u001b[0mpre_doc\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0minner\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__doc__\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1894\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mpre_doc\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/home/rxu17/anaconda2/lib/python2.7/site-packages/matplotlib/axes/_axes.pyc\u001b[0m in \u001b[0;36mhist\u001b[0;34m(self, x, bins, range, normed, weights, cumulative, bottom, histtype, align, orientation, rwidth, log, color, label, stacked, **kwargs)\u001b[0m\n\u001b[1;32m   6190\u001b[0m             \u001b[0;31m# this will automatically overwrite bins,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   6191\u001b[0m             \u001b[0;31m# so that each histogram uses the same bins\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 6192\u001b[0;31m             \u001b[0mm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbins\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhistogram\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbins\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mweights\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mw\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mhist_kwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   6193\u001b[0m             \u001b[0mm\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mastype\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfloat\u001b[0m\u001b[0;34m)\u001b[0m  \u001b[0;31m# causes problems later if it's an int\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   6194\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mmlast\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/home/rxu17/anaconda2/lib/python2.7/site-packages/numpy/lib/function_base.pyc\u001b[0m in \u001b[0;36mhistogram\u001b[0;34m(a, bins, range, normed, weights, density)\u001b[0m\n\u001b[1;32m    500\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mmn\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0mmx\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    501\u001b[0m         raise ValueError(\n\u001b[0;32m--> 502\u001b[0;31m             'max must be larger than min in range parameter.')\n\u001b[0m\u001b[1;32m    503\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mall\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0misfinite\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mmn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmx\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    504\u001b[0m         raise ValueError(\n",
      "\u001b[0;31mValueError\u001b[0m: max must be larger than min in range parameter."
     ]
    }
   ],
   "source": [
    "# plotting the scatterplot of the float variables\n",
    "#for v in house_train.select_dtypes(include = ['float64']).columns.values[1:(house_train.shape[0]-1)]:\n",
    "sns.pairplot(house_train.select_dtypes(include = ['float64'])) \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a result of the above, we have a bunch of categorical variables that we need to change to numeric form if we are to perform regression. We also have some variables with only years that we will change from year to number of years till our current year: 2017. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1.3 Summary Statistics\n",
    "Now we look at stats such as R-Squared, P-value of the non categorical variables. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Variable</th>\n",
       "      <th>R_Squared</th>\n",
       "      <th>P_value</th>\n",
       "      <th>F_stat</th>\n",
       "      <th>Correlation</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>MSSubClass</td>\n",
       "      <td>0.007104</td>\n",
       "      <td>1.266472e-03</td>\n",
       "      <td>10.431466</td>\n",
       "      <td>-0.084284</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>LotFrontage</td>\n",
       "      <td>0.123763</td>\n",
       "      <td>2.602442e-36</td>\n",
       "      <td>169.350639</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>LotArea</td>\n",
       "      <td>0.069613</td>\n",
       "      <td>1.123139e-24</td>\n",
       "      <td>109.090355</td>\n",
       "      <td>0.263843</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>OverallQual</td>\n",
       "      <td>0.625652</td>\n",
       "      <td>2.185675e-313</td>\n",
       "      <td>2436.770591</td>\n",
       "      <td>0.790982</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>OverallCond</td>\n",
       "      <td>0.006062</td>\n",
       "      <td>2.912351e-03</td>\n",
       "      <td>8.891623</td>\n",
       "      <td>-0.077856</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>YearBuilt</td>\n",
       "      <td>0.273422</td>\n",
       "      <td>2.990229e-103</td>\n",
       "      <td>548.665821</td>\n",
       "      <td>-0.522897</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>YearRemodAdd</td>\n",
       "      <td>0.257151</td>\n",
       "      <td>3.164948e-96</td>\n",
       "      <td>504.714855</td>\n",
       "      <td>-0.507101</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>MasVnrArea</td>\n",
       "      <td>0.228000</td>\n",
       "      <td>1.458509e-83</td>\n",
       "      <td>428.237393</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>BsmtFinSF1</td>\n",
       "      <td>0.149320</td>\n",
       "      <td>3.394110e-53</td>\n",
       "      <td>255.923517</td>\n",
       "      <td>0.386420</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>BsmtFinSF2</td>\n",
       "      <td>0.000129</td>\n",
       "      <td>6.639987e-01</td>\n",
       "      <td>0.188780</td>\n",
       "      <td>-0.011378</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Variable  R_Squared        P_value       F_stat  Correlation\n",
       "0    MSSubClass   0.007104   1.266472e-03    10.431466    -0.084284\n",
       "1   LotFrontage   0.123763   2.602442e-36   169.350639          NaN\n",
       "2       LotArea   0.069613   1.123139e-24   109.090355     0.263843\n",
       "3   OverallQual   0.625652  2.185675e-313  2436.770591     0.790982\n",
       "4   OverallCond   0.006062   2.912351e-03     8.891623    -0.077856\n",
       "5     YearBuilt   0.273422  2.990229e-103   548.665821    -0.522897\n",
       "6  YearRemodAdd   0.257151   3.164948e-96   504.714855    -0.507101\n",
       "7    MasVnrArea   0.228000   1.458509e-83   428.237393          NaN\n",
       "8    BsmtFinSF1   0.149320   3.394110e-53   255.923517     0.386420\n",
       "9    BsmtFinSF2   0.000129   6.639987e-01     0.188780    -0.011378"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# some feature engineering: Changing years: Year Built changed to how many years since current year, Year Remodeled changed to how many years since current year\n",
    "current_yr = 2017\n",
    "house_train['YearBuilt'] = abs(house_train['YearBuilt'] - current_yr)\n",
    "house_train['YearRemodAdd'] = abs(house_train['YearRemodAdd'] - current_yr)\n",
    "\n",
    "def singleVarModelStat(dataset, variables, dep_var):\n",
    "    single_var_stat = pd.DataFrame(columns = ['Variable', 'R_Squared', 'P_value', 'F_stat', 'Correlation'])\n",
    "    i = 0\n",
    "    for v in variables:\n",
    "        formula = dep_var + \"~\" + v\n",
    "        model = ols(formula, data = dataset).fit()\n",
    "        single_var_stat.loc[i] = [v, model.rsquared, model.f_pvalue, model.fvalue, np.corrcoef(dataset[dep_var], dataset[v])[0,1]]\n",
    "        i += 1\n",
    "    return single_var_stat\n",
    "\n",
    "single_var_stat = singleVarModelStat(house_train, house_train.select_dtypes(include = ['int64', 'float64']).columns.values[1:35], 'SalePrice')\n",
    "single_var_stat.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2.1 Replacing Missing Values\n",
    "There are many ways to replace missing values - mean, mode, or using machine learning tools to predict the missing values:\n",
    "For simplicity:\n",
    "- using mode for categorical missing values\n",
    "- using mean for continous missing "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Id</th>\n",
       "      <th>MSSubClass</th>\n",
       "      <th>MSZoning</th>\n",
       "      <th>LotFrontage</th>\n",
       "      <th>LotArea</th>\n",
       "      <th>Street</th>\n",
       "      <th>Alley</th>\n",
       "      <th>LotShape</th>\n",
       "      <th>LandContour</th>\n",
       "      <th>Utilities</th>\n",
       "      <th>...</th>\n",
       "      <th>PoolArea</th>\n",
       "      <th>PoolQC</th>\n",
       "      <th>Fence</th>\n",
       "      <th>MiscFeature</th>\n",
       "      <th>MiscVal</th>\n",
       "      <th>MoSold</th>\n",
       "      <th>YrSold</th>\n",
       "      <th>SaleType</th>\n",
       "      <th>SaleCondition</th>\n",
       "      <th>SalePrice</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>60</td>\n",
       "      <td>RL</td>\n",
       "      <td>65.0</td>\n",
       "      <td>8450</td>\n",
       "      <td>Pave</td>\n",
       "      <td>Grvl</td>\n",
       "      <td>Reg</td>\n",
       "      <td>Lvl</td>\n",
       "      <td>AllPub</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>Gd</td>\n",
       "      <td>MnPrv</td>\n",
       "      <td>Shed</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>2008</td>\n",
       "      <td>WD</td>\n",
       "      <td>Normal</td>\n",
       "      <td>208500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>20</td>\n",
       "      <td>RL</td>\n",
       "      <td>80.0</td>\n",
       "      <td>9600</td>\n",
       "      <td>Pave</td>\n",
       "      <td>Grvl</td>\n",
       "      <td>Reg</td>\n",
       "      <td>Lvl</td>\n",
       "      <td>AllPub</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>Gd</td>\n",
       "      <td>MnPrv</td>\n",
       "      <td>Shed</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>2007</td>\n",
       "      <td>WD</td>\n",
       "      <td>Normal</td>\n",
       "      <td>181500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>60</td>\n",
       "      <td>RL</td>\n",
       "      <td>68.0</td>\n",
       "      <td>11250</td>\n",
       "      <td>Pave</td>\n",
       "      <td>Grvl</td>\n",
       "      <td>IR1</td>\n",
       "      <td>Lvl</td>\n",
       "      <td>AllPub</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>Gd</td>\n",
       "      <td>MnPrv</td>\n",
       "      <td>Shed</td>\n",
       "      <td>0</td>\n",
       "      <td>9</td>\n",
       "      <td>2008</td>\n",
       "      <td>WD</td>\n",
       "      <td>Normal</td>\n",
       "      <td>223500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>70</td>\n",
       "      <td>RL</td>\n",
       "      <td>60.0</td>\n",
       "      <td>9550</td>\n",
       "      <td>Pave</td>\n",
       "      <td>Grvl</td>\n",
       "      <td>IR1</td>\n",
       "      <td>Lvl</td>\n",
       "      <td>AllPub</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>Gd</td>\n",
       "      <td>MnPrv</td>\n",
       "      <td>Shed</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>2006</td>\n",
       "      <td>WD</td>\n",
       "      <td>Abnorml</td>\n",
       "      <td>140000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>60</td>\n",
       "      <td>RL</td>\n",
       "      <td>84.0</td>\n",
       "      <td>14260</td>\n",
       "      <td>Pave</td>\n",
       "      <td>Grvl</td>\n",
       "      <td>IR1</td>\n",
       "      <td>Lvl</td>\n",
       "      <td>AllPub</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>Gd</td>\n",
       "      <td>MnPrv</td>\n",
       "      <td>Shed</td>\n",
       "      <td>0</td>\n",
       "      <td>12</td>\n",
       "      <td>2008</td>\n",
       "      <td>WD</td>\n",
       "      <td>Normal</td>\n",
       "      <td>250000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 81 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   Id  MSSubClass MSZoning  LotFrontage  LotArea Street Alley LotShape  \\\n",
       "0   1          60       RL         65.0     8450   Pave  Grvl      Reg   \n",
       "1   2          20       RL         80.0     9600   Pave  Grvl      Reg   \n",
       "2   3          60       RL         68.0    11250   Pave  Grvl      IR1   \n",
       "3   4          70       RL         60.0     9550   Pave  Grvl      IR1   \n",
       "4   5          60       RL         84.0    14260   Pave  Grvl      IR1   \n",
       "\n",
       "  LandContour Utilities    ...     PoolArea PoolQC  Fence MiscFeature MiscVal  \\\n",
       "0         Lvl    AllPub    ...            0     Gd  MnPrv        Shed       0   \n",
       "1         Lvl    AllPub    ...            0     Gd  MnPrv        Shed       0   \n",
       "2         Lvl    AllPub    ...            0     Gd  MnPrv        Shed       0   \n",
       "3         Lvl    AllPub    ...            0     Gd  MnPrv        Shed       0   \n",
       "4         Lvl    AllPub    ...            0     Gd  MnPrv        Shed       0   \n",
       "\n",
       "  MoSold YrSold  SaleType  SaleCondition  SalePrice  \n",
       "0      2   2008        WD         Normal     208500  \n",
       "1      5   2007        WD         Normal     181500  \n",
       "2      9   2008        WD         Normal     223500  \n",
       "3      2   2006        WD        Abnorml     140000  \n",
       "4     12   2008        WD         Normal     250000  \n",
       "\n",
       "[5 rows x 81 columns]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# This method checks for missing in dataset, removes them and replaces with the mean of that particular predictor var\n",
    "#  if its an numeric value other wise it replaces the missing value with the most common value \n",
    "#\n",
    "def fillMissingValues(dataset, typeItem):\n",
    "        dataset_obj = dataset.select_dtypes(include = [typeItem]).copy()\n",
    "        dataset_null = dataset_obj.isnull().any()[dataset_obj.isnull().any() == True]\n",
    "        for v in dataset_null.index.values:\n",
    "            if typeItem == 'int64' or typeItem == 'float64':\n",
    "                mean_val = np.mean(dataset[v])\n",
    "                if typeItem == 'int64':\n",
    "                    mean_val = int(mean_val)\n",
    "                dataset_obj = dataset_obj.fillna({v: mean_val}) \n",
    "            elif typeItem == 'object':\n",
    "                cur_var = dataset_obj[v].value_counts()\n",
    "                max_value = cur_var[cur_var.index.values[0]]\n",
    "                pop_value = cur_var.index.values[0]\n",
    "                for i in cur_var.index.values: # check for most frequent value\n",
    "                    max_value = cur_var[i]\n",
    "                    if cur_var[i] > max_value:\n",
    "                        max_value = cur_var[i]\n",
    "                        pop_value = i \n",
    "                dataset_obj = dataset_obj.fillna({v: pop_value}) \n",
    "        return dataset_obj\n",
    "\n",
    "# This function replaces the updated columns of the previous processes in the original dataset\n",
    "def replaceOldDataset(old_dataset, new_columns):\n",
    "    for col in new_columns.columns.values:\n",
    "        if(old_dataset[col].dtype == 'float64' or old_dataset[col].dtype == 'int64'):\n",
    "            old_dataset[col] = new_columns[col]\n",
    "        else:\n",
    "            old_dataset[col] = new_columns[col]\n",
    "    return old_dataset\n",
    "\n",
    "#since for my dataset, we have missing values for every type\n",
    "house_train_miss1 = fillMissingValues(house_train, 'int64')\n",
    "house_train_miss2 = fillMissingValues(house_train, 'float64')\n",
    "house_train_miss3 = fillMissingValues(house_train, 'object')\n",
    "\n",
    "house_train = replaceOldDataset(house_train, house_train_miss1)\n",
    "house_train = replaceOldDataset(house_train, house_train_miss2)\n",
    "house_train = replaceOldDataset(house_train, house_train_miss3)\n",
    "\n",
    "house_train.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2.2 Encoding Categorical Values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Id</th>\n",
       "      <th>MSSubClass</th>\n",
       "      <th>MSZoning</th>\n",
       "      <th>LotFrontage</th>\n",
       "      <th>LotArea</th>\n",
       "      <th>Street</th>\n",
       "      <th>Alley</th>\n",
       "      <th>LotShape</th>\n",
       "      <th>LandContour</th>\n",
       "      <th>Utilities</th>\n",
       "      <th>...</th>\n",
       "      <th>PoolArea</th>\n",
       "      <th>PoolQC</th>\n",
       "      <th>Fence</th>\n",
       "      <th>MiscFeature</th>\n",
       "      <th>MiscVal</th>\n",
       "      <th>MoSold</th>\n",
       "      <th>YrSold</th>\n",
       "      <th>SaleType</th>\n",
       "      <th>SaleCondition</th>\n",
       "      <th>SalePrice</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>60</td>\n",
       "      <td>3</td>\n",
       "      <td>65.0</td>\n",
       "      <td>8450</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>2008</td>\n",
       "      <td>8</td>\n",
       "      <td>4</td>\n",
       "      <td>208500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>20</td>\n",
       "      <td>3</td>\n",
       "      <td>80.0</td>\n",
       "      <td>9600</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>2007</td>\n",
       "      <td>8</td>\n",
       "      <td>4</td>\n",
       "      <td>181500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>60</td>\n",
       "      <td>3</td>\n",
       "      <td>68.0</td>\n",
       "      <td>11250</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>9</td>\n",
       "      <td>2008</td>\n",
       "      <td>8</td>\n",
       "      <td>4</td>\n",
       "      <td>223500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>70</td>\n",
       "      <td>3</td>\n",
       "      <td>60.0</td>\n",
       "      <td>9550</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>2006</td>\n",
       "      <td>8</td>\n",
       "      <td>0</td>\n",
       "      <td>140000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>60</td>\n",
       "      <td>3</td>\n",
       "      <td>84.0</td>\n",
       "      <td>14260</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>12</td>\n",
       "      <td>2008</td>\n",
       "      <td>8</td>\n",
       "      <td>4</td>\n",
       "      <td>250000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 81 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   Id  MSSubClass  MSZoning  LotFrontage  LotArea  Street  Alley  LotShape  \\\n",
       "0   1          60         3         65.0     8450       1      0         3   \n",
       "1   2          20         3         80.0     9600       1      0         3   \n",
       "2   3          60         3         68.0    11250       1      0         0   \n",
       "3   4          70         3         60.0     9550       1      0         0   \n",
       "4   5          60         3         84.0    14260       1      0         0   \n",
       "\n",
       "   LandContour  Utilities    ...      PoolArea  PoolQC  Fence  MiscFeature  \\\n",
       "0            3          0    ...             0       2      2            2   \n",
       "1            3          0    ...             0       2      2            2   \n",
       "2            3          0    ...             0       2      2            2   \n",
       "3            3          0    ...             0       2      2            2   \n",
       "4            3          0    ...             0       2      2            2   \n",
       "\n",
       "   MiscVal  MoSold  YrSold  SaleType  SaleCondition  SalePrice  \n",
       "0        0       2    2008         8              4     208500  \n",
       "1        0       5    2007         8              4     181500  \n",
       "2        0       9    2008         8              4     223500  \n",
       "3        0       2    2006         8              0     140000  \n",
       "4        0      12    2008         8              4     250000  \n",
       "\n",
       "[5 rows x 81 columns]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# This changes categorical values (objects) to type int (creates an Encoder object)\n",
    "def encodingCategorical(dataset):\n",
    "    le = LabelEncoder()\n",
    "    for var in dataset.columns.values:\n",
    "        le.fit(dataset[var])\n",
    "        dataset[var] = le.transform(dataset[var])\n",
    "    return dataset\n",
    "\n",
    "house_train_miss3 = fillMissingValues(house_train, 'object')\n",
    "house_train_miss3 = encodingCategorical(house_train_miss3)\n",
    "house_train = replaceOldDataset(house_train, house_train_miss3)\n",
    "\n",
    "house_train.head()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2.3 Multicollinearity \n",
    "Another main issue in regression is the deal with multicollinearity which will increase standard errors. We will locate the variables with high multicollinearity by using variance inflation factors (VIFs)and remove the variables that have low correlation with Sale Price"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# setting base variables and dependent variables (so we don't have to keep writing them out)\n",
    "variables = house_train.columns.values[1:(len(house_train.columns.values)-1)]\n",
    "dep_var = house_train.columns.values[len(house_train.columns.values)-1]\n",
    "total_variables = house_train.columns.values[1:len(house_train.columns.values)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/rxu17/anaconda2/lib/python2.7/site-packages/statsmodels/stats/outliers_influence.py:167: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  vif = 1. / (1. - r_squared_i)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>variables</th>\n",
       "      <th>VIF</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>MSSubClass</td>\n",
       "      <td>15.130476</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>MSZoning</td>\n",
       "      <td>36.462287</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>LotFrontage</td>\n",
       "      <td>19.947081</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>LotArea</td>\n",
       "      <td>3.451729</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Street</td>\n",
       "      <td>280.817175</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     variables         VIF\n",
       "0   MSSubClass   15.130476\n",
       "1     MSZoning   36.462287\n",
       "2  LotFrontage   19.947081\n",
       "3      LotArea    3.451729\n",
       "4       Street  280.817175"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# used to find the VIF of each variable when all variables are inserted into the model\n",
    "def VIF(dataset, variables, dep_var):\n",
    "    features = '+'.join(dataset[variables].columns)\n",
    "    y, X = dmatrices(dep_var + '~' + features, dataset, return_type ='dataframe')\n",
    "    vif = pd.DataFrame()\n",
    "    vif['variables'] = X.columns[1:] # exclude id col\n",
    "    vif['VIF'] = [variance_inflation_factor(dataset[variables].values, i) for i in range(0, dataset[variables].shape[1])]\n",
    "    return vif\n",
    "\n",
    "vif_multi_var = VIF(house_train, variables, dep_var)\n",
    "vif_multi_var.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2.4 Eliminating Features\n",
    "Here, we eliminate features based on VIF factors greater than 10 and correlations with Sale Price less than 60%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# removing features based on VIF and correlation with Sale Price\n",
    "single_var_stat = singleVarModelStat(house_train, variables, dep_var)\n",
    "i = 0\n",
    "for v in variables:\n",
    "    if(vif_multi_var.iloc[i]['VIF'] > 10 and abs(single_var_stat.iloc[i]['Correlation']) < 0.60):\n",
    "        variables = list(variables)\n",
    "        variables.remove(v)\n",
    "        i += 1\n",
    "    elif(single_var_stat.iloc[i]['Correlation'] < 0.05):\n",
    "        variables = list(variables)\n",
    "        variables.remove(v)\n",
    "        i += 1\n",
    "    else:\n",
    "        i += 1\n",
    "        continue\n",
    "house_train_new = house_train[total_variables]\n",
    "\n",
    "#pd.write_csv(\"house_train_new.csv\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Eliminating features using PCA (method 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjYAAAIbCAYAAAD4hNTdAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa93789cc>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# gather the best components using PCA \n",
    "def PCA_analysis(dataset):\n",
    "    pca = PCA(n_components = 20)\n",
    "    X_train = pca.fit_transform(dataset[variables])\n",
    "    plt.plot(np.cumsum(pca.explained_variance_ratio_))\n",
    "    plt.title(\"Explained variance by different principal components\")\n",
    "    plt.xlabel(\"Principal Component\")\n",
    "    plt.ylabel(\"Fractional Explained Variance\")\n",
    "    plt.show()\n",
    "    return X_train\n",
    "\n",
    "X_train_pca = PCA_analysis(house_train_new)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3.1 Multivariate Linear Regression Prediction\n",
    "To start off simple, we're going to use linear regression as our first model for predicting on the test set using the training data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgMAAAFnCAYAAAA7VkqGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nLZA9AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa72b450c>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# splitting data into testing and training data\n",
    "#dataset = house_price_new\n",
    "#X_train, X_test, y_train, y_test = train_test_split(dataset[variables],dataset[dep_var], test_size = 0.5, random_state = 42)\n",
    "\n",
    "# we have to fill missing values in the test set\n",
    "house_test_miss1 = fillMissingValues(house_test, 'object')\n",
    "house_test_miss2 = fillMissingValues(house_test, 'int64')\n",
    "house_test_miss3 = fillMissingValues(house_test, 'float64')\n",
    "\n",
    "# first we have to convert the test set to numeric data as well\n",
    "house_test_miss1= encodingCategorical(house_test_miss1)\n",
    "house_test_new = replaceOldDataset(house_test, house_test_miss1)\n",
    "house_test_new = replaceOldDataset(house_test_new, house_test_miss2)\n",
    "house_test_new = replaceOldDataset(house_test_new, house_test_miss3)\n",
    "\n",
    "# setting up training and testing sets\n",
    "y_train = house_train['SalePrice']\n",
    "X_test = house_test_new[variables]\n",
    "X_train = house_train_new[variables]\n",
    "\n",
    "lr = LinearRegression() # creating our linear model\n",
    "lr.fit(X_train, y_train)\n",
    "\n",
    "y_pred = lr.predict(X_test)\n",
    "\n",
    "plt.plot(y_pred) # visualizing our predictions\n",
    "plt.title(\"Linear Regression House Sale Price Predictions\")\n",
    "plt.ylabel('Sale Price $')\n",
    "plt.xlabel(\"House ID\")\n",
    "plt.show()\n",
    "\n",
    "#print(np.sqrt(mean_squared_error(y_pred, y_test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3.2 Random Forest Predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgMAAAFnCAYAAAA7VkqGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa6eb524c>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rf = RandomForestRegressor()\n",
    "rf.fit(X_train, y_train)\n",
    "y_pred_rf = rf.predict(X_test)\n",
    "\n",
    "plt.plot(y_pred_rf)\n",
    "plt.title(\"Random Forest House Sale Price Predictions\")\n",
    "plt.ylabel('Sale Price $')\n",
    "plt.xlabel(\"House ID\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# 3.3 Model Selection "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>LotArea</th>\n",
       "      <th>LandSlope</th>\n",
       "      <th>Neighborhood</th>\n",
       "      <th>Condition1</th>\n",
       "      <th>HouseStyle</th>\n",
       "      <th>OverallQual</th>\n",
       "      <th>RoofStyle</th>\n",
       "      <th>RoofMatl</th>\n",
       "      <th>MasVnrArea</th>\n",
       "      <th>Foundation</th>\n",
       "      <th>...</th>\n",
       "      <th>GrLivArea</th>\n",
       "      <th>BsmtFullBath</th>\n",
       "      <th>HalfBath</th>\n",
       "      <th>Fireplaces</th>\n",
       "      <th>GarageCars</th>\n",
       "      <th>GarageArea</th>\n",
       "      <th>WoodDeckSF</th>\n",
       "      <th>OpenPorchSF</th>\n",
       "      <th>ScreenPorch</th>\n",
       "      <th>PoolArea</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>484</th>\n",
       "      <td>7758</td>\n",
       "      <td>0</td>\n",
       "      <td>19</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>999</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>264</td>\n",
       "      <td>0</td>\n",
       "      <td>132</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>145</th>\n",
       "      <td>2522</td>\n",
       "      <td>0</td>\n",
       "      <td>7</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>50.0</td>\n",
       "      <td>2</td>\n",
       "      <td>...</td>\n",
       "      <td>1709</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>380</td>\n",
       "      <td>0</td>\n",
       "      <td>40</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>428</th>\n",
       "      <td>6762</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>7</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>108.0</td>\n",
       "      <td>2</td>\n",
       "      <td>...</td>\n",
       "      <td>1208</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>628</td>\n",
       "      <td>105</td>\n",
       "      <td>54</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>280</th>\n",
       "      <td>11287</td>\n",
       "      <td>0</td>\n",
       "      <td>20</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>340.0</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1982</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>575</td>\n",
       "      <td>0</td>\n",
       "      <td>84</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1198</th>\n",
       "      <td>9100</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>7</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2</td>\n",
       "      <td>...</td>\n",
       "      <td>1212</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>573</td>\n",
       "      <td>356</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 22 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      LotArea  LandSlope  Neighborhood  Condition1  HouseStyle  OverallQual  \\\n",
       "484      7758          0            19           2           2            5   \n",
       "145      2522          0             7           2           5            6   \n",
       "428      6762          0             5           2           2            7   \n",
       "280     11287          0            20           2           5            7   \n",
       "1198     9100          0             5           2           2            7   \n",
       "\n",
       "      RoofStyle  RoofMatl  MasVnrArea  Foundation    ...     GrLivArea  \\\n",
       "484           1         1         0.0           1    ...           999   \n",
       "145           1         1        50.0           2    ...          1709   \n",
       "428           1         1       108.0           2    ...          1208   \n",
       "280           1         1       340.0           1    ...          1982   \n",
       "1198          1         1         0.0           2    ...          1212   \n",
       "\n",
       "      BsmtFullBath  HalfBath  Fireplaces  GarageCars  GarageArea  WoodDeckSF  \\\n",
       "484              1         0           0           1         264           0   \n",
       "145              0         0           0           2         380           0   \n",
       "428              1         0           0           2         628         105   \n",
       "280              0         1           1           2         575           0   \n",
       "1198             0         0           0           2         573         356   \n",
       "\n",
       "      OpenPorchSF  ScreenPorch  PoolArea  \n",
       "484           132            0         0  \n",
       "145            40            0         0  \n",
       "428            54            0         0  \n",
       "280            84            0         0  \n",
       "1198            0            0         0  \n",
       "\n",
       "[5 rows x 22 columns]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# we've randomnly split the training set into the four corresponding sets of data\n",
    "X_train, X_test, y_train, y_test = train_test_split(house_train_new[variables], house_train_new[dep_var], test_size = 0.4)\n",
    "X_train.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/rxu17/anaconda2/lib/python2.7/site-packages/sklearn/neural_network/multilayer_perceptron.py:564: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (200) reached and the optimization hasn't converged yet.\n",
      "  % self.max_iter, ConvergenceWarning)\n"
     ]
    }
   ],
   "source": [
    "# Our many models\n",
    "\n",
    "models = [[\"AdaBoost\", AdaBoostRegressor()], [\"KNN\", KNeighborsRegressor()], [\"SVR\", SVR()], [\"GaussianNB\", GaussianNB()], [\"NeuralNet\", MLPRegressor()], ['RandomForest', RandomForestRegressor()], ['LinearRegression', LinearRegression()]]\n",
    "\n",
    "model_results = pd.DataFrame(columns=[\"Model\", \"RMSE\"])\n",
    "index = 0\n",
    "for i, j in models:\n",
    "    j.fit(X_train, y_train)\n",
    "    y_hat = j.predict(X_test)\n",
    "    mse = mean_squared_error(y_test, y_hat)\n",
    "    model_results.loc[index] = [i, np.sqrt(mse)]\n",
    "    index += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Model</th>\n",
       "      <th>RMSE</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>AdaBoost</td>\n",
       "      <td>36816.597360</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>KNN</td>\n",
       "      <td>48933.180367</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>SVR</td>\n",
       "      <td>83321.981220</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>GaussianNB</td>\n",
       "      <td>55755.867461</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>NeuralNet</td>\n",
       "      <td>55320.721896</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>RandomForest</td>\n",
       "      <td>35199.663628</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>LinearRegression</td>\n",
       "      <td>45157.495225</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              Model          RMSE\n",
       "0          AdaBoost  36816.597360\n",
       "1               KNN  48933.180367\n",
       "2               SVR  83321.981220\n",
       "3        GaussianNB  55755.867461\n",
       "4         NeuralNet  55320.721896\n",
       "5      RandomForest  35199.663628\n",
       "6  LinearRegression  45157.495225"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can conclude from the above that RandomForest and AdaBoost are the best performing, and with some parameter tuning, we can get the overall results to improve. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3.4 Checking for Overfitting\n",
    "We want to check for overfitting by seeing the RMSE values on the training set for each model. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "models = [[\"AdaBoost\", AdaBoostRegressor()], [\"KNN\", KNeighborsRegressor()], [\"SVR\", SVR()], [\"GaussianNB\", GaussianNB()], [\"NeuralNet\", MLPRegressor()], ['RandomForest', RandomForestRegressor()], ['LinearRegression', LinearRegression()]]\n",
    "\n",
    "model_results_train = pd.DataFrame(columns=[\"Model\", \"RMSE\"])\n",
    "index = 0\n",
    "for i, j in models:\n",
    "    j.fit(X_train, y_train)\n",
    "    y_hat = j.predict(X_train)\n",
    "    mse_train = mean_squared_error(y_train, y_hat)\n",
    "    model_results_train.loc[index] = [i, np.sqrt(mse_train)]\n",
    "    index += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Model</th>\n",
       "      <th>RMSE</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>AdaBoost</td>\n",
       "      <td>26689.171070</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>KNN</td>\n",
       "      <td>38221.397516</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>SVR</td>\n",
       "      <td>80020.533187</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>GaussianNB</td>\n",
       "      <td>17700.229921</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>NeuralNet</td>\n",
       "      <td>47476.458267</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>RandomForest</td>\n",
       "      <td>13335.595078</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>LinearRegression</td>\n",
       "      <td>32285.922388</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              Model          RMSE\n",
       "0          AdaBoost  26689.171070\n",
       "1               KNN  38221.397516\n",
       "2               SVR  80020.533187\n",
       "3        GaussianNB  17700.229921\n",
       "4         NeuralNet  47476.458267\n",
       "5      RandomForest  13335.595078\n",
       "6  LinearRegression  32285.922388"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_results_train"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 4.1 Parameter Tuning\n",
    "Let's delve into parameter tuning for the various models. First up is Random Forest: \n",
    "[Image](https://databricks.com/wp-content/uploads/2015/01/Ensemble-example.png)\n",
    "\n",
    "How Random Forest works: \n",
    "\n",
    "Parameters to tune:\n",
    "        ◦ n_estimators – more trees, less likely to overfit\n",
    "        ◦ max_features – (30%-50%) of features, and smaller means less overfitting(best range(2-6 features)\n",
    "        ◦ max_depth – decrease means decreasing complexity of learned models (like a regularization term)\n",
    "        ◦ min_samples_leaf – set greater than one"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RandomForestRegressor(bootstrap=False, criterion='mse', max_depth=5,\n",
      "           max_features=11, max_leaf_nodes=None, min_impurity_decrease=0.0,\n",
      "           min_impurity_split=None, min_samples_leaf=1,\n",
      "           min_samples_split=2, min_weight_fraction_leaf=0.0,\n",
      "           n_estimators=1000, n_jobs=1, oob_score=False, random_state=None,\n",
      "           verbose=0, warm_start=False)\n",
      "37170.4122027\n"
     ]
    }
   ],
   "source": [
    "rf = RandomForestRegressor(n_estimators = 1000, max_features = int(len(variables)*0.5), max_depth = 5, bootstrap=False)\n",
    "print(rf)\n",
    "rf.fit(X_train, y_train)\n",
    "y_hat = rf.predict(X_test)\n",
    "print(np.sqrt(mean_squared_error(y_hat, y_test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# 4.2 One Hot Encoding\n",
    "Now, we're going to take a different approach in encoding our values. We're going to take our categorical variables, and change the categorical variables to dummy variables based on the levels. \n",
    "\n",
    "For example, if a Variable was School Year, then we make variables for Sophmore, Junior and Senior then put a 1 if its true, 0 if false. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looking at our variables again, to simplify things, we're going to combine 1st floor and 2nd floor square feet. We're also going to ignore other square feet variables (usually in a house listing, the other square feed are not displayed). \n",
    "\n",
    "We also researched typical factors that determine a house's price:\n",
    "- Demographics\n",
    "- Size\n",
    "- Condition\n",
    "- \n",
    "**Specific Variables to Change:**\n",
    "MonthSold will be converted to season: Summer, Spring, Fall, Winter\n",
    "1stFloor + 2ndFloor => TotalSqFeet"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# We're going to remove all variables except basic ones:\n",
    "# House Age\n",
    "# Garage \n",
    "# Garage Size (cars)\n",
    "# Total Square Feet\n",
    "# Total Bathrooms\n",
    "# Lot Size\n",
    "# Type of House\n",
    "# Community\n",
    "# Fireplace\n",
    "# Street - Pave or Gravel\n",
    "# Covering on House Exterior1st\n",
    "# ExterCond and ExterQual\n",
    "# Foundation\n",
    "# BsmtCond\n",
    "# Basement (yes or no)\n",
    "# HeatingQC\n",
    "# CentralAir\n",
    "# BsmtFullBath + BsmtHalfBath + HalfBath + FullBath\n",
    "# KitchenQual\n",
    "# Kitchens\n",
    "# Functional - categories: typical, deductions, bad deductions\n",
    "# GarageQual\n",
    "# GarageCond\n",
    "# PavedDrive - yes or no\n",
    "# Pool - yes or no\n",
    "# Fence - yes or no\n",
    "# MiscVal\n",
    "\n",
    "house_train = pd.read_csv(\"//home/rxu17/Documents/house_train.csv\")\n",
    "#print(house_train.columns.values)\n",
    "\n",
    "variables_to_keep = ['LotArea', 'Street', 'Neighborhood', 'OverallCond', 'YearBuilt'\n",
    "                    , 'YearRemodAdd', 'RoofMatl', 'Exterior1st', 'ExterCond', 'Foundation', 'BsmtCond', \n",
    "                    'HeatingQC', 'CentralAir', 'TotalBsmtSF', '1stFlrSF', '2ndFlrSF', 'BsmtFullBath', 'BsmtHalfBath', \n",
    "                     'FullBath', 'HalfBath', 'BedroomAbvGr', 'KitchenAbvGr', 'KitchenQual', 'Functional', 'TotRmsAbvGrd', \n",
    "                     'Fireplaces', 'GarageCars', 'GarageCond', 'PavedDrive', 'PoolQC', 'Fence', \n",
    "                     'MiscVal', 'MoSold', 'YrSold', 'SalePrice']\n",
    "house_train = house_train[variables_to_keep]\n",
    "\n",
    "house_train = house_train.rename(columns = {'1stFlrSF': 'FirstFlrSF', '2ndFlrSF':'SecFlrSF'})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# changing month sold to seasons\n",
    "house_train['Spr'] = 0\n",
    "\n",
    "house_train.loc[(house_train['MoSold'] < 6) & (house_train['MoSold'] > 2),'Spr'] = 1\n",
    "\n",
    "house_train['Sum'] = 0\n",
    "house_train.loc[(house_train['MoSold'] < 9) & (house_train['MoSold'] > 5),'Sum'] = 1\n",
    "\n",
    "house_train['Aut'] = 0\n",
    "house_train.loc[(house_train['MoSold'] < 12) & (house_train['MoSold'] > 8),'Aut'] = 1\n",
    "\n",
    "house_train['Win'] = 0\n",
    "house_train.loc[(house_train['MoSold'] > 11) & (house_train['MoSold'] < 3),'Win'] = 1\n",
    "\n",
    "house_train = house_train.drop('MoSold', axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# removing other square feet \n",
    "# combining 1st, 2nd floor, basement sq feet\n",
    "\n",
    "house_train['TotalSqFt'] = house_train['FirstFlrSF'] + house_train['SecFlrSF'] + house_train['TotalBsmtSF']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "result = [word for word in house_train.columns.values if 'SF' in word]\n",
    "house_train = house_train.drop(result, axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# changing variables YrSold and HouseAge to how old was house when sold:\n",
    "house_train['HouseAge'] = house_train['YrSold'] - house_train['YearBuilt']\n",
    "house_train['YrRemodel'] = house_train['YearRemodAdd'] - house_train['YearBuilt']\n",
    "house_train = house_train.drop(['YearBuilt', 'YrSold', 'YearRemodAdd'], axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# combining bathrooms in basement with rest of house\n",
    "house_train['TtlBath'] = house_train['BsmtFullBath'] + house_train['BsmtHalfBath'] + house_train['FullBath'] + house_train['HalfBath']\n",
    "house_train = house_train.drop(['BsmtFullBath', 'BsmtHalfBath', 'FullBath', 'HalfBath'], axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# new column pool or no pool\n",
    "house_train['Pool'] = 1\n",
    "house_train.loc[house_train['PoolQC'].isnull(), 'Pool'] = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# new column fence or no fence\n",
    "house_train['FenceYes'] = 1\n",
    "house_train.loc[house_train['Fence'].isnull(), 'FenceYes'] = 0\n",
    "\n",
    "house_train = house_train.drop(['Fence', 'PoolQC'], axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>variables</th>\n",
       "      <th>VIF</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>LotArea</td>\n",
       "      <td>3.040201</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>LandSlope</td>\n",
       "      <td>1.382035</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Neighborhood</td>\n",
       "      <td>5.383055</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Condition1</td>\n",
       "      <td>6.082163</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>HouseStyle</td>\n",
       "      <td>5.094480</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>OverallQual</td>\n",
       "      <td>38.410192</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>RoofStyle</td>\n",
       "      <td>4.346964</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>RoofMatl</td>\n",
       "      <td>4.499994</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>MasVnrArea</td>\n",
       "      <td>1.705279</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>Foundation</td>\n",
       "      <td>6.245054</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>TotalBsmtSF</td>\n",
       "      <td>25.902748</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>FirstFlrSF</td>\n",
       "      <td>48.598150</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>GrLivArea</td>\n",
       "      <td>28.007912</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>BsmtFullBath</td>\n",
       "      <td>2.017291</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>HalfBath</td>\n",
       "      <td>2.741826</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>Fireplaces</td>\n",
       "      <td>2.755689</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>GarageCars</td>\n",
       "      <td>34.051685</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>GarageArea</td>\n",
       "      <td>29.640500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>WoodDeckSF</td>\n",
       "      <td>1.810386</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>OpenPorchSF</td>\n",
       "      <td>1.759502</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>ScreenPorch</td>\n",
       "      <td>1.161303</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>PoolArea</td>\n",
       "      <td>1.067810</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       variables        VIF\n",
       "0        LotArea   3.040201\n",
       "1      LandSlope   1.382035\n",
       "2   Neighborhood   5.383055\n",
       "3     Condition1   6.082163\n",
       "4     HouseStyle   5.094480\n",
       "5    OverallQual  38.410192\n",
       "6      RoofStyle   4.346964\n",
       "7       RoofMatl   4.499994\n",
       "8     MasVnrArea   1.705279\n",
       "9     Foundation   6.245054\n",
       "10   TotalBsmtSF  25.902748\n",
       "11    FirstFlrSF  48.598150\n",
       "12     GrLivArea  28.007912\n",
       "13  BsmtFullBath   2.017291\n",
       "14      HalfBath   2.741826\n",
       "15    Fireplaces   2.755689\n",
       "16    GarageCars  34.051685\n",
       "17    GarageArea  29.640500\n",
       "18    WoodDeckSF   1.810386\n",
       "19   OpenPorchSF   1.759502\n",
       "20   ScreenPorch   1.161303\n",
       "21      PoolArea   1.067810"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# used to find the VIF of each variable when all variables are inserted into the model\n",
    "def VIF(dataset, variables, dep_var):\n",
    "    features = '+'.join(dataset[variables].columns)\n",
    "    y, X = dmatrices(dep_var + '~' + features, dataset, return_type ='dataframe')\n",
    "    vif = pd.DataFrame()\n",
    "    vif['variables'] = X.columns[1:] # exclude id col\n",
    "    vif['VIF'] = [variance_inflation_factor(dataset[variables].values, i) for i in range(0, dataset[variables].shape[1])]\n",
    "    return vif\n",
    "\n",
    "vif_multi_var = VIF(house_train_new, variables, dep_var)\n",
    "\n",
    "#house_train_new = house_train_new.drop(['TotRmsAbvGrd', 'KitchenAbvGr'], axis = 1)\n",
    "\n",
    "vif_multi_var"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>LotArea</th>\n",
       "      <th>OverallCond</th>\n",
       "      <th>BedroomAbvGr</th>\n",
       "      <th>KitchenAbvGr</th>\n",
       "      <th>TotRmsAbvGrd</th>\n",
       "      <th>Fireplaces</th>\n",
       "      <th>GarageCars</th>\n",
       "      <th>MiscVal</th>\n",
       "      <th>SalePrice</th>\n",
       "      <th>Spr</th>\n",
       "      <th>...</th>\n",
       "      <th>Y</th>\n",
       "      <th>N</th>\n",
       "      <th>Typ</th>\n",
       "      <th>Min2</th>\n",
       "      <th>Min1</th>\n",
       "      <th>Mod</th>\n",
       "      <th>Maj1</th>\n",
       "      <th>Maj2</th>\n",
       "      <th>Sev</th>\n",
       "      <th>P</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>8450</td>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>8</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>208500</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>9600</td>\n",
       "      <td>8</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>181500</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>11250</td>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>223500</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>9550</td>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>7</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>140000</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>14260</td>\n",
       "      <td>5</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>9</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>250000</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 88 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   LotArea  OverallCond  BedroomAbvGr  KitchenAbvGr  TotRmsAbvGrd  Fireplaces  \\\n",
       "0     8450            5             3             1             8           0   \n",
       "1     9600            8             3             1             6           1   \n",
       "2    11250            5             3             1             6           1   \n",
       "3     9550            5             3             1             7           1   \n",
       "4    14260            5             4             1             9           1   \n",
       "\n",
       "   GarageCars  MiscVal  SalePrice  Spr ...  Y  N  Typ  Min2  Min1  Mod  Maj1  \\\n",
       "0           2        0     208500    0 ...  0  0    0     0     0    0     0   \n",
       "1           2        0     181500    1 ...  0  0    0     0     0    0     0   \n",
       "2           2        0     223500    0 ...  0  0    0     0     0    0     0   \n",
       "3           3        0     140000    0 ...  0  0    0     0     0    0     0   \n",
       "4           3        0     250000    0 ...  0  0    0     0     0    0     0   \n",
       "\n",
       "   Maj2  Sev  P  \n",
       "0     0    0  0  \n",
       "1     0    0  0  \n",
       "2     0    0  0  \n",
       "3     0    0  0  \n",
       "4     0    0  0  \n",
       "\n",
       "[5 rows x 88 columns]"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# @method create_dummy_var changes all our categorical variables into dummy variables based on levels they have\n",
    "# @param dataset our original house prices dataset\n",
    "# @param variables that are our independent variables\n",
    "# @return newdataset data frame with dummy variables in place of categorical variables\n",
    "def create_dummy_var(dataset):\n",
    "    new_set = dataset.select_dtypes(include = ['object']).copy()\n",
    "    for var in new_set.columns.values:\n",
    "        for label in new_set[var].value_counts().index.values:\n",
    "            dataset[label] = 0\n",
    "            dataset.loc[dataset[var] == label, label] == 1\n",
    "        dataset = dataset.drop(var, axis = 1)\n",
    "    return dataset\n",
    "\n",
    "house_train_new = house_train\n",
    "print(type(house_train_new))\n",
    "house_train_new = create_dummy_var(house_train_new)\n",
    "\n",
    "house_train_new.head()\n",
    "#house_train_new.select_dtypes(include = ['object']).copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>LotArea</th>\n",
       "      <th>Street</th>\n",
       "      <th>Neighborhood</th>\n",
       "      <th>OverallCond</th>\n",
       "      <th>RoofMatl</th>\n",
       "      <th>Exterior1st</th>\n",
       "      <th>ExterCond</th>\n",
       "      <th>Foundation</th>\n",
       "      <th>BsmtCond</th>\n",
       "      <th>HeatingQC</th>\n",
       "      <th>...</th>\n",
       "      <th>Aut</th>\n",
       "      <th>Win</th>\n",
       "      <th>TotalSqFt</th>\n",
       "      <th>HouseAge</th>\n",
       "      <th>YrRemodel</th>\n",
       "      <th>TtlBath</th>\n",
       "      <th>Pool</th>\n",
       "      <th>FenceYes</th>\n",
       "      <th>Pave</th>\n",
       "      <th>Grvl</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>8450</td>\n",
       "      <td>Pave</td>\n",
       "      <td>CollgCr</td>\n",
       "      <td>5</td>\n",
       "      <td>CompShg</td>\n",
       "      <td>VinylSd</td>\n",
       "      <td>TA</td>\n",
       "      <td>PConc</td>\n",
       "      <td>TA</td>\n",
       "      <td>Ex</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2566</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>9600</td>\n",
       "      <td>Pave</td>\n",
       "      <td>Veenker</td>\n",
       "      <td>8</td>\n",
       "      <td>CompShg</td>\n",
       "      <td>MetalSd</td>\n",
       "      <td>TA</td>\n",
       "      <td>CBlock</td>\n",
       "      <td>TA</td>\n",
       "      <td>Ex</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2524</td>\n",
       "      <td>31</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>11250</td>\n",
       "      <td>Pave</td>\n",
       "      <td>CollgCr</td>\n",
       "      <td>5</td>\n",
       "      <td>CompShg</td>\n",
       "      <td>VinylSd</td>\n",
       "      <td>TA</td>\n",
       "      <td>PConc</td>\n",
       "      <td>TA</td>\n",
       "      <td>Ex</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>2706</td>\n",
       "      <td>7</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>9550</td>\n",
       "      <td>Pave</td>\n",
       "      <td>Crawfor</td>\n",
       "      <td>5</td>\n",
       "      <td>CompShg</td>\n",
       "      <td>Wd Sdng</td>\n",
       "      <td>TA</td>\n",
       "      <td>BrkTil</td>\n",
       "      <td>Gd</td>\n",
       "      <td>Gd</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2473</td>\n",
       "      <td>91</td>\n",
       "      <td>55</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>14260</td>\n",
       "      <td>Pave</td>\n",
       "      <td>NoRidge</td>\n",
       "      <td>5</td>\n",
       "      <td>CompShg</td>\n",
       "      <td>VinylSd</td>\n",
       "      <td>TA</td>\n",
       "      <td>PConc</td>\n",
       "      <td>TA</td>\n",
       "      <td>Ex</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3343</td>\n",
       "      <td>8</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 34 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   LotArea Street Neighborhood  OverallCond RoofMatl Exterior1st ExterCond  \\\n",
       "0     8450   Pave      CollgCr            5  CompShg     VinylSd        TA   \n",
       "1     9600   Pave      Veenker            8  CompShg     MetalSd        TA   \n",
       "2    11250   Pave      CollgCr            5  CompShg     VinylSd        TA   \n",
       "3     9550   Pave      Crawfor            5  CompShg     Wd Sdng        TA   \n",
       "4    14260   Pave      NoRidge            5  CompShg     VinylSd        TA   \n",
       "\n",
       "  Foundation BsmtCond HeatingQC ...  Aut  Win  TotalSqFt HouseAge YrRemodel  \\\n",
       "0      PConc       TA        Ex ...    0    0       2566        5         0   \n",
       "1     CBlock       TA        Ex ...    0    0       2524       31         0   \n",
       "2      PConc       TA        Ex ...    1    0       2706        7         1   \n",
       "3     BrkTil       Gd        Gd ...    0    0       2473       91        55   \n",
       "4      PConc       TA        Ex ...    0    0       3343        8         0   \n",
       "\n",
       "   TtlBath  Pool  FenceYes Pave Grvl  \n",
       "0        4     0         0    0    0  \n",
       "1        3     0         0    0    0  \n",
       "2        4     0         0    0    0  \n",
       "3        2     0         0    0    0  \n",
       "4        4     0         0    0    0  \n",
       "\n",
       "[5 rows x 34 columns]"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# encoding variable Paved Drive and Central Air from T or F to 1 or 0\n",
    "house_train.loc[house_train['PavedDrive'] == 'T','PavedDrive'] = 1\n",
    "house_train.loc[house_train['PavedDrive'] == 'F','PavedDrive'] = 0\n",
    "\n",
    "house_train.loc[house_train['CentralAir'] == 'T','CentralAir'] = 1\n",
    "house_train.loc[house_train['CentralAir'] == 'F','CentralAir'] = 0\n",
    "\n",
    "house_train.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      LotArea  OverallCond  BedroomAbvGr  KitchenAbvGr  TotRmsAbvGrd  \\\n",
      "1118    13825            6             3             1             6   \n",
      "906     13501            5             3             1             8   \n",
      "1269    11344            5             3             1             7   \n",
      "1451     9262            5             3             1             7   \n",
      "879      7000            8             3             1             6   \n",
      "\n",
      "      Fireplaces  GarageCars  MiscVal  Spr  Sum ...  Y  N  Typ  Min2  Min1  \\\n",
      "1118           0           1        0    0    0 ...  0  0    0     0     0   \n",
      "906            1           3        0    0    1 ...  0  0    0     0     0   \n",
      "1269           0           1        0    0    1 ...  0  0    0     0     0   \n",
      "1451           1           3        0    1    0 ...  0  0    0     0     0   \n",
      "879            0           1        0    0    1 ...  0  0    0     0     0   \n",
      "\n",
      "      Mod  Maj1  Maj2  Sev  P  \n",
      "1118    0     0     0    0  0  \n",
      "906     0     0     0    0  0  \n",
      "1269    0     0     0    0  0  \n",
      "1451    0     0     0    0  0  \n",
      "879     0     0     0    0  0  \n",
      "\n",
      "[5 rows x 87 columns]\n",
      "1118    140000\n",
      "906     255000\n",
      "1269    144000\n",
      "1451    287090\n",
      "879     136500\n",
      "Name: SalePrice, dtype: int64\n"
     ]
    }
   ],
   "source": [
    "# new training/testing splits for new cleaned dataset\n",
    "variables = house_train_new.drop('SalePrice', axis = 1).columns.values\n",
    "dep_var = 'SalePrice'\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(house_train_new[variables], house_train_new[dep_var], test_size = 0.4)\n",
    "print(X_train.head())\n",
    "print(y_train.head())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "               LotArea  OverallCond  BedroomAbvGr  KitchenAbvGr  TotRmsAbvGrd  \\\n",
      "LotArea       1.000000    -0.005636      0.119690     -0.017784      0.190015   \n",
      "OverallCond  -0.005636     1.000000      0.012980     -0.087001     -0.057583   \n",
      "BedroomAbvGr  0.119690     0.012980      1.000000      0.198597      0.676620   \n",
      "KitchenAbvGr -0.017784    -0.087001      0.198597      1.000000      0.256045   \n",
      "TotRmsAbvGrd  0.190015    -0.057583      0.676620      0.256045      1.000000   \n",
      "Fireplaces    0.271364    -0.023820      0.107570     -0.123936      0.326114   \n",
      "GarageCars    0.154871    -0.185758      0.086106     -0.050634      0.362289   \n",
      "MiscVal       0.038068     0.068777      0.007767      0.062341      0.024763   \n",
      "SalePrice     0.263843    -0.077856      0.168213     -0.135907      0.533723   \n",
      "Spr          -0.051181     0.012687     -0.039562     -0.026958     -0.024206   \n",
      "Sum           0.046438     0.059459      0.055085      0.016621      0.020223   \n",
      "Aut          -0.008133    -0.043704      0.022675      0.036137      0.045494   \n",
      "Win                NaN          NaN           NaN           NaN           NaN   \n",
      "TotalSqFt     0.307234    -0.143814      0.354034      0.026759      0.672596   \n",
      "HouseAge     -0.014832     0.377325      0.068960      0.175918     -0.096955   \n",
      "YrRemodel    -0.005926     0.526147      0.052951      0.089513      0.043776   \n",
      "TtlBath       0.184407    -0.149461      0.267732      0.009117      0.482310   \n",
      "Pool          0.087166    -0.009158      0.072162     -0.014677      0.093828   \n",
      "FenceYes     -0.046566     0.170748      0.028826     -0.055905     -0.066833   \n",
      "Pave               NaN          NaN           NaN           NaN           NaN   \n",
      "Grvl               NaN          NaN           NaN           NaN           NaN   \n",
      "NAmes              NaN          NaN           NaN           NaN           NaN   \n",
      "CollgCr            NaN          NaN           NaN           NaN           NaN   \n",
      "OldTown            NaN          NaN           NaN           NaN           NaN   \n",
      "Edwards            NaN          NaN           NaN           NaN           NaN   \n",
      "Somerst            NaN          NaN           NaN           NaN           NaN   \n",
      "Gilbert            NaN          NaN           NaN           NaN           NaN   \n",
      "NridgHt            NaN          NaN           NaN           NaN           NaN   \n",
      "Sawyer             NaN          NaN           NaN           NaN           NaN   \n",
      "NWAmes             NaN          NaN           NaN           NaN           NaN   \n",
      "...                ...          ...           ...           ...           ...   \n",
      "Plywood            NaN          NaN           NaN           NaN           NaN   \n",
      "CemntBd            NaN          NaN           NaN           NaN           NaN   \n",
      "BrkFace            NaN          NaN           NaN           NaN           NaN   \n",
      "WdShing            NaN          NaN           NaN           NaN           NaN   \n",
      "Stucco             NaN          NaN           NaN           NaN           NaN   \n",
      "AsbShng            NaN          NaN           NaN           NaN           NaN   \n",
      "Stone              NaN          NaN           NaN           NaN           NaN   \n",
      "BrkComm            NaN          NaN           NaN           NaN           NaN   \n",
      "AsphShn            NaN          NaN           NaN           NaN           NaN   \n",
      "ImStucc            NaN          NaN           NaN           NaN           NaN   \n",
      "CBlock             NaN          NaN           NaN           NaN           NaN   \n",
      "TA                 NaN          NaN           NaN           NaN           NaN   \n",
      "Gd                 NaN          NaN           NaN           NaN           NaN   \n",
      "Fa                 NaN          NaN           NaN           NaN           NaN   \n",
      "Ex                 NaN          NaN           NaN           NaN           NaN   \n",
      "Po                 NaN          NaN           NaN           NaN           NaN   \n",
      "PConc              NaN          NaN           NaN           NaN           NaN   \n",
      "BrkTil             NaN          NaN           NaN           NaN           NaN   \n",
      "Slab               NaN          NaN           NaN           NaN           NaN   \n",
      "Wood               NaN          NaN           NaN           NaN           NaN   \n",
      "Y                  NaN          NaN           NaN           NaN           NaN   \n",
      "N                  NaN          NaN           NaN           NaN           NaN   \n",
      "Typ                NaN          NaN           NaN           NaN           NaN   \n",
      "Min2               NaN          NaN           NaN           NaN           NaN   \n",
      "Min1               NaN          NaN           NaN           NaN           NaN   \n",
      "Mod                NaN          NaN           NaN           NaN           NaN   \n",
      "Maj1               NaN          NaN           NaN           NaN           NaN   \n",
      "Maj2               NaN          NaN           NaN           NaN           NaN   \n",
      "Sev                NaN          NaN           NaN           NaN           NaN   \n",
      "P                  NaN          NaN           NaN           NaN           NaN   \n",
      "\n",
      "              Fireplaces  GarageCars   MiscVal  SalePrice       Spr ...   Y  \\\n",
      "LotArea         0.271364    0.154871  0.038068   0.263843 -0.051181 ... NaN   \n",
      "OverallCond    -0.023820   -0.185758  0.068777  -0.077856  0.012687 ... NaN   \n",
      "BedroomAbvGr    0.107570    0.086106  0.007767   0.168213 -0.039562 ... NaN   \n",
      "KitchenAbvGr   -0.123936   -0.050634  0.062341  -0.135907 -0.026958 ... NaN   \n",
      "TotRmsAbvGrd    0.326114    0.362289  0.024763   0.533723 -0.024206 ... NaN   \n",
      "Fireplaces      1.000000    0.300789  0.001409   0.466929 -0.033283 ... NaN   \n",
      "GarageCars      0.300789    1.000000 -0.043080   0.640409 -0.049554 ... NaN   \n",
      "MiscVal         0.001409   -0.043080  1.000000  -0.021190  0.024409 ... NaN   \n",
      "SalePrice       0.466929    0.640409 -0.021190   1.000000 -0.052974 ... NaN   \n",
      "Spr            -0.033283   -0.049554  0.024409  -0.052974  1.000000 ... NaN   \n",
      "Sum            -0.015789    0.007106  0.008484   0.014503 -0.565570 ... NaN   \n",
      "Aut             0.041919    0.044704 -0.016068   0.040202 -0.289850 ... NaN   \n",
      "Win                  NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "TotalSqFt       0.477765    0.536413 -0.011186   0.782260 -0.052015 ... NaN   \n",
      "HouseAge       -0.148544   -0.538727  0.034545  -0.523350  0.031417 ... NaN   \n",
      "YrRemodel      -0.087316   -0.308898  0.033751  -0.217503  0.020195 ... NaN   \n",
      "TtlBath         0.341565    0.468671 -0.022698   0.613005 -0.051915 ... NaN   \n",
      "Pool            0.103225    0.021637  0.033900   0.093708 -0.024944 ... NaN   \n",
      "FenceYes       -0.041131   -0.175726  0.028128  -0.172184  0.000744 ... NaN   \n",
      "Pave                 NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "Grvl                 NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "NAmes                NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "CollgCr              NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "OldTown              NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "Edwards              NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "Somerst              NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "Gilbert              NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "NridgHt              NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "Sawyer               NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "NWAmes               NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "...                  ...         ...       ...        ...       ... ...  ..   \n",
      "Plywood              NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "CemntBd              NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "BrkFace              NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "WdShing              NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "Stucco               NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "AsbShng              NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "Stone                NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "BrkComm              NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "AsphShn              NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "ImStucc              NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "CBlock               NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "TA                   NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "Gd                   NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "Fa                   NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "Ex                   NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "Po                   NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "PConc                NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "BrkTil               NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "Slab                 NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "Wood                 NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "Y                    NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "N                    NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "Typ                  NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "Min2                 NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "Min1                 NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "Mod                  NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "Maj1                 NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "Maj2                 NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "Sev                  NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "P                    NaN         NaN       NaN        NaN       NaN ... NaN   \n",
      "\n",
      "               N  Typ  Min2  Min1  Mod  Maj1  Maj2  Sev   P  \n",
      "LotArea      NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "OverallCond  NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "BedroomAbvGr NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "KitchenAbvGr NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "TotRmsAbvGrd NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "Fireplaces   NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "GarageCars   NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "MiscVal      NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "SalePrice    NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "Spr          NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "Sum          NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "Aut          NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "Win          NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "TotalSqFt    NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "HouseAge     NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "YrRemodel    NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "TtlBath      NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "Pool         NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "FenceYes     NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "Pave         NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "Grvl         NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "NAmes        NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "CollgCr      NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "OldTown      NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "Edwards      NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "Somerst      NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "Gilbert      NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "NridgHt      NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "Sawyer       NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "NWAmes       NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "...           ..  ...   ...   ...  ...   ...   ...  ...  ..  \n",
      "Plywood      NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "CemntBd      NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "BrkFace      NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "WdShing      NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "Stucco       NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "AsbShng      NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "Stone        NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "BrkComm      NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "AsphShn      NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "ImStucc      NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "CBlock       NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "TA           NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "Gd           NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "Fa           NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "Ex           NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "Po           NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "PConc        NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "BrkTil       NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "Slab         NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "Wood         NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "Y            NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "N            NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "Typ          NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "Min2         NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "Min1         NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "Mod          NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "Maj1         NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "Maj2         NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "Sev          NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "P            NaN  NaN   NaN   NaN  NaN   NaN   NaN  NaN NaN  \n",
      "\n",
      "[88 rows x 88 columns]\n"
     ]
    }
   ],
   "source": [
    "# grabbing the correlation matrix for our new variables\n",
    "print(house_train_new.corr())\n",
    "house_train_new = house_train_new[house_train_new.columns.values[0:20]]\n",
    "#house_train_new = house_train_new.drop(['Win'], axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "house_train_new = house_train_new.drop(house_train_new.columns[[17]], axis = 1)\n",
    "#df.drop(df.columns[[0, 1, 3]], axis=1)\n",
    "#house_train_new.iloc[:,17].namecolumns[[17]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "39051.6607946\n"
     ]
    }
   ],
   "source": [
    "# our linear regression fit\n",
    "lr = LinearRegression()\n",
    "lr.fit(X_train, y_train)\n",
    "y_hat = lr.predict(X_test)\n",
    "print(np.sqrt(mean_squared_error(y_test, y_hat)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Model</th>\n",
       "      <th>RMSE</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>AdaBoost</td>\n",
       "      <td>34064.975695</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>KNN</td>\n",
       "      <td>50442.611528</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>SVR</td>\n",
       "      <td>82243.936569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>GaussianNB</td>\n",
       "      <td>47832.257084</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>NeuralNet</td>\n",
       "      <td>46712.166963</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>RandomForest</td>\n",
       "      <td>34308.913905</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>LinearRegression</td>\n",
       "      <td>39051.660795</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              Model          RMSE\n",
       "0          AdaBoost  34064.975695\n",
       "1               KNN  50442.611528\n",
       "2               SVR  82243.936569\n",
       "3        GaussianNB  47832.257084\n",
       "4         NeuralNet  46712.166963\n",
       "5      RandomForest  34308.913905\n",
       "6  LinearRegression  39051.660795"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# using our various models\n",
    "models = [[\"AdaBoost\", AdaBoostRegressor()], [\"KNN\", KNeighborsRegressor()], [\"SVR\", SVR()], \n",
    "          [\"GaussianNB\", GaussianNB()], [\"NeuralNet\", MLPRegressor(solver = 'lbfgs', alpha = 0, hidden_layer_sizes = (int(len(variables)/2)))], \n",
    "          ['RandomForest', RandomForestRegressor()], ['LinearRegression', LinearRegression()]]\n",
    "\n",
    "model_results = pd.DataFrame(columns=[\"Model\", \"RMSE\"])\n",
    "index = 0\n",
    "for i, j in models:\n",
    "    j.fit(X_train, y_train)\n",
    "    y_hat = j.predict(X_test)\n",
    "    mse = mean_squared_error(y_test, y_hat)\n",
    "    model_results.loc[index] = [i, np.sqrt(mse)]\n",
    "    index += 1\n",
    "    \n",
    "model_results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RandomForestRegressor(bootstrap=False, criterion='mse', max_depth=5,\n",
      "           max_features=43, max_leaf_nodes=None, min_impurity_decrease=0.0,\n",
      "           min_impurity_split=None, min_samples_leaf=1,\n",
      "           min_samples_split=2, min_weight_fraction_leaf=0.0,\n",
      "           n_estimators=500, n_jobs=1, oob_score=False, random_state=None,\n",
      "           verbose=0, warm_start=False)\n",
      "32540.0071437\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgMAAAFnCAYAAAA7VkqGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzsnXecVcX5/z/3bmHZZUF2ARG7sSvFgiJKFBUFEhOigIig\nMZYo1ogF+EkxiJDgEsSA0WhEjQgK6hdLAJGiICysixSVvsCywBbY3m6b3x9377mnzKn3nFv2Pm9f\nvth7yjPPnDNn5plnnplxMcYYCIIgCIJIWtyxVoAgCIIgiNhCxgBBEARBJDlkDBAEQRBEkkPGAEEQ\nBEEkOWQMEARBEESSQ8YAQRAEQSQ5qbFWgCDkXHDBBTjjjDOQkpICAPD7/ejduzdeeOEFZGZm2pLG\nsWPHcP3112PXrl22yBOTn5+P+++/H6eddprk+MCBA/HUU0/Znp6Y/fv34/jx4+jdu7fi3OjRozF0\n6FD8/ve/F44dPnwYt9xyC37++WdH9dLixIkTmDZtGnbs2AEASE1Nxb333ovhw4dr3vfJJ59g6dKl\nmD9/vuG0XnvtNbz77rvo1KkTAIAxhj59+mDcuHFo27at4vq8vDx069YNd911l/EMqTB69GgUFRWh\nXbt2YIwhJSUFd955J+69996I5BYUFOC5557DqlWrDOn73Xff4Ve/+hW6detma/6IxIaMASIuef/9\n99G1a1cAgMfjwV/+8he88cYb+Mtf/hJjzYxxyimnYNmyZVFPd+XKlfD5fFxjIF6ZOnUqunXrhpkz\nZ8LtduPAgQO48847cd555+Gyyy6zPb1bb70V06ZNAxAsW0899RTmzp2LZ555RnHt2LFjbU372Wef\nFYyx8vJy3HnnnTj77LPx61//2hb5RvSdP38+HnnkEXTr1s32/BGJCxkDRNyTnp6Ofv36YdWqVQCA\nxsZGjB8/Hr/88gu8Xi9uvfVWPP/88wCCva8bb7wRK1aswOHDh9G7d2/k5eXB5XJh8eLFmDt3Ltq1\na4fbbrtNkB8IBPDqq69i+fLlAIBevXph0qRJyMzMxOjRo9GvXz988803OHjwIB5//HFUV1dj6dKl\ncLvdeOONN3D66aebyk9+fj5mzJiBxsZGZGdnY9KkSejevTs++eQTrFq1CrW1tbjkkkvw3HPPYdGi\nRXjnnXfg8XjQq1cvvPzyy8jIyMCmTZswffp0NDc3gzGGJ554Am3atMEbb7yBtLQ01NTUYNy4caaf\n9f/+9z/MnTsXPp8PXbp0wUsvvYQzzjgD48aNwxlnnIExY8YAgOT3f//7X3zwwQdgjKFdu3aYPn06\nzjvvPOzduxdTpkxBeXk50tPT8fLLL6N79+6KNHfv3o2BAwfC7Q6OWp511ln4/PPPkZubCwD45ptv\nMHv2bHg8HmRlZWHatGm46KKLJDJqamowdepUbNu2DT6fD2PGjMEdd9yhm9/09HTceeedmD17Np55\n5hmMGzcOHTp0wPfff48xY8Zg7dq1Qj537NiBSZMmob6+Hp07d8b06dNx+umnG86nnM6dO2PgwIFY\nv349fv3rX+PGG2/E7bffjs8//xzvvPMO3G43pkyZgqKiIgDAhAkTcP311wMA5s2bh0WLFqFjx464\n8cYbBZni98LTd8mSJdi4cSP279+PZ599Ft9++61w/c6dOzFlyhRUVVWhTZs2eOaZZ9CvXz/k5+dj\n1qxZuOqqq7By5Uo0NzdjxowZuOqqq7B7925MnDgRdXV18Hq9uOeeezBq1CjdvBNxCCOIOOP8889n\nR48eFX5XVVWxu+++m82bN48xxtjbb7/NHnjgARYIBFhVVRW76qqr2ObNmxljjI0aNYqNGjWKNTY2\nsvr6enbNNdewgoICVlVVxXr16sX27t3LGGNs6tSp7Pzzz2eMMfbFF1+wIUOGsPr6eubz+dgjjzzC\n5s6dK8h74IEHmNfrZatWrWI9e/ZkS5YsYYwx9vjjj7N//OMfCv03btzIbr75Zm7e6urq2NVXX80K\nCgoYY4wtW7aM3XLLLczv97MlS5awXr16saKiIsYYY5s3b2bXXHMNO3bsGGOMsYkTJ7IZM2Ywxhi7\n/fbbWX5+PmOMsaKiIvb0008zxhh7/vnnBd3ljBo1in322WeSY8XFxeyiiy5ijDFWUlLCrrjiCnbg\nwAHhOd97771cuaHftbW17Morr2S1tbWMMca++uor9uabbzK/389uueUW9tFHHzHGGCsoKGDXXXcd\n83q9Cr1mzJjB+vTpw/71r3+xn376ifn9fuGc1+tlV155JduyZQtjjLHXXntN0GnJkiXC3+PHj2fP\nPfcc8/v97Pjx4+z6669nu3btUqQ1Z84cNmHCBMmxr7/+mg0fPlzI12233caampoU+R4wYABbs2YN\nY4yxd955hz344IOm8sl7/tOmTWOvvPIKY4yx/v37sxdeeEE4d8899wjl68CBA+yqq65iJ06cYHv2\n7GG9e/dm5eXlzOfzsTFjxrD+/fsb0jeUTuh7CV3v9/vZoEGD2Oeff84YY2zbtm2sd+/erLa2lm3c\nuJFdeuml7Ouvv2aMMfbvf/+b/fGPf2SMBb+BTz75hDHG2PHjx9kjjzzCmpubFXkn4h8KICTiktGj\nR2PgwIG46aabcNNNN6FPnz548MEHAQB/+tOfMG/ePLhcLnTo0AHnnXceDh8+LNw7cOBAZGRkIDMz\nE2eddRaOHj2KrVu34swzz8SvfvUrAMCQIUOE69esWYMhQ4YgMzMTKSkpuP3227F+/XrhfP/+/ZGa\nmorzzz8fjY2NuPXWWwEA559/PsrKyrj6Hz16FAMHDpT8/9FHH2Hbtm3o2rUrrrjiCgBBl3VlZSVK\nSkoABHvFZ511FgBg1apVGDx4ME4++WQAwF133YUVK1YAAHJzc/HZZ59h3759OOuss5CXl2fouc6c\nOVOi0x//+Efh3Pr163H11VfjzDPPBAAMGzYM+fn58Pl8qvLatGkjeF0qKiowaNAgPPjgg0LswtCh\nQwEAV1xxBXJycrBlyxaFjGeffRZ/+ctfsG7dOgwfPhzXXXcd5s6di0AggNTUVHz//ffo1asXAODK\nK69EcXGxQsbq1atxzz33wO12IycnBwMGDBCelRZ1dXVYsGABBgwYIBy75ppr0KZNG8l1RUVFqKys\nFHrmo0aNwmuvvWYqn3KKi4uxbNkySdo33HADAKChoQH5+fnC+znzzDNxxRVXYO3atdi8eTN69+6N\nTp06ISUlBb/73e8UstX0VePw4cOoqKjAb37zGwBA9+7d0a1bN2zfvh0AkJWVhZtvvhkAcMkll+DI\nkSMAguVw+fLl+Omnn9CxY0fMmzcP6enpunkn4g8aJiDiklDMwIkTJzBw4EAMHjwYqanB4nrgwAHM\nmDED+/fvh9vtxrFjx3D77bcL97Zr1074OyUlBX6/H9XV1cjOzhaOd+jQQfj7xIkTkt8dOnTA8ePH\nhd9ZWVmCLPFvt9uNQCDA1V8tZuDLL79E+/btJceys7OF9MR61NbW4uuvv8a6desABIPdvF4vAODl\nl1/G66+/jvvuuw8ZGRl4+umnMXDgQK4uYsRj1kA4gBAAKisrJbplZ2eDMYbKykpVeWlpaZg/fz7+\n9a9/4bXXXsMFF1yAyZMno76+Hk1NTRg0aJBwbV1dHaqqqhQy3G43hg8fjuHDh6OhoQFr1qzB1KlT\nkZubixEjRuD999/Hp59+Co/HA4/HA5fLpZBRW1uLp556SnhHzc3Nqs9j+fLl+OGHHwT9BwwYIDGK\nxO8gRGVlpaT8pKamIjU1FTU1NYbzCQSNsddffx2MMbRv3x7jxo1Djx49FGnX1taCMYYRI0YI5xoa\nGtCnTx80NDRIdJGXJy191Thx4gSys7Mlz7Z9+/Y4ceIEOnXqJJElLvfPPPMM3njjDTz11FNobm7G\nn//8Z9x9992q6RDxCxkDRFyTk5OD0aNHC5UoAPz1r3/FJZdcgrlz5yIlJUVSYarRvn171NbWCr9P\nnDgh/N2pUydJ5V1VVSVEm9tNbm6uJC3GGKqrq5Gbm4v9+/dLru3SpQv+8Ic/CPEQYjp16oSJEydi\n4sSJWLduHR5//HH069cvYt3EPdrq6mq43W507NhRYfhUV1cLf1988cWYM2cOPB4P3nrrLUyePBmv\nvPIKsrKydIMo6+vrsWnTJvTv3x8AkJmZicGDB2Pbtm3YvXs3CgsL8e9//xsff/wxTjvtNKxfvx4T\nJ05UyOnSpQvmzp2L888/Xzef4gBCo3Ts2BFVVVUIBAJwu93wer0oLS1Fly5dDOUzhNwYUyM3Nxcp\nKSlYsmSJYHyGWLBggaQs84w1NX3lM1zE6VVXV4MxJhgEVVVVQtyGGllZWXj66afx9NNPY9u2bXjw\nwQfRt29fnH322bp5JOILGiYg4p777rsPW7ZswaZNmwAAx48fx0UXXYSUlBSsX78eBw8eRENDg6aM\n7t27o6ioCAcOHAAAfPrpp8K5G264AUuXLkVjYyN8Ph8WL14suFftpkePHqioqBAa3S+//BJdu3bl\nVtKhQMiQ4bJy5Uq8+eab8Hq9GD16tDBEcckllyA1NRVutxupqamShsIM1157LQoKCgQ3/MKFC3Ht\ntdciNTUVnTt3xs6dOwEE3duFhYUAgF27duGJJ56Ax+NBeno6Lr30UrhcLpx66qno2rWr0EieOHEC\nTz/9tOI9uVwujB8/Hp988olwrKKiAuvXr0fv3r1x4sQJ5Obmolu3bmhsbMSnn36KhoYGMNlmqzfe\neCMWLlwIAPD5fHj55Zfx008/WXoOPM466yx07dpVGHpYvHgxJk2aZDifZklNTcX1118v5CkUNHv0\n6FFcdtll+OGHH3DixAn4/X4sXbrUsL4h2fIyctppp6Fr16746quvAACFhYWoqKiQeC14PPzww9iz\nZw+A4LBZu3btuJ4bIv4hzwAR97Rr1w4PPfQQ/va3v2Hx4sV45JFHMH36dMybNw833XQTHnvsMcyZ\nM0cRYS4mJycHzz//PO677z5kZWVh2LBhwrmBAwdi165duP3228EYw9VXX4177rnHkbxkZmZi9uzZ\nmDp1KhoaGpCTk4NZs2ZxK9BLLrkEDz/8MEaPHo1AIIDc3Fy8+OKLSEtLw9ChQwXXttvtxgsvvIC2\nbduif//+eOaZZ1BSUoI5c+aY0q1r16546aWXMGbMGHi9Xpx22mmYOnUqAGD48OF47LHHcMstt+Di\niy+WxE2cdtpp+O1vf4u0tDRkZWVh0qRJcLlcmDVrFqZMmYLZs2fD7XbjvvvuU6wTkZmZifnz5yMv\nLw//+te/AARd93fffTcGDRqE5uZmLFiwADfffDNOPvlkTJgwAVu3bsUTTzwheBMA4KmnnsKLL74o\n6NWvXz9ccMEFpvKvhcvlwquvvopnn30Ws2bNEqLzjebTClOmTMHkyZPx8ccfAwB+97vf4ZRTTsEp\np5yCESNG4A9/+ANOOukk/OY3v8Hu3bsN6QsEPSNPP/00nnjiCcn1s2bNwuTJk/HPf/4Tbdu2xauv\nvqqbj1GjRmHs2LHC8NXIkSOFmBcisXAxuYlNEARBEERSQcMEBEEQBJHkkDFAEARBEEkOGQMEQRAE\nkeSQMUAQBEEQSQ4ZAwRBEASR5CTt1MLycmtzsdXo2DETlZWRzS1ujdBzUULPhA89Fz70XJTQM+Gj\n91w6d85WPUeeAZtITU2JtQpxCT0XJfRM+NBz4UPPRQk9Ez6RPBcyBgiCIAgiySFjgCAIgiCSHDIG\nCIIgCCLJIWOAIAiCIJIcMgYIgiAIIskhY4AgCIIgkhwyBgiCIAgiySFjgCAIgiCSHDIGCIIgCCLJ\nIWOAIAiCIJIcMgYIgiCIhKWx2YfvdxyF1xeItSoJTdJuVEQQBEEkPgu+3o31O46hrLIRQ/qdE2t1\nEhbyDBAEQRAJS9Gx4A60RyrqY6xJYkPGAEEQBEEkOWQMEARBEESSQ8YAQRAEQSQ5ZAwQBEEQRJJD\nxgBBEARBJDlkDBAEQRBEkkPGAEEQBEEkOWQMEARBEAkPi7UCCQ4ZAwRBEETC4oq1Aq0EMgYIgiCI\nhIU8Avbg2N4E+fn5ePLJJ3HeeecBAM4//3w88MADeO655+D3+9G5c2fMnDkT6enpWLp0Kd599124\n3W4MHz4cw4YNg9frxbhx43DkyBGkpKRg+vTpOP3007Fz505MmTIFAHDBBRfgxRdfBAC89dZbWLZs\nGVwuFx577DFcf/31TmWNIAiCiDPIQxAZjm5UdNVVV2HOnDnC7/Hjx2PkyJEYNGgQZs2ahcWLF2PI\nkCGYO3cuFi9ejLS0NAwdOhQDBgzA6tWr0b59e+Tl5WHdunXIy8vD7NmzMW3aNEyYMAE9evTA2LFj\nsXbtWpxzzjn46quvsHDhQtTV1WHkyJG47rrrkJKS4mT2CIIgiDiBPASREdVhgvz8fNx0000AgP79\n+2PDhg3YunUrunfvjuzsbGRkZODyyy9HYWEhNmzYgAEDBgAA+vbti8LCQng8HpSUlKBHjx4SGfn5\n+ejXrx/S09ORk5ODU089FXv37o1m1giCIIgYQB4Be3DUM7B37148/PDDqK6uxmOPPYbGxkakp6cD\nAHJzc1FeXo6Kigrk5OQI9+Tk5CiOu91uuFwuVFRUoH379sK1IRknnXQSV8YFF1ygqlvHjplITbXX\nc9C5c7at8loL9FyU0DPhQ8+FDz0XJaFn4k4J9mnbtEml5wTrZcUxY+Css87CY489hkGDBqG4uBj3\n3HMP/H6/cJ4xvlPHzHGzMsRUVjboXmOGzp2zUV5ea6vM1gA9FyX0TPjQc+FDz0WJ+Jn4/QEAgKfZ\nl/TPSa+saBkKjg0TnHzyyRg8eDBcLhfOOOMMdOrUCdXV1WhqagIAlJaWokuXLujSpQsqKiqE+8rK\nyoTj5eXlAACv1wvGGDp37oyqqirhWjUZoeMEQRBEckAxA5HhmDGwdOlSvP322wCA8vJyHD9+HLff\nfjuWL18OAFixYgX69euHnj17Yvv27aipqUF9fT0KCwtx5ZVX4tprr8WyZcsAAKtXr8bVV1+NtLQ0\nnHPOOSgoKJDI6NOnD9asWQOPx4PS0lKUlZXh3HPPdSprBEEQRJxAMQP24NgwwY033ohnnnkG33zz\nDbxeL6ZMmYKLLroIzz//PBYtWoRu3bphyJAhSEtLw9ixY3H//ffD5XLh0UcfRXZ2NgYPHozvv/8e\nd911F9LT0zFjxgwAwIQJEzBp0iQEAgH07NkTffv2BQAMHz4co0aNgsvlwpQpU+B20xIKBEEQrR3y\nCNiDixkZYG+F2D22RON6fOi5KKFnwoeeCx96LkrEz+SFt/JxpKIeV1zQGY/+oXuMNYstcRkzQBAE\nQRBOQ8ME9kDGAEEQBEEkOWQMEARBEAlLUo5zOwAZAwRBEASR5JAxQBAEQSQsFDNgD2QMEARBEESS\nQ8YAQRAEkbBQzIA9kDFAEARBEEkOGQMEQRBEwkIxA/ZAxgBBEARBJDlkDBAEQRAJC8UM2AMZAwQR\nY37cU4Ep/9mEhiZvrFUhCCJJIWOAIGLMnCXbcKisDvk/l8ZaFYJIOChmwB7IGCAIgmjhh13l+ODr\n3bFWgyCiDhkDBEEQLcz9dDu++eEwqus9sVaFIKIKGQMEQRByGIWlEckFGQMEQRAEkeSQMUAQBCHH\nRWFpRHJBxgBBEASR+NDITkSQMUAQBEEQSQ4ZAwRBEDJokCABoZcWEWQMEARBEESSQ8YAQRBcauo9\nmPpuAXYdqoy1KtGHepmJB8UMRAQZAwRBcPm6oBhFR2sw88MfY61K9KGGhUgyyBggCIJLMs+uSxZb\n4MsNB/Dx6r2xVsMekri82gEZAwRBEHKSZAXCJWv343/5h2Kthj0kxytzDDIGCILQhCVhLZt8OU5g\nyCNgC2QMEAShQvLWskniGGgd0LuyBTIGiJhReqIBBTvLYq0GQRCtgeS1XW2BjAEiZox/cyPmfbYD\nlbXNsVaFICQwcg0kHvTKIoKMASLmNHl8sVaB0IIqWSKeIY+ALZAxQBBxQry1uclcx5JjIIGgd2UL\nZAwQBEHISMYZFAlPMluvNkDGAEEQmiRls5iUmU5w6J1FBBkDBEFwSeYVCIkEgsqpLZAxQBAEIYM6\nmQkEvSxbIGOAIAhCBrUvRLJBxgBBEIQcmk6QONAwgS2QMUAQBCGDTAEi2SBjgCAIQg5ZA4kDvStb\nIGOAIAhCBrUvRLJBxgBBEFxcSTy3kPYmSCCSt5jaChkDBEEQBJHkkDFAEDr4/AG8v2IXDpXWxloV\nIkqQYyCBoHdlC2QMEIQOG346htWFJXjpvQJH0yFvZ/xA7QuRbJAxQBA6NHn8AACfP7maiKQ2Tsg1\nkDgkdUG1DzIGCIIgZJApQCQbZAwQBEHISTJroDXMnkj8HMQWMgaImNMK6qHWSRK7X5OtSCZbfgkl\nZAwQMYcqIiLeaA09ZVO0guwmse1qC2QMELEn2SpeFegpELGCUelLesgYIGIOVUNEvJFs9mlryG8r\nyEJMIWOAiD3x/hXHu34OQW5XgkgeHDUGmpqacPPNN+OTTz7B0aNHMXr0aIwcORJPPvkkPB4PAGDp\n0qW44447MGzYMHz88ccAAK/Xi7Fjx+Kuu+7CqFGjUFxcDADYuXMnRowYgREjRmDy5MlCOm+99RaG\nDh2KYcOGYe3atU5miXCAJG1riTgm2dzmrcEzQMZrZDhqDLz++uvo0KEDAGDOnDkYOXIkFixYgDPP\nPBOLFy9GQ0MD5s6di/nz5+P999/Hu+++i6qqKnzxxRdo3749PvzwQzz88MPIy8sDAEybNg0TJkzA\nwoULUVdXh7Vr16K4uBhfffUVFixYgDfeeAPTp0+H3+93MluEzUQ7WCvQGmo+wlGSr4gkXYYJGY4Z\nA/v27cPevXtxww03AADy8/Nx0003AQD69++PDRs2YOvWrejevTuys7ORkZGByy+/HIWFhdiwYQMG\nDBgAAOjbty8KCwvh8XhQUlKCHj16SGTk5+ejX79+SE9PR05ODk499VTs3bvXqWwRCU7+z6V44G+r\nsa+kOtaqxD9JvGthstEajJ9WkIWY4pgx8Le//Q3jxo0Tfjc2NiI9PR0AkJubi/LyclRUVCAnJ0e4\nJicnR3Hc7XbD5XKhoqIC7du3F67Vk0EkDtGsiBavCRqKa34siV6iRMLRGhpHMyRZdgkOqU4I/eyz\nz9CrVy+cfvrp3PNqbmEzx83KkNOxYyZSU1MMXWuUzp2zbZXXWtB7Lid1zIzas3OnBO3fjIw03TQZ\nY9hXUo2MtunCMbv05Mlp1y4jrspQVpb9+dYjXvJ/0klt40YXwPnn0im3HTLaONIcOEbomaS2fNNt\n2qTG1TuLFVafgSNvf82aNSguLsaaNWtw7NgxpKenIzMzE01NTcjIyEBpaSm6dOmCLl26oKKiQriv\nrKwMvXr1QpcuXVBeXo4LL7wQXq8XjDF07twZVVVVwrViGUVFRYrjelRWNtia586ds1FeTlvcyjHy\nXCor61Hexl7DTI2APwAAaGr06uq1Yccx/PuLnyXH7HjHas+krq4prspQfb1H+DsaesXTN1RZ1YDy\nzLRYqwEgOs+lvKIWGemJYwyIn4mv5ZtubvbFTfmJFXplRctQcGSYYPbs2ViyZAk++ugjDBs2DGPG\njEHfvn2xfPlyAMCKFSvQr18/9OzZE9u3b0dNTQ3q6+tRWFiIK6+8Etdeey2WLVsGAFi9ejWuvvpq\npKWl4ZxzzkFBQYFERp8+fbBmzRp4PB6UlpairKwM5557rhPZIhwiui5Z4+Pgu4orHdQj/knqiIEk\n85sn8rBIUpdTG4maKfj444/j+eefx6JFi9CtWzcMGTIEaWlpGDt2LO6//364XC48+uijyM7OxuDB\ng/H999/jrrvuQnp6OmbMmAEAmDBhAiZNmoRAIICePXuib9++AIDhw4dj1KhRcLlcmDJlCtxuWj6B\nsIPkrmaSOX4wgdvGpIPelT04bgw8/vjjwt/vvPOO4vzAgQMxcOBAybGUlBRMnz5dce25556LBQsW\nKI6PHj0ao0ePtkFbIhbEa68kmRvDpCdOy6RTxOs3aAb6XCODutBEzInFpjBGUqTKJXlJtkWHWoP1\nk/g5iC1kDBAxJ5ofsVpvPxBg+HDlHhw4VhNFbRKfJo8PHm/rW+SrNfSUzZDI2SWj3R7IGCBiTwxq\nInllv3VfBb4uKMZf5xcIx1w0TqDLmFnf4pE8WgI80Ulk4yeBVY8ryBggYk5sXLLSNJt5vdso2wL/\nXbEba7Yk3mJIrbEyjsXQFREZZLpHBhkDRMyJZr0b753995bvirUKAuQZSR5ag/GT+DmILWQMEKY4\nVFqLZk/rGyN2cfoV1BQmF+IGsRW0jaawM7v+QMBGafrQd2oPZAwQhjlcVocp72xG3qIfbZXbGnol\nROLDVP5OCmzK8Dtf/YIH/74Gjc0+ewQaIOnelUOQMUAY5uiJ4BLOe1vBjn+GphaSmzy5kFgD0d9W\ne/bHW/HdtiNRTTeEXbn9bttRAECpzcu9E85DxgBhGKeaxqjGDJjIRbKbAsmW/4B4mCDKaZdVNmLb\nvuN456udUUtT4pFLYO9cspVTpyBjgIg5iVsNEa2VZCiTTg6LJLBtkbSQMUDEnljUHLQEISGDJXHQ\nQCI33gmselxBxgARc+Jh08LkW37WAElmDElmE0S5PMQkiJaKPCGCjAEi5sRrneSmAMKkgqn+aJ2I\nDZ5EntFDX6k9kDFAxB7qFMUnSfaQWAwDCGNBArf/hAOQMUDEnETulbRmku2ttJLgekskcn4TWPW4\ngowBwjBOec2jumuhmWuT3P+YbEYaS7JxAonxkwT5JbQhY4CIOUnW5hBxS7ItR8y4fyYaSW6z2wYZ\nA4QJHFt2yCG5GikaqO2TfQXC5GgQwyTbzELWOmwBwibIGCBiTlQbHTMNfJLXkMmW/ViuMxDrmYWt\nYdGhZBvWshsyBgjDOBkz4PH68dqSbdh5sNKZRCwQSPbKJcnyH8vGJCYpx3AvBiL+IGOAiD0M2Lyz\nDFv2VODvH26JiQq8PQsCgeSuIJMt97EMqIuFISJZZyDqqdtPsg/rRQoZA0TMYWDwR6nhNVNdkGcg\n1go4z6Hb7E6FAAAgAElEQVTSWhSX1QGI7aJDMS9qsU6fiDlkDBCxJ04rophX0DEmGbI/5Z3NmPyf\nTQDMLTq0YOVurNhcbJseMfEMtLIAQooZiIzUWCtAJA6tZy6BMZLdM6BXuba2ytfMokMrCw4DAG7p\nfbrtaceC1vYuCfNoegbEBSQQCOCnn35CWVmZ40oRyUVsIo/1r0n2mAE9WvfTiW7uYmF4OplkLBYx\nopiByFA1BlatWoXbbrsNAODz+XDnnXciLy8Pf/7zn/HJJ59ETUEijnDsW4texWGmviDPgN4FUVEj\nakiGCZIiZiDZFlkitFA1Bv75z3/i9ddfBwAsX74cp5xyCv7zn/9g0aJF+PDDD6OmINH6ideKKBCI\ntQaxRd8WiNMXZ5FYlsPYzCbg/52o0FBHZKjGDJSVlWHevHkAgC1btiA3Nxfjx48HABQXF2P8+PGY\nPn16dLQk4gLe9Ds7iMUnbCTN1tbYmUcvZiBKakSJWO5aGPOhMrsVaGVlIxlQNQa6du2Kl19+GQ0N\nDbj11luxePFitGvXDj6fD0OGDCFDgLCNeLXokz1mIE5fi2NI28bWHzMgpjW86ljGDHy0ai82/nwM\nM8f0RYo7MSfpqRoDv/3tb/Hb3/4WjY2NuPfee9GuXTtUVFRg/PjxGDBgQDR1JOKFJIvPSXJbQJfW\nZizEdAXCmAQQtq65hbF8f8s2HQIA1DZ4cVK7NjHTIxJUjYE//vGPuO222+ByuZCTkwMAaNOmDYYN\nG4ZbbrklagoSrZ94bVRYklsD+u8lsZ+PvPEw6jV3otFpdXsT2CwvUYjXuswImusM5ObmSn5nZ2eT\nIUDYTkzG5g18tbF23cYavfeS6LaS4v0aXI7YiWzHpFcrWVfB3vTjdeiPUCcxBzeI1kUU6w0z44pJ\nX5+18qmF8piQgFG3uQP5jsXEFSdfXyy+HVpnIDLIGCAM4+QKhPHYk0h2z4AeiT7bQms/DK2cOVEu\nYl3+W0NRj/UzTHR0jYGSkhI88cQTGD16NADgo48+woEDB5zWi0gmYjxeCvAXI0r62QR65xP88Sg9\nA6IfybDokIOJRrdhJo+AHegaAxMnTsTvf/974eWeffbZmDhxouOKEclDNHuYtGuhCVp59hW2nmSd\nAQ2vQSvxDEhtH7tjBmwVp5daNBNrtegaA16vFzfddJMwHtO7d2/HlSLiE6c+uUgqjoPHalFW1Wif\nMiIS3TNQ0+BBs8dv+X69BkK6sU/iPSv5MIHRjYqcyGosipqZjZnMy45deQgwhk2/lKKu0as4t2Dl\nbqzeUuJY2on4HYQwFDNQU1MjGAN79uxBc3Ozo0oRcUoclvMX52/GuH9tcES21e/6cFkdJv9nEw6X\n19mrkEmemrMOT8z5zvL9ZqYWJmIdKDf2jGbBibwmciPCI5ajHgU7y/Cv//sJcxZvU1yzsuAw3l++\nK8qaJQa6Wxg/+uijGD58OMrLy3HbbbehsrISM2fOjIZuRAullQ3ISE9Fh6z0mOphpyuxockXlhun\n6xFbHSZ4f8UuFJfVYcHXu/HcyMstybALr8+5OHVxWxosG4k1duuXbT5hdKMiJ4a1YrMcsXPGXHSz\nIy13pZVBT+HekuqoagEkplEcQtcY6NOnDz777DPs3r0b6enpOPvss9GmTWKusJSojH9jIwDgP+Nu\njK0iNhX0Jo8Pj83+ViRWKvjF+Ztxfc9uuOGyUxX3Fh2twaJv9uDPv78UHbMtlMMo7FqYWE2iOmay\nH2kluLKgGF4GDOp9emSCTKDwDBhdZyBKnoH/W1eE9FQ37rntUvsTlKdve8yAvryiozVYln8I9w2+\nEBnpuk2RVmoR3GsviTzDRneYYPPmzZg8eTJ69OiBCy+8EA8//DA2b94cDd2IOMOuYl5T71EIFss+\neKwW76m48uZ+uh27D1fj/9btt0kbdSzvWtgypJbIvQTASMyAfRlcsHIPPv5mj23yjKA1tVAr69Fa\ngfD/1hXh4zX7bE+Lm2YMliCc8UEhNu8sw5otRxTnquuasWHHMVPPOnRtLI3xRP7mdY2BWbNmYcyY\nMcLvv/71r8jLy3NUKSI+saugK4K4LegQacCVkdsj9QzEsl6wpcHSESFpSxKwFhR7Bhhjkvcd5TWH\nYjJzRWzsxcAWEIawvH6l1T3jg0L8+4ufsX3/CdvS1CqjjDF4fdaDbY2kEe/oGgOMMZx55pnC79NP\nPx0pKSmOKkWEiafC5ZQuluRaVMVMr8FqfoU1C2IcUR0pJuIHE7JHJPYMWDFI7STmcTNxNpsgNO5f\nWdtk4GpjX7WWRq8s/BF/fmUtfBzDxAyJ+B2E0B2o6datG2bOnImrrroKjDF899136Nq1azR0I5Ac\nc93NhJ6JFwdy2lCyPEzQglXtSk804OSczMjStuPRmPEM2JBctJF4AmSeAS1a6zoDPn8APx+oxEVn\ndkRaKr+f6PX5sfbHI+hzSVe0a5umLtsm68rgG5H8Ul2VWEPYLwcrAQANzT60z7QeqJ2I30EIXc/A\n9OnTkZWVhQ8//BALFy7EySefjJdeeikauhGIvEGyE8cKOjMvm4FF1OApdqzjyLLuGYhs1HL8mxsj\nuh+QusBXbC7G15uLTcvQDYZK8C1wxd8WY5B5OqIdQGi/TN00Zel/teEgZn+8FZ9+qx6P87/8Q1iw\ncg/e+uJnw7LN6BEJes/QiLHnjvDbjSdPrllUPQOMMbhcLqSlpeHhhx+Opk6EiHjyDDg2TAATngHR\nTXY+G17DF6n82MYMhP9e2BKYN8BkpL6e/sqphcb5cOUenNo5C7/u2c3UfXYijRkw7uloLTEDcvYc\nrpL8y6O8ZYGvEp01NGyrKwyJaQnYNbFIllMk8jplqsbAvffei/feew8XX3yxpKcTMhJ++eWXqCiY\n7CT6KnhcFBGETMO3Jyf04VtFJR2OQKuPPpSVWK/CFjEmRJhN7uuCoKcilsaAeJ0Bxpj0fcXBbAKr\nzFm8Dad1aYfbf32O4USDwyTBv11uG+LxY+IaiFZCGinEgVFnFVVj4L333gMA/Pzzz3C7aXPDWBFP\nZcspXazEDDBm74fHk8QsWgNi74VVQkZ3JPdHipno7Hgqp0ZReAYMjnrE+wqEP+6twI97K3SNAaVN\nHjxipLbXLRsGZISwyytixpPlmC4J+B2E0H3v9957bzT0IFSIB/dhCKcW1LCWxchiBjjiFFh+9q5I\nvReR1ym2OJTMRYGZEGvfi5uzeBvmfrrd0r1+yVRCuWdAK2bAAc+A7RLNJcpYuMxEGvMSlBedBt5u\nYZGqbVd9fbi8Du8t3wWPN/LpjkbRnU1w0UUX4dVXX8Vll12GtLRw9Og111zjqGJEkHgyBhytsQzK\nFjwDsPbhqtVzdsYM2LLoiRl3CYdoTC20Gj+o3es25xH5cW+FiZSlyD0DEj0sS7WoS8xnE4R1cBsY\nJtC7IjZTJYOJqpUfI884UiPGrnz/7YNC1Df5cEpuJgZcGZ1VOXWNgVBsQEFBgXDM5XKRMRAlrLqq\nncCpob3geK2xe12iasjWAEKeZ8By0IC6TMP6RGgN2FFu9PSXLFpjkzVgKnwkQvyKRYekeqjhRMNt\nW7ydhRX7QgoIK/gZeP5m1T12ogEfrNiF0QMvRJeT2sr0MClMR6dIik/kowT2ZKa+Ze+WSHYdNYuu\nMfD+++9HQw9ChTiyBWyzBhTT+mAinzYt72fko7c8SmCDkpG7KyO7v0ULw6fNNEJajWmAMbijtKCs\n2NgLmHE1OfBN2hUobFWKOPt2DBPI3/H8/+3E7uIqLPh6N54a1jOYDozE/JkxbvTOJ45nQJBnrzhN\nVGMGSktL8cQTT+C2227DX//6V9TX10dRLSJEPM0msC3QR+EaMP4RhqqpgDz6226dEMEwgR2egYiN\nnWh4Bvh/O5mmncj3JpDkR8tgcUAX28bYLTaeDOG6xshce7PmQmjmhp+zwl+0XrmRdCKeTmx3ZqL4\nQagaA5MnT8bVV1+NvLw8nHTSSfjHP/5hSnBjYyOefPJJjBo1CsOGDcPq1atx9OhRjB49GiNHjsST\nTz4Jjye4Yc3SpUtxxx13YNiwYfj4448BAF6vF2PHjsVdd92FUaNGobg4OBVp586dGDFiBEaMGIHJ\nkycL6b311lsYOnQohg0bhrVr15p+EPFKIk9VUYPnGTCcTfE0Vwtpqy9OxokZiNAQi+zVRZZ2dGIG\nrAUNaJfp6JV3qWeAKRpHVeJ6mMDEtbIfQsyADcMEhvSwY9qNplwpTnoDw/cnbn2tOkxQV1eHu+++\nGwBw/vnnY/To0aYEr169GpdeeikefPBBlJSU4E9/+hMuv/xyjBw5EoMGDcKsWbOwePFiDBkyBHPn\nzsXixYuRlpaGoUOHYsCAAVi9ejXat2+PvLw8rFu3Dnl5eZg9ezamTZuGCRMmoEePHhg7dizWrl2L\nc845B1999RUWLlyIuro6jBw5Etddd12r2EMhngIIHauwGAOz4Jq0pI+JpUojDBmIiMgrJTuUMH7a\nVMiA5ni8CUERIl2OWGYQ6sQ12I1yRUxriZiL3RDlXzQ7J1qzCVxwRbySqJk0aZhAG1XPQKQFYvDg\nwXjwwQcBAEePHsXJJ5+M/Px83HTTTQCA/v37Y8OGDdi6dSu6d++O7OxsZGRk4PLLL0dhYSE2bNiA\nAQMGAAD69u2LwsJCeDwelJSUoEePHhIZ+fn56NevH9LT05GTk4NTTz0Ve/fujUj/eCGORglsC46R\nGzgBC8MEjEVmKPG8E3KsDxMYWxFNi3iY4qS/HLHoT5vGdqPZs/LLIgaNegacMNDl37nlsX8z70H2\nw0wAoe5sAgPHnQhU1JQVDc+A3c13FOt/zXUGGGMIBAIItIz3yH8bYcSIEXjmmWcwYcIENDY2Ij09\nuAlEbm4uysvLUVFRgZycHOH6nJwcxXG32w2Xy4WKigq0b99euFZPRmsgnmIGnCyYhmcTiCsQC/q4\nTPTbI26YIokZiPBhR90zYMo9rX5xNB1h8gBCZjVDNiCdmWE9HsbqrA6GsEFiZGqhbjKyC0LfHU8/\nbeNQVxUFat94QsYMRBHVYYLNmzfj4osvFn4zxnDxxRcL84CNLke8cOFC/PLLL3j22WclBVytsJs5\nblaGmI4dM5Gaau8wQufO2bbKA4AGXzgvTsg3Q7vsDOFvM7rIr61ulk6XycpK535EvDRSW3ZTS2+T\nipycLNP6pKaF7xff065dG4UsozrJadMm+FmlpLpVr9eTk5vbDpkZ6rvC6dHEsdfNlp82ovR59zaL\nnk9ubhZyO7RVXMOjocmrKjc3tx2yNHbDU8PKt5GZFX7nOTlZqG6ZzgUAWe3aqMps9Nv/TWZmhnXp\n1ClbEdxoNB2tZyunXlS3tG/fVjAC2makqd6b0VIm3G71sg0A7bKlzy8tLVjXpqenCMeDHjSGzMx0\nVVnZGu8hdDxUJ6SmBWVnZSm/ZQBIadPEPS7mpJMyI3qn7Tu0tbWe1no2alhNX9UY2LlzpyWBIXbs\n2IHc3FyccsopuOiii+D3+5GVlYWmpiZkZGSgtLQUXbp0QZcuXVBREV44pKysDL169UKXLl1QXl6O\nCy+8EF6vF4wxdO7cGVVV4U00xDKKiooUx7WorGyIKH9yOnfORnl5ra0yAaDieHhDECfkm6FWtLe4\nUV14z+XECenMlLq6Zq5FzkvD31IRHy6txQuvrzetj88bbCWbm32Se2o4eeN5ZYyk4/EEGxWvN8C9\n3khZKS+vQ2aG7sxfVY4fV24kY7b8NDaGGxbeveL3WFFRh4DHp7iGR4Oo0ZXLLa+oRYMFI8jKt1Fd\n3Sj8XVFRhyrR79raZlWZ4nzb9U3W1YXLX1l5jaLsGU2nsVn92coR56OqqgHeltXuPB6f6r1NLcYG\nC/DLdoiamibJea8vJNsvOh7MY32D+rOureOfE39DPpns+vpm4TrxvZW1/ONijp+oR9sU60PklZUN\nttbTdfXqz4aHXt2iZSg4tulAQUEB/vOf/wAAKioq0NDQgL59+2L58uUAgBUrVqBfv37o2bMntm/f\njpqaGtTX16OwsBBXXnklrr32WixbtgxAMBjx6quvRlpaGs455xxhAaSQjD59+mDNmjXweDwoLS1F\nWVkZzj33XKeyFlXiye1k3/Qn2W/OMTVCn+nBY7U4VKa9c5qmAIVSykNWh2jC8TaRPK/InnU01hmQ\njLEn+DCBYjliDaT5tiuORio/YDENq9eKv0EjUwv1UjGmhmg5UTuwJYDQWR3iGetdDx1GjBiB//f/\n/h9GjhyJpqYmTJo0CZdeeimef/55LFq0CN26dcOQIUOQlpaGsWPH4v7774fL5cKjjz6K7OxsDB48\nGN9//z3uuusupKenY8aMGQCACRMmYNKkSQgEAujZsyf69u0LABg+fDhGjRoFl8uFKVOmtJrNleJq\nNoFdcjiR04ZlO7QeTUQ6yYi9KWBPI6Vf4UsbU8NyNS6NZnmX7E3AIBtD1zBYZH/bM3tEXRczhp1l\nI5CFn70Tswl4Eu1aadLeIMMIjXCb9IgFjhkDGRkZyMvLUxx/5513FMcGDhyIgQMHSo6lpKRg+vTp\nimvPPfdcLFiwQHF89OjRpqc/JgLxZAzYtwIh71hs8ylPXT5ma4tQM7dGmHw0tjBmqj907tPQTX6q\nsdmHtm2cqaakexMww/lRrK9gx46/Mk+AdNqjU54B0d8iz0jC7WDMjMkxtjdBhKroCGj2+vHJ2v24\n8fJTcXJOpup1odUZo1kt6nafPR4PPvjgA7zyyisAgK1bt6K5uVnnLsIuWByZmva5ROW9cPPDBHYj\nTz+SWRwuG7yf8TDfWVcE4/4ZmVyR4geO1eDRf3yLJWv3mZBuHMneBFC6zdUQP1v7VuWUegasDkVY\nVkc0NOGywxowgC2jaaLbzZRXNZyeTbC6sARfFxQjb9GPxuRFpI05dI2BKVOm4NChQ8jPzwcA/PTT\nTxg3bpzjihFB4skz4JQm8opYm8gqKqN3R+QZCK0zEMk6CNZTB2DPlFS92T9M5Vp9uernxGpv338C\nAPDlhoOGZZtBvmuh0QbYia28JTECLf/xzulhziiTGj9mViDUQ15vhdcHYaJj+utxmPqGQsaMiv5G\n+lWRewa0z9e3BGCKgxm5OLU6owa6xsD+/fsxfvx4ZGQEp5WNHDkSZWVljitGBImndQbssksUHzhj\nhis8p3a0k+sUiRFm2xbGkdxuc7HRG9oxlRwnPoP3t9PIXfFGU3YigFDTM2CiDrA8TCBK046YAcXD\n1JDptGveTEKRe+TsKQ9m1kOxC11jIDU1OF4XKiANDQ1oamrSuoWwkViPpTsBf7U1Y/m06xPhzWgQ\nE4lnwJaNiqzfCsCmFQhlvVXti03I1UonisXdr1h0SNogq+GEvloxA2bepXV9mKGNiow2UobUsLm9\n0yujRp5NvC06FM3vQTcyZ+DAgbj33ntx+PBhvPTSS/j2228xcuTIaOhGIM6WI3agFxQ8YKLQR1iB\nqNZzsvT9fhsa00judaCHElowzLAMyb28NPjX6usm/S3pocOBllaFgGw+n+EOpsy9bgdM0vhbNzgi\n8wyYMcsj18NISTTncdKWqyZLvkdFJNjmGTC0v7O96BoDo0aNQo8ePbBp0yakp6dj1qxZuPTSS6Oh\nG4HWGTPA65XHOp/y1G0ZnokkZiDC5Hn6M5i0pRyLYpcPE1hKMmL88pgBg428M8ME6gfMpCH3KGj1\n8uU96dDjsCfexJlrte4XxKjkWe05ymeVRKRLRHdz5MWDZ2DDhg2S35dccgkAoLa2Fhs2bMA111zj\nrGYEgPiKGbBvaqG8MTDeK3NsLE2mgD+CrzC8UVHs4AVLMcZMBV1IPQPK3FjtUSlDRqxVxpFW3NJh\nAqbvChHOGbvMDPJGXPzZm6oCxPcFGNxaq+nJPDuCZ8CBFki8wZhwTJh1E50GWC1b8j0qItLFTs9A\nlFE1BubNm6d6k8vlImMgSsS6xyzGNs+A/Dcz/hHZt1CJzCCRnbdjamFk6wxEWEHyPANmRZpo9My1\nV/Z4BiL9NMRDQYqgPY377HQr8+TIvwdTngEVmfrph+MU7MiTWr0lPWrTtoUG9Vb1DFh81hqq2IYT\nM1fUUDUG3n//fdWbQksKE84j3iAywBi+WH8AV17YBd06Zanf5BQOxQwwE6IjNwbUXIjS3xEFEIZk\nRvAhRzxMwLnf7oBGibwIgtwsB8tFWFH6/VL/CZN3ldXSlWY8Ih14MuWeMnMBhMafpdrIhBMLVvG+\nW/tnzzGpXG2VBMR1bOTfnV2ZaQkaiIdhghBHjhzBf//7X1RWVgIILkKUn5+PW2+91XHlCOnHvXVv\nBT5bV4QvNhzEm8/eEHVd7BqxUMoxPkwQLcSR1eY/8GB1VF7VhF2HKnHBGR1Npx/5FsY8z4A5mXrD\nBFYD6dQaIbNEWmZ8smECKwGRkXwTNQ0e7CmuwuXnd9bxDBiXKTEi9JRTSdNsOTl4rBYLVu7GQ7dd\nwhOtipFZN4YcA6F/dT0D/ON2egb0iF6nxzy6Uwufe+45nHTSSfjxxx9x6aWXorKyEn//+9+joRsB\naUEN7fbm88fRsoQW4AWQRWvRoXCi8p/SA/6W7kKqhR3MxB/y3xZsMX1/i0IRwTNgTI8S6DVIlt37\ncs+QuFHmileRoy7TCGLPgGKYQEOeXhv7xtKfsHzTId30X/lwC+Z+ugM/H6hEANIGSerut+YZ0LtP\naswxoYdsJDnxNa//3w7sOVyNT7/br5+2jlFpCYO3GwkgjLTDY5dnwKbFGU2hawykpKTgoYceQqdO\nnXD33Xfj9ddfxwcffBAN3QhIC1csrEUxdo1f8b6XaFnMhqcWttQKKSnObnilVkFF+qT5z9jeqkXP\nc9DY7MPcT7fjmx8OY9ehSv6NsN6oW170qAWfX9oYWlm8hlf55/9cikWr9uqKOVwe3EK4orpR0zMQ\nMGH7S4cXjF8LUZqmG7TQ8IJsdobh2yO2BZhYDdPpiPO7sqAYz85bj2aP35ouEdZj2/Ydxz8/2R4e\npoynYYLm5mYcO3YMLpcLxcXF6NatG0pKSqKhGwHE1d4Ezs0mgKRnpIVjexPIfocqtrQUFxqVl2ti\nRke1XEe8e5oNAYS6gX068r754TB+2FWOH3aVAwD+M+7GoG4yYZZnJUh0ZaYtRV9A5hmQyFO/T/JJ\nKgwba+9NfF99kxcLVu6RnDOaM6kRYcKwQjgrRm4TP+rQXgZmjYjQrBvN+ywUCLNvQPycdhQFl8De\nf7QGF51pYXgvwu929sdbI7o/EnS7PQ888AA2bNiA+++/H7///e/Rp08fXHbZZdHQjYDMM+DwEpWH\nSmvx9hc/o9nLt4rtMlLl3wszEzPg0LaniuWII/EM2GANROwZ4B2LQCjPK6TXiBsdzrLFM2Ahb9LZ\nBPKhC62E1a+zogeTpf/VxoPYXVwl/La6AqFuAKFKkISRdyC+JLSXQcCADN5RI0ZLTb0HC1buRk29\nR1UXoYyqDQeYOG61mrE75CAuZhOEuPnmm4W/N23ahPr6enTo0MFRpYgwkoLq8DDB9P8Wotnrxxld\nszHgytMV521bYIVzwPDUQtXZACZX19NJL+SmsxQzYOJFqX7sET5q/qJD5oSaaWzNyFYsR21DsJw1\nY0DqGZA2CuoCtcblrY4Zi59JQ7NPlp4ZOVa9LNY8CoBoXQ2NYRuttTeM6Llg5W5s+qUMVXUejBmi\nsuidVc8A5warw5G2GwNRHCZQ7fbU1dVh/vz5wu+FCxfijjvuwMSJE1FRUREN3QhIC4PTIQMhj4DX\n5+zYRCRTC1VlGryOt/gJ73dAMAac9QwYGce0An82gUkZJtIwJZszTBRO01ov2Ir15JOMcTPDY95a\nwwlWX5vmLolWPQM6jbqaMWUkOXFjKXgGTK7k5xI8Chp5b/m3tiG421+V3m5/MP9N2bmwWyLvJaNa\n002aNAnHjx8HABQVFWHWrFl4/vnn0bdvX0ybNi1qCiY7Tq9AWFHdiCde/Q7b9h3XvdaqO1eO4qM0\n4RkwPYnYIPLbhQBCt3ljIMZxngBUZhPY+c4iQNmAWnX3i3qzFtTzyT0DBoVoeQasxwyIf0jPWfc2\n6BgDqrqYGyYIewb459UwFDPQQkqLh463/kd4mCD0rzlvm63GgO55s94567qYRbWmKy4uxtixYwEE\nFxkaOHAg+vbtixEjRpBnIIo4PUywurAEdY1ezFm8TThmZLxPfoWZ6Y6RxAyoPQKzFSZvG2UxkQwT\nRNBJ1j0eiVzTngEdr7lVN738UlXXto7MgIlrechjBgx7BiyeU79J28VudZhA95sQXxvB9LrwegHq\neeDep1RDlRRXyBjgLrQtlWPgm9JbnMnqNs7G66F46DJIUTUGMjMzhb83bdqEPn36CL9t2e+aQNHR\nGny37YjmNU57Bjqf1DaYjpFCrBJwtGDlbjw0cw2q6vRdeEExSjex8ZgBPh+v3mfsWaksdKJooCIY\nJjDXO9Q3vKygtlGRGXiLCu05XIVH/7EW+4/UyIxDM65s5ftXO2cUK71niWcA0v0otPIjccXbFDMg\nNYKsyzQ1TCD622/RxQ+EtzwOaORBq8kw8t2GAnm1yzVr0UPtm+Ibe7bWsTZX19EMIFSt6fx+P44f\nP45Dhw5hy5YtuPbaawEA9fX1aGw0O9mK4DH13QK889VONMoChsQ4vU9RVts0w9eqje2uLDgMANhX\nUmNaTgjD+VSpVb4uKMaWPeUGEpf8ozgeIhLPgJnvV90zENmL591tWiancv9o1V40NvuDC8xYDVZT\nOGWsyYl06EK+a6F0S2P1+7SWLbaqknQbZ+sy5VshG0U6ZKJ/o/gSN2dqoaoI8XEjMQNMmkYky4Sr\n1V9GylHpiQbNejqchu3WQNRQnU3w4IMPYvDgwWhqasJjjz2GDh06oKmpCSNHjsTw4cOjp2ESoFXA\n1ab/2IWp4CTJfdZlyS8LfozKe3lbsGo1zTUtQUaaaasooeYZsDK10Ex9pXpphO/alnUGxPI4RhRT\nu7d9mf0AACAASURBVFhXrrpnwFQDH6FHQd4ASowDrWQ1PkmrPTmtIZdg3owZpRI5Fj0DTg4TiJ+P\nkWGC0PWpLcbA0eMNqK5rRufO2eFrZGXTiIEt9QworxVXO00eH8a/uRHtM9Mw+4l+6srC/s5bFG0B\ndWPg+uuvx7p169Dc3Ix27doBADIyMvDss8/iuuuui5qCyY7TuxZa3QSFawxYkBO6UdW4kBsDGnWi\nR2V9BKnM4L/y71+uk+AZcFsZEovcGoj0rduxN4Ge9aDW01IjZNzxjcGQTIvl0fBdYcQrEAbMeAY0\n9LX6uWouf2xq8SATPV4VI8zsMAE/gFAqQ+sr0sqf3DMAAH/553p8nvd7zsX8tOWy5H/z1xkIpxda\nBl6ts2F1h8l4Q3OdgbS0NKSlSd3IZAhEl4DB3opVrK5wGEljo+xNqUW/m9NJbbEkbuo6skP6WIsZ\nMH0LR0ZkQuzYtVDqCeK8H5UxWFWdAgzuFKUxYLkBjVCGNBiNyVz1+g2UXIfgucg9A2bOaV2rbwuI\nDAeTngHJMEEoZkArAJNjxRuZTRB6nikaRrmwwVLot8518qu4xoiZ6cEqf+tebFa4wzi78DoRMZFG\nTOvLN9MT01bFqCz+1EJeeuYybMQYCLsUtXt04b0JHJ5NoBZAGOG75m9UZE6org4aPUGuToFQpS1/\n9uYaovB95tKX45d5BuQxBKrpquigd58WWt+OU1sYSzwDJgMIxbhNDBPozUpRO6dlDBhJQ3440rIj\nkWskVkKG0Rj8uAggJKKHppvM4QhCc/vHi/6OoCevtAX4m8TwVwZT/4o8Hn03B1P8wf0prE7n9GwC\np7yKvHITSVp27IIYkqHVgJpx/atVwr8cOIHSEw26+vg0phYaT1fdsDGDVuMU+l1W2YCdByuhhTgL\nZmYTSO4zmQehh68qXe0+/fRCZ7TW+xA8Ai1yVGcTqHhNIglKVMq194OO5qgDGQNxgPZ2qeLKUf26\n1VtKsPGnYxbSNnW15n3GAwhllZ2KPLNTfgwNE7SIVIqWHohsaqHpW5QyIuwRcIcJzOqg4QpywZxL\nGhC9T1nlaXkJXY56Pn8AMxf+iPFvbtTVJSATYNgzoJFvq+2K9gqEwX/HvbERf/9wC7w+9XJuxjOg\n1iCaLb+8FQh/KqrE7I+3asbxhMx67ZiB4Dm3lmfAaCdEXH/pxVZYfo/Wr+M9B6djxsSQMRAHaFUg\nUktf/br3l+/Cm5//bCFta71YvjFgXk7wAP/b48nTDCDUqCTDSQn9iOA9Xj/8gYBymECIGXBmmMDj\n9WNV4WHUN6kFJZlOVnY/zzNgXSjnlUmOGpEctgWk90nbZBPlUWKctvQKDbbG8sVr5AGEmjEDGvm2\n8owZR45UN+nZZq96RSDp7es+C76Hw2weXJxpf0VHa7Bt33EU7CoLXsPRL3TUiCEkHyaYteAHxUJn\nwhCgiji1+otXr5oxUKXeLOvfmJezcFs0AxJ1NyoinMfouuROWInWRVq3YvmeAU7jxUlDq2k2tAe5\nrMJ4cf5mdOuUha45mZLLnF506IsNB/HF9wdwyVn8bVIdiRkwKVPP/Sk5ZCZmQHKfvFG3qp8gzhDi\nIYLg/WaGCaT3qZ0zg1bjI//t8foBlfVBzMRfqHkGtDodPHgBhIo0uIt9MV091TwDq384jO5n5aDX\neZ04hipfoKoxoGM46zXwpjxkGhUYbxVXp9eZEUOegThAM3hIVBoiHdvSk6+H9APSPm9UTuiAYU+D\nhmvAUAChTHZ5VRPKqxqVnoEIAgiNtEhllcEx7eKyOhURkb3rSIZxwjrw/waUwwRG2g+/YAxIDVyr\nY65SW8ScNSD/lhigGDYwlrDslB0xA7Jz8vpBayMxvUZOcq04DaMBhJzPQXD3WyxfRhYd4n32QuPZ\ncpH821bK4r84vfgaM0aV7vvXOM17r07HjIkhYyAO0Co/krXGHSgYVud1RyKL5xngVQhm9xm3Mpsg\n1COUN76CZ8DCRkVmKkXVVxoHngFeC6Xq0jcgW5gCJrtWup6+GfWMlRkeShez8UWHtFYLtLrfp553\nUFy2PZrGgMFGHZAob3hqIeecsAKhyfop7NbXyLvgPVB/18IZM8aPilckLErbWODpKJerBc+44RkD\n5BlIMrQXHBH9bbCiCzCG0soGQ42z1dXyImls5GkyptaT5dysYQ1ojaWKpEr+CTAW1EeU1sJv9kS2\nHLEB3C7t8dJIhwm4z9OsDL171QwDFcJTC0X3yb1CZpTk9IKNPjfeeLPRRYek93EKs1kUz0BmLAeA\n+sZwbIlWUJ48xmjXoUpMe78ANQ0eZbIqQXRGGmcxLo1hglCj5+J8uKE0tYYlwgaD+jVh3aRylbL4\nx/VmypgJxIzkw+UNE0QzZoCMgThAO4AwfPLbH7U3NQrx2XdFGP/GRmz6pUz3WlOFTafSNr7okPw6\nlamFJkPiDa1AKP+XBXsGYrHf/HBYZAw4M5tAb1qVmWGC6nqP4vnxx29N9tx07hUf+W7rUXy54YCm\nPL/QYIsbHvXerJ6+PLe+0efm58QMSD0DGga6TH+pHEPJK9CaUhlgDLWi1e/kngGfP4DSygbsOVwl\nublwdzn+tmAL9pXUYGVBsWb6hqcWck4ZmSLIExC63MgwgVakvXLYUTdpmTdKu2MjTnp14WHNayNp\nu/meATIGkgqjAYQlFfWG5G3YcRQAsGP/cd1rza0zoF1RN3r8xhocnmeAdxn3I1WXb2ZqoXhKWyAQ\nkCjgDzChsXAqgDDcm1KTYSyt/Udq8JfX1uGDr3dL7+c8UfPDBNr3io9t3lmGJWv3AwBO1DRhzuJt\nKK2UbmjG9QxAveI1Q+gxGvYMhGJCWlzcDJDNJtBAwyNitfIOaDxrxoA6Fc9AdV0zHpq5BuPf2Ijp\n/y2UlL1vt4o7DxwPl8SLIN6nwZieIdw6ZVmN8LCRtifCHwigiRMcrGYEqElTW8CNtwqrmlH6/ord\nQrwPT1gkjTc3ZiB6tgAZA07hDwQw8e18SW/p49V78em3+xXXGp1aaJzgx7l+xzEsXVekeaUpx4Cy\nIyZh8Zp9WLRqr64c+Qcj7x1q6aalrpExS7FnQDwdTV6pe4VFh+yZWvjLwUpMe68AtS3u2vAmLZF9\n7TsPBRehWVVYIjnOq5glgXsBhl8OVmrPWRcbfypX8Fiydh9+3FuB/J9LpTqJDDGxTlantUkr95Z3\nafB+YVGpVLeQrt/gMAEnWdXfRtFbgVBsDIgbjX1HamTXGk9TfKm4vJgfJgjrqTgnM0J4vWi9YYIX\n/p0vM2wEZST6iuOA1LRX/sWPGdBavEk+HKllyJmBP5uAPAMJz/GaZpSU1wu9JQD4X/4hfP79AcW1\nWgEqVoIGxcEpn+kYA1aDEtXK6IrN2u5I3r3BFQh519nQu1WTycKVkD+gTN/b0vuysmshT8efD5zA\nviM1KClv8e4IFShfRuSromk/u2+3HsHMD7fgw5V7NIRoyHOpvwv5tL0Q/EWHZJWpujYc/ZjiT+Mx\nA8EL01JCxoBxz4DW8rOW1xnQGKJgjEnWo9BaT0MtfZ5JK75UumuhQUtIhubuq1xPlQHPAGMKD1MI\nXqdC/K9SljJtnhz5easjqWbPk2eglWLmwQYYg88fsG0FKqPrXgPmKi+1j0lOwc4yVFTxP2DuvSqe\nAV6Hwa6AmoCoR8p77s0tH6apNdFb4FV8Ias/9D5dOgGEMz/cgh/3VJhOO4ReudlXUg0A2L7/hOo1\nTPUH57cItdXiQs9Z3pNS8wyYmtLFuV+L0PtIa/EMCIGkPOGa6fIbJDMwpm5Ahc6LYxw8GoGy5oxI\n/nPXHiZQ70VrbfijNcxkJGbA7Dnu9Sr36scMaCdkdddNObxFh5yYQaYGGQMOobWGvhzGgIdmrsG4\nNzYozxlxfcsKIC9yVw1zbkVjFca8z3Zgwr/Vl4Pl2AL8dQscmUoZ/jv0EWt5BuwKIPT5Qg1hizEg\n04HH//IPmk5bSwfelDitYqo3LKSmu1tFaPh6SbWsGoClO5VV/LfQy9S8RUAxW4TJxs210tVoOK0Y\n76ylM6CWeNBQERkDGlMLra4oKl2O2FzjbGT1x7ArX3QMSuPQSHoKmQbegcfrx4Yd/OXafdweufo7\n5nVmjOgrvpb3hegN7TkNGQMOYaZ3Hiq8FdVNque0iKS4aK4appGQXtS2Vk/HaMxAgDFU1TVjuygQ\nMuJhAkma4XTk+QlVuJamFiryxwSrP/TB8/aAtxO992qsktFoIDQei9rSDDzPQEDDM6CnIu9atXz5\n/AHsO1It/JZvRMUgbRALd5errmjJVH9Y9wxoLyQkXR1RHOehaAgtGtBG13rgGoUtN/g1Ms83TlvO\nmRxeUNOFa2u28Nl3Rfhxb4Xo2vBFjbzgRIme5o1S9Wv1DSY12U5DxoBDmBpnsmgZh6+ReQZM7fZp\noichSdN4Gla1YAyY9PYm/OOjrTh6vF6hgxxD3hhRD0XsGZAL9kTgGVCso4CwWzr0rsy8Iytwe3Cc\nACrDngHhb+3GOsCYvmdA0ZNTS7PlWRnSL2Ro8EvIp9/tx7T3fhAC0UJphoaBArIGt7bBi/eW79RP\nVz5MYKH6DoiMxaAM+XlpvrTW0zAzTCBp8AzGDGjFovAada1AWb13JtdL7Zy8VPPEHSyt5eoMAE3N\nPsX18/+3E4da7jGz2JquY0DjAu4QDA0TJD7moqKN96L5ackOmGhpjEwH8vr8+HjNXpSJAnki8kZw\nGku1yiIURV1V2ywcU8PIMw97BsKVfyCgrMLDngHpJ2IpQEzkBpYPEziF7qJQLX9rGVB6vSNewxcI\nMN2YAXnwlrQyNeEZ4Bg3avf8VBSMjfhhV7mQLhCOb2BM2bPdUcSPp9B2IWvrzJcnjSSXNwDymQ5a\nM0DUGg/ea5bPLhHro6Wrmhzteix0sVKW5nRhjf1G/AGGIxX1aJQ15lozHuQ6A3zPQF2jF1PfLQjq\nrrcCIccoVcNsXR/NYQLaqMghzIzd8casQsgXR+GhjBkwjpHCtvbHI/jfxkOm7zOcJlOrZMJ/cwLR\nLSauTFPbMyCbGgX956tcACg8bCIfJjCiqpm0NI9LnqcBo4Rzvdp5cbqqngHOOgPyd8/00pSkpfxb\n7Xl0bNcGh0rrUFUnNSpTQmMaTLlRkZrrXqvyt2YMMG1jICA9Jo0ZkF5rdRaK1lQ6ua5q93KX9Q3f\n2HKt2OgIHVPXi9dQh/D7A3jhrXxFWjxx8hIpvobnGQDC+dEPZDVhwGoZWtzdE7Xl2Ql5BhxCMZan\nUQp4UaQhGlQKqlS29LeVeAU567cfxXvLgm7ShiaODhEUUo4toBozoPhbI10jH44wFxnhoCzGgIBM\ncOidpMgHwI2koegtsqgPExjd60GuyL6SaiHQStLz5gU38dINaAUQttwnaxDUpnmZqVj1AghPym4D\nAIIxEDLKwsMESi9ZyBjw+QOShX7ESfDetVkCjEkMD/l7UgQQejViBkykLzG8JIsOaRkDvGPqz17w\nvnFkh/7U0lne6+/WKUv4W7HZFJP+K8GlNOrV0pBjxuDTN2Dj1zNAxoBDKD5ojZZKXBHIX77afvdi\nIuul84+//eUvWPPjEXi8fr6L0XKKvI+LcRtyaWXFhGuNytXWQSpf7oEJTd+S71poZExYfgVj4Xcc\n7pE7aw3wn6eyIpZrMe39H/DvL36GX7Yqo1HPQIAxuNQCCDmNBpPpqudybfb4sWZLCZo8PlMNS3Zm\nOgAIy/qG7g0PEzBF4xL6/fQ/1+PhvLVcvXjvWkt/HoEAkwTcKhs5JjFUtIINTe1CKtI+koVzjDRw\nPINBaLw1dG7ySBvqVNEQFG+RHnkiDU1erN9+lDv0EkLL+wDwjTOV5HQrRuFazufPn1quLc9OaJjA\nIeQvVst9Jy7UPn8Aaakpwu/6Rn3PgPxbNDOtUXc8TEWe7QaISsMiv0crVSMqiXsP0u2hpRVL2DOg\nvoKaehrKykO5zoC+HKts3lmGknL+1sghhDqpRQ+fPyCJj5DZApyhKJeq90HNMyBsYSyRq/QUiM/J\nWbJ2H1b+cBiHSmvRt/spnPS5SUMexhDSXbIcscrLFa/+J9eL967F1xl5z3LPoPybDMjKqnidAbnG\nVgPOjC46pLXOAA95b93sMIF8GWKxcc4zmgDpM3n7y1+whbNexz8WbUW3Tll4YmgP1WECeR5CKI0B\n7TKrdq0cw948hyDPgEMoCpDiA+d/3PI5xA3N5j0D5mIGOMdksvnBR9bSC8pXWtZaUcohPWZ+uAX7\nZcuvSq838+FI3dPyiiUUx2FpBUKFXqLZBKHX65AxUNvgweuf7UDR0VrFObVFdZauL8JDM9dI9r7g\nNUhi1DwkWgGEoR6gYphAIlcki5NGSMfDFfXc4QW1MqDQv+V3ijiA0GBDqrVMs9qQhxbyRYS4ngGR\nLPEeHHIj1lTMgOhSo8MzWsMEPOQePfFQUegurfvlLnzx96g2fVksb8/hau41ZVWNwlTDRo+6MeD1\nKReDkw+Z6ZVZMVqvR8+b5zRkDDiEvCKQf6SSecOinoFk7DDA0Nisv/mOohBFGDMgjTLmrygnvsaM\nJyJ4r+w39D+EAAuupa+FoZgBkYdBnHf5MIGwKI1tngEm/A2oj6tHitbqdGLlQ3+5XS589l0RAGD7\nvvB6DvKFmHRnJwjX6S86pHj/Kg2RlksVDKip9yiuVXs/8rKknE3AJOPmmmh4Brj66yB3+/OG0cT1\nh8QY8CvLmlEkRpjRRYd4M0g0GzilESBPWzNmQOYZEH+PckMobFyIjhl4Hlp1bG2DJ3qeAd4wgcnN\nnyKBjAGH0PMMiAuFuDIQ/20keFAuizEW8WwCyccExh3fFt+l1q6pbWmr+PiZctEfuR7GGnojFWG4\nQRJfzutRuQC4FIaQEUWUegnDBNEcBJQhqVe0GlqE3pGoXHEjxXmVl7pnIDxMwG+YAfUhAzl7S6ox\n99MdCl3UPQNiAzc8c0DsGQgEjH07AekHIsGaZ0DaGCk6DkwqS+w6V3hwLHoGpMMEGrdY9AyE0grH\nDkg7HGrIpxaKh7IUM62kSanqK6fJ40NGegr3XHW9Rzf+S/JLJ0GeIbxk7T78crCSAghbK/qegfDf\n4nnDYmOgvlF9iECrN2UqZkDXM8AU463yNNUq/yVr96OhyYu6Ri+mvV8g9Ow5toBKL1Oqhx6Geu3C\ntdJGiBeM5Ha7FB+ImTTE9ygCCI28IpP1wKHSWs0AR17gm1iNj1aHd5z0y9ZeCPfsRP+abRh4ngGm\nLL9GZCnTVd4vOS96vQ/NXCOMIwueAQSDWOUBo7rpyn5LJv1p6P/i/M3C380+7ZgB8ZoYANAscmvL\n10ZQM0C4cT8yo8yI3nqzfpTXS+/jvSe5zGMn5FsEhxHH8PhUGmW1dSt4eH0B+PwMmRn88DmfP8D1\n1HAThn6nRX5vWWUjvtxwEDM/3MI3uKPYdyBjwCH0rEnxeTXPQD1vSl8Lah9TwKRngFd4A7LCrRdA\nqJWeP8CwqvAw9pXUYOaHWxT3AlCdWmi0l2jumnCaenOrXS6XIu9Gvk1e5RGeWhiWbTdT3tmsfQG3\nzGisCSApB8ryzHsWTR6/qhErNMhiuVB/z6acKIyvZ1iW9Hjh7uDiQ/KYAcVUUq4sUbIWXcYHj4Vj\nOuT7YHA9Ay3H0lLdmp4BUysQqpR/I4273jG5rIDs/TCNsjXhTfV9TaSeAbXZBMZ0A8LxAm3b8I2B\nQEA500n523g9Fbo35G2VrC+h0yFyGppN4BDyIBMtC15iDIgKR4PGtMIAY3AjPEdaSNdk4eFbo9Ie\nOT9mIPy3VsNmZO+D4Fxzzr2iY0YquZBRYWhBHybNO0++283pwRt4vPK8BBgUMQNGTIG9JdXY+PMx\n9Lm4q4Gr+WnL9ZBfp/ao5I29vJyoeWomvp2vqkN4ERepImY8A2r6ev0BTH13M07JzeKeV6tUUyQx\nA4wze0Ra0btc0r2bFWItfIuhoOG0VHdw91LO9xF63pltUlHX6BV0UcQMqLwXvfJmdGqhntGulNvS\n+Lc8mECAoehoDU7umBm+xsS4uNhzowggFNJSHFIltIZKu4w07nn5TI7gMXPGkuS8Qc+d1jGnIM+A\nQ2h5BuRuP4+OZ4AXkCWXF04XJgMIlcfkFbJe26p1nud+5xVvvQ+h2asfSKkmmytTNkzA62W4uZ4B\n494HcZrymAGjnoE3l/5s6LoQ2j0J442rn8kXA2qRIOrhGQ0q1NKNMfWelZl68EhFPYqO1uJ7lZ3p\neIsmAbLliANMMUwgDsjkrpOg0Ws02kn3tAwThsat5d8MC4SfdWZGKvyBcHlSWxvBCGLdld4Ivhyu\n0a7RmIdnEwR/V9V5MPXdAnz4zW7dtHhIPAOqAYTGvBwAUNey7kS7TDVjgCnqJq2ZNnqNt9nvI5oh\nRmQMOIS8UEi3CJW+ZLVhgtAHn56mfE1qU4GCAYRmtk/W9wzwGi5x+loNG2/6Dy8CW8/9aNgY0PsY\nRf9qVYZAsNeoXNPcgA5gyEhPQZ+LTwYASNcZAI5XNyo2TrELreWrpQ1VyEOhvXRwiNBzlfTuTVZU\naosOSV3GyjTFqJW09FTtqkzdM+AW0uJ5BsSL3oTaHsm3p5gmyzds/IFAMKaDo0fI4Ai5quWzCwIs\n/NxDY9uhoQJFZLuJXrZ0hUn1fEjvUZ7X9gzwr/l+u9RoM9oDFr8f5SwMqY6AfqxRdX1wRcrQolRy\nxIaYIFNp7Yf/1EyNk09RBcP3opJnIOHR8gQEmHxLUvWphYBy4ZvgufDf8t6UvAHzBwL4dusR1DR4\nIEevdxdAZAvkcD0DXAtY+5jWhiVS2XoXhK+TBBAajBkwqoPLFXZpiocJGGP4419XCBvn2I1HYxMb\nbsWi5hlQmVoozBcP6Fd8cnirSDJOzyt8LqSitX0cPv12P74uKFakKUYZMyAzBkRGqBFPiJrX4NNv\nizDlnc1Yt+2oQpeQZ7CtSkR7MNg1+Hdmm2APNmQMKDwDZhoPzvvl6S7XRXar9uwDwXhUTZqbvhri\ndQbkszB4wvWNgWCdmN1WyzMgOyZfZ8CEZ0BLHb34LadxNGbg73//O3744Qf4fD78+c9/Rvfu3fHc\nc8/B7/ejc+fOmDlzJtLT07F06VK8++67cLvdGD58OIYNGwav14tx48bhyJEjSElJwfTp03H66adj\n586dmDJlCgDgggsuwIsvvggAeOutt7Bs2TK4XC489thjuP76653Mmi7i8uIPMIVxIJlaKF5nwK+s\nfLjGgLj3Ljsub782/lSK+f/biXO3dcCE0VfI5HB0F1fWAf6Kcq9+vBVDbzgX1/U4RfND5m3CxBsT\n5XsGwgflK5GpwXPp+fwBpKcFK1pxz0ZrnQEg6EK25BlgABA2JLTWnbcbTaOJ01CpNbPymIEAY2j2\n+gWDMqDmztGAt1GRXIyVqXkAf5jn8+8PAAAGXHm6qqzQMEHIHSyPjxGXiwCnYVMaA/wec8GuMgDA\nzwcr0be7NAbEKxsmkCMet5Z7BuT5NrxWAqTvgbsOCkcdofdtsAEM8G7gXRcAUtz671z8euSzMBRp\nQt9gra5rMQbUhglkm0QBwfx+8u0+MBZcnXLjT6Wic9rpaQWccj0DUbQGHDMGNm7ciD179mDRokWo\nrKzEH/7wB1xzzTUYOXIkBg0ahFmzZmHx4sUYMmQI5s6di8WLFyMtLQ1Dhw7FgAEDsHr1arRv3x55\neXlYt24d8vLyMHv2bEybNg0TJkxAjx49/n97XxpnR1Gv/XT3OWf2PTOTfSeTQDaykGSyAAZiCCib\nCQkkgIIYQ0S8IOZGVK7IKnjBBUUQ5OWKCFERvWw/eIkXTYgvhBsSFTCISkJMZibL7Ms5p98Pfaq7\nqrqquvvMOYlk6vkyZ3qprq6u5V/Pf8N1112H3/72txg7diyeeeYZPP7442hvb8fFF1+MBQsWwLLE\ng+togP6IaY5q4o1S6AWzr8/PDIgM+KLoWYn0u3uvPxpXUJwBkXABAK2dfXjomT9jwdQhyslAlIRJ\n6E0QEMwkKJmI6B4AePC//4RX/7gf3/78QpQWxVlKj7qW1z8CzsTjF4TCDE47c6/zH+06mus4A3x5\nKnUKs4hl3kNlQMi0VRq4/nu/d+1YZN4Eyrq664JcMObHiQ+SCouYHebZkjUyyJsglRaNM/HY4+tM\n/6ZrzdeFqAkKE+LpmDEgzAgDPRI1gdRmIIBcCc0MCOI5hAlfHHaRDBof9HjkmYFsKHWXGZCoCdK2\nv5+nbRu/2fJ36fUquKczrxHkxXFchCOePXs27r33XgBAeXk5urq6sG3bNixevBgAcPrpp2Pr1q3Y\nsWMHpkyZgrKyMhQWFmLGjBnYvn07tm7dijPPPBMA0NjYiO3bt6O3txd79+7F1KlTmTK2bduGhQsX\nIpFIoLq6GsOGDcPu3bvFFTtKYHadads3qbDeBFScAYGricjdSUZHOuWyI19GPwLBeqp0WrxrZ8uQ\nnxOrCfzXBTEDQclERPcAcKX2w22Z1LXU89jcBCGZgVB1yNyfuZk1QgtRQATw5akZFFvwUx4tkGcG\naFdXEX0aBCEzAPlOO8rkHpTqO8ibwGXhOANCWkjkjShFCKNL5+tCFrXCApWaICMMFBBmIJmpn2BH\nnwXCWsyLmQFVuery+OcFfXN6YySLthmlX5IollIDwrQ/tXV/Fmi/8KgWBo4LmwHLslBc7LiPbNq0\nCYsWLUJXVxcSCUcCq6mpQVNTE5qbm1FdXe3eV11d7TtumiYMw0BzczPKy8vda4PKOJag+w+vJkin\n2fOBNgOCQCgybwLb9idlKZT40JLrVcecDWKQtCs/L1ITiAwIg1wQg5KJiO6hyzSoHSDg7HAYAy+R\nmsAwfPrqUGoCsPYGTFbKY8gMMBN45q/UmyBtK3XK2Sw68qBD3oE3/tLsi8lAQ7bBFTE7NGR9lCwu\nSUliqpQgm6CoHUX/y/oK33aezYDE191WGBAqLNuDoKKog+w4whsQhmMGyOcL8oag+6vMPibKX2uV\nqQAAIABJREFUAuoaECptBri2UXlPBDIg7P/MJlFQ7nFjMwAAL774IjZt2oSHHnoIS5YscY/LO1v4\n41HLoFFVVYxYLLdqhNraMvd32X4va1xlVTHaqB1bTU0JTGrgp6keniiIu+UUlziCU4FgZ19VVYLa\nqiIAQBc1YVVXlyAeZ6+vqvB8euk6AkAs7i+7gIrGVVlZjJLWHt81dHlKYSCVRklJAXN9QQE78OIJ\nSzjLl5UVur8DNn4uqmtK0dHVh0ef+TPOnDPSPV5RUYTa2jLKINBAeUWRe15UfDxmoba2lDlWU1OK\n8hIxpUhgmgYsy0BxhnosoijIIgkdqQL/zWgUcpNYokA8qQFAaVmhWxbJjMn3FYLy8iKYlBBaUlLI\nnDdNg/muYVBUlEBtbRlKS737KquKUdLiRZx7b18rtvzpAC78yAle3QyvDRKSBbOoSN6utbVliEvu\nKyt13ou0Gy84l5V7faSqqhg1FUUootq8rLSQHfd7vERaVdUlqK12xh4xfCtIxFBdw/YpghrK956G\nbduIZbwl6gc598YLYqitLfN9b9n3LCkp8PWj0lLvm/L9v7qmVEidW8RrwzDc8vwhuz0UFjrzmeoa\nwJkTS4sTyqirAPud+5JcrTN1Sig2PzzaMllhR4+oEp4vLS2EzTGzJaXyfp9IWMrxSuZbM9Onm9o9\no+4CQawDg2rnsIh6vVu3rO4KiVdeeQU/+MEP8OCDD6KsrAzFxcXo7u5GYWEh9u/fj7q6OtTV1aG5\n2UsxeeDAAUyfPh11dXVoamrCxIkT0dfnBNmora3F4cOH3WvpMt577z3fcRUOHZKHvMwGtbVlaGry\n3MUOH+5yfzc1teMgFWKzqbkdh9u9BbaLCi506EinW05rWzcA8W6yubkNSDodueWgl22uqamNUTsA\nwKHDncx5Gj2CHXcn5XXQcrAdba1dvmsIDhxoRdoGigosmIbhi5qYTNno7PDetampjXlfAOjtSQoZ\nhMNHvOe2dsgFEhpNTW344a//iF1/PYjfv/mBe/yf+9tQGjddA6u0beMg1Qf4NgOcSfhgSwdzrLm5\nDT2d6gU9mUzDtoHuzHs2U9+nrT3ce/Dv9I/9baivLkYBN9m3c+1CP4tHa2uX+/27M9kwk5LdVcvB\nDuabtLaxfaC3L4W2TP8Mi7a2bjQ1taG11bvv4MEOXzk73jmARVMGu33TgNdve/vEDFGroi5NTW3o\nkiwyPd1OXyffhd8ht7R4Qn1zczvSvUl0UOPjCNWmAHC41etTzS3tMFOs1X93T59vDBKkJd8ibdvo\nzoyrVIb5aWrpQFNTm+/7y96zo73H91y63XlmrKmpDd0CYaDPZSTSbnmisUvQ3uE8VxotMIMDTW3o\nKk740kXzoOembi7bYDpto6mpDT2KyK08Drf1IBEz0XpEPMcdOdLlq9MRybUA0N2dlH5fwJtv07bT\nxgep8drR6Z8bkqm0sjwe/DokOi9D3tQEbW1tuPPOO3H//fejsrISgKP7f/755wEAL7zwAhYuXIhp\n06Zh586daG1tRUdHB7Zv345Zs2Zh/vz5eO655wAAL7/8MubMmYN4PI6xY8fitddeY8qYO3cuNm/e\njN7eXuzfvx8HDhzA+PHj8/VqocD7GPP5wmWuhSQIBhDOgDCVTruhVZ3n+nX4Ir09Xw57zPvd2+eP\niEaDnBpVX4YRdf4dTxjXQl5v7NaDOhheTWC7ukT62bf+1+t46pW/MtcFqgkENgNh62DAozRp6j4b\nHeB7+1px08P/D9/5+Zv+Z3HN26PIWih0pQxJZfsjEIazn5A93y3X9n97YaTCAATRy0FqArJYWdwH\nZ2x4JK6R7IOCnylTscji4ztt5BjyxjM787bOPtz31C78dS+b0lvWDqKj9DHSR4mdi6w5PQNCun7y\ntif9M6jf87k7woCPM0DeKEoZyVQaMcsU5l8hZan0/DyiqlTTAWqCo2kzkDdm4JlnnsGhQ4dw7bXX\nusduv/123HjjjfjZz36GoUOH4rzzzkM8Hsd1112HK664AoZh4Oqrr0ZZWRmWLVuGLVu2YNWqVUgk\nErj99tsBABs3bsRXv/pVpNNpTJs2DY2NjQCAFStWYPXq1TAMAzfddBPMEDHG8wnegJD96KzxFd2p\nD1O0kcqAkJz7v9v3uiloAdbymIBeFEnnp6/nQR+7/SfbMWqwXJqkI+qJBpRIGBC5FgYZz4RJ5ezc\nIw9A8/Tv/+YaYIETmoQGhIY/oJJwUrVtdPUkUZyh+Ww4goApci3MQgm4P8Mq/elv/hTOMmM0IWgb\ngDQRJsX18ccZEDw34kTlxamnxgL8GStTCpsBGYINCMXHydgicSB4+xyRW6jSZsAW/2brIj5RIVG7\n2Jn5wzQMt2+/+PoeoYeN3PBPcFxwLGYZ6E365xD+FlXfENUn6Ftef98WXHfRdAyvFYeTzicsSx5P\nJExuAhpB76n2PhFszI4H18KLLroIF110ke/4ww8/7Du2dOlSLF26lDlGYgvwGD9+PB577DHf8TVr\n1mDNmjX9qHFuwViJct4EaZs9zwoDHlVEdmPioEPOuX9wkezS8HcqPsRxBaXzFnW2V97cx/xPJ1Xh\nQR5lmoawnmENCEWqELrNunrDMwNxRTQ6m/rLszc8nHDEkgIovPD/3semze/ijrXzUF1e6DADhiEU\nBrIR9BMSPTDg/34qbwL62SkuV4KvXNsG/bKiKGxRX8X9ntyCyVeBDtDEQxaAKBlgQCibVF1mIHM/\nLSgDvDDg1ZlAtWu0bRtv/f0Qnnrlr4wuXNYHKkpl7m1OuZZpIJGx9ZC52srekxxu7+rDps3v4ux5\no4TfL2aZ6E2mpQaZbtAhW9432OfKvyWP3+74AKsWnxB4nQwiQSUMLNMQxlIBJAaEAcxAT18KP372\nLZw5awTGDi1nzpPvYMDJzvjws39mnsWjVGLYmA/oCIR5Ak35pFL+nO0yNQHxewUod6eAOAPMcwW7\nbJrq5PVf/WGhLNNwn0XvhGmEdS0M8rENW8+0DaUwAIrmDAo6ZAgmCVE1mo90I5W2cZC4L5IBn7m1\nt59Bh0ThqGXlqZgBevl2qXjJGhqUqIhnt8JARBk7wgDHDAjo+CBkqyYgY4uMQZ8wIFITQN4v+R3z\nnT99A+/sOcKMO9mCXSExTLVtZzNhmkZA31aoCTIV++X//BX/s+MDPPibPwm/HzFUlDID3F+nbHl9\nRIGaZEil0v3aCbt1i9gxLdOUx9uwBYKwoo42gN/v3Idtf9qPWx59zX+eKuueJ3fgIGWczZc7sq4U\n/76aDRKXT2hhIE/wxxlgd4ciZsAyDbR29ProVKHNAKHnuZ2SyC+WyXfgi3ue/eAriFtu5zYNQ+gC\n2RcqN4EtXJSymRgCmQHbu05F9wIyZkAutNALMa1i+OX/eLYK2bxT3FIJA+z/oZkBypCSxvCM9wQf\nX0Km148Cd5fI1MlPw9J5HHhIXSGzVhNkYkG4wgD7AHq8fPcXO9Ha0atc/LKJMwA4fU22C0xnxodp\nGErBEFAs4pnDZLPRKWEWyPv/+Nm3sK/Fb4xKjx/vmD+MM113/noZkimxulD0fPFJ5k9oRFUTiPKt\n0PUjNksqzYwNlgUG/P2ipCge6LmUS2hhIE/gg0mochOQa2sqCpFK264RIVkgRQNNNigcQYM9xgYy\n4hfi4HeRoSBhuXU0jShqAn9ZMn1ZVAM+24ZLpQrPc+Wr4KQwljMDe5ra8fIbe91yyILiTHwGRGYr\n2QhfqnpGi0DoZwY+aGYnfCJI8Yu9SNcZVVEg89Pny1apCeRlB6gJJGURJoAIcrzgRQvS/zzYiade\n+auSIg+zYxbVpbgw5u7KeZDNQyhmIEAAIe8Tt0xh+5L2eOsfh3HPkzsEdfF/w3TalodSdtkgZbUB\nIJO+uR8TUpYQJSQjSNu2jxVTGWTzhsmi884P+KSWKKmc84G8xxkYqGB2YSlRBEL/PTXlhThwqAuH\n23tQXpJQJypyuWj+uYLOS/njhk1VGgam4d1vGOJ6hvEmkK11adsRMqIkX7Ft20f1sheQ64J3ECK1\nB12Vr/7oDwDg6gXJRGsjwwwI9NvZsKBhDLQIohoQ8ohTNLFq0csqAqHLDLBjgS+HLOxRys9WTUB2\n2oRR4RdkPpx2T1+KjUXAT+hhmAFBXUsKY65ALRLE0q6aQB0bRc4MEGHAec+//bMNTYf9LnK0MNTa\n4Xfzs232L/ldWGD53Irp54YRHJMh1ASqcsi5qHOaZZpC9hWAMGthoDCgeFZacR3fXwJCM+QcmhnI\nE9hdGNvJeTUBAaEJezk3G0uwuKnChfKTiSo2fjauK4tnDgdALM6d+x0DQn89k6m0MkqbqE4ERE8a\nBSIDSvbZ3q4zaOKRUZ88jmToPrIQ27YjHIl2G9m0t/J9eANCpc2AB9niGbcM9zzDonCX22n1DkiE\n3l6vfdxybP/3T3HMQJjHBKoJJO9LjDOJz7rKgBAgTAb7P3PeFv+mj4mqUpIZ+8Joo5k2cgwI+6cm\noIUb0eLNPF/Rfxk1AWypkBLWmwAgaoLg66Swub8hYVkqA0I10yq6Pgwz4FzH38seyCZjan+ghYE8\ngZ6kU2kbBw55UriIegI8lzjX6EbBDBBjLP5M2hYYEFITmj+WecCLCHDBorEYUlPsuEwSgsIwhAt3\nMumX9sMmVyHuVFFAjK3kF3h/ghYz0WAU3UPcHvsoNQHtTUAjqzC+KjUBVx9V1kI2roL4w5PFMM1R\nJ3x/zcZmgBjR8fpm386L2DMI6i1DUH1kpwsyY458Q5+agGsnm5MGVJbmUoFdyAw4wkBM5Eac2Z2a\nRpBxrMqbwDme5KP2caDfXzTyaJbbe6bcrsWLzaB8LACnT/YnXHeWsoDPToSGyJsgSPBUvat3zgZf\nU9+308zA8QH6u775bgue3fYP5pxooiC7FD7oSjRvAv85kUW0d312g88yDaRSFDNgiPXV3b2pQDsF\n1QSWjc2AKtoZu9tVv3tYVoJQzAwzADEz0F+bAd9OlSsubG4CKTNAqwmo43xWwGzUBO3dRBhgj/Nt\ncqi1B0++vBuHWr3kUkH9VPXNRQIygccMEDUBF2eAC+J0qK2HMdLki6X//+fBTt983nykC7f95HVf\nPUoyAYdEdgO0N4ETIEfeL2UqNREzIALNjAiZLUHGRkc1J99Z09eqkEwHCPJOBaToS6bxf55/Oytv\nAhlSEdUENFsqAs12qfoOIFZT5hNaGMgT6A60868tzDmZ9bw7EVNUEqD2JhA9l5eulcxAFouTYTh1\nSlFUu2kYbgYwGr/YvJvJ9w3A1+tVgW9EA8IwgB9+8TThPUHMQJgFkSDIZoDA9SagbAYgYUqyYWLo\nCdwXgpVnBpTCAMtWiRCjDQgVTAJHHIRCeyYOPH2fSE1gA3h22z/QQoUtDnqW6lvy9g80yJgjE7zK\ntRAA3nn/MF79E5W/niuPfs4Dv/6T7/x7+9qEAbSKMnYIokWVLEikP8ZVrqYhbQZkYIURdf8nv9O2\nXHCWuRaK7HqSyTSaj0QLcc1j8xt7IwupKnWgnbZ9kQGVEV3TaiE57baZ/yKfmkBeTF6ghYE8IYgq\nEjMD4dUEqh2AyhXGzwzI6ymDAcc+gI6fYBgGWjv9wgAA3wDn6ycTSGSUt22LJxNStmqw0tN3S8DE\nI5ojVOZBbjyBDKUrVDNEXkLZ9+FdB30Z8BThiOkr5TYDYmZAtKOMSul2yNQEIQQkco88a6F6NyZ7\nBk+783S3Ku4+XS/vf+XlUpCxL+rXxF2YLLgquwFZM7jMQMD7xKhOr1ITOM/ymAGVNT65hsbQGn9S\npgOHu/C9X+5U1i8fIHYSMiaPn59EthYEIiaBhooZ4Puwthk4TsCkz+Xd02yx8RpxifOkabkwoNoB\n+OMMeAtITrwJMp4DtBRsGhAyA7I60iATLv+Wz7z6d6k/tKrssMzA3mZ5Uh9AsttR0pSZJC6Za4ST\nSxY6UVqY8wkDEYpjJvIANQEfjljkW82rDoLQ0d3nt0VQ1IWGSFdNQ6kmSMv7uZWh3gmCmAFZvbz/\ns5MGSLuLhIEUJwyo7AbSEqmHdy2UgWYGgtQEdNmyhcv9btxtgwXCQBiEad2o34DYaYhckkXCwOtv\nN/muIwhOpU3/ljO4gDymRr6ghYE8gR40YYz8AFZfC4AKRyy20gf8Hca2/ayBKM5AT28Kz237h9oV\nTQIDXvRBN/iRaaBekoKVB//qpH5BxlFhkE7bgQY+BHuaAoQB4c5eDnpXbhqG0LUwG8M7mhngw9BG\nES5oHa9UTWCxqiq3DoJFJGji8z8f6OxOcu534QRSl5JWqJRkEBmBERiGgThlJ+BzLQxYPP3PinS5\nC2KNL1ITEANCkkRJ5V4YtEkIEq5VAa6cctgyyTFVOF/AL0TUhZwrskG2agJRQKd0Olp5rFG1qG5U\n3+fO8YymZgaOA7z9j0N48uV33f97OT2daAKMWQYVJ51lBkQ7VG/B4yIQCmwG2DgDTod74uXdeOLl\n3WhpjZ5Sl9gMAF4HNg0DV58/GZecOQEjBdkLacgkYmV8gJCw7SDK2NPP7j+oTmMtavd/7G/Dbf/1\nOpqPdPkmbvKdbdsGDPH9sl3F2fNGSWPT07tyfqcahdkhl6qiFBKB7MXX3mcED/KdTxxdhcljq51n\n98OjgODt9w+FFAbYMcFDxVKQCH4imIbBLID8Nw1iBmga3HGjzU4aSCiYATcCYQg1gdQzxwbue2pX\n4MJGuxYGedPQbnTSrH8Sb4LFM4djSE1xXhITRTYgtEi7hmMGVKDtU0SbAVVJPmEg9FNzAy0M5AH3\nbmJTzXZ2+42+eKMUyzJdCZU3IBT5HssSswTlJiCD81BbdCHAgxd6mCxUpgFUlBZg8czhgVb4/HxF\nFtFcMAM2bOWO1YaNwdVFoSx1Re/xg1/9EX/ZcwS//J+/+iYPz7XQmQiiCPaqa2kKnKfDowkDzrUy\n2w7A2xkebu9lFhbSh8qLE+41qrCsMrR39TELw2+2/F2ZCMuru/NXygwo6qIyIDRNg2EDotoMkNn9\n1v96HVd9c3P2NgNEGJAI/nTMDaXNgIIZoFOdyxCFGQC1qZGrCcRtX1GSwC2fnouTT6gNrBMjoIVo\n36ifQM0MRPOacTysnN9iZkB+Lz+etJrgOABvxMXvxITMAJUUJ5QBoWTye+S5t5FM2Rg/rAJLZo8A\nILYZKCvOPhuWYXh6NrJIGKZ6R0GDt3gn7ls5EQbsAD9g29l91VcXBZYlkmnokLr85OHGJIctTdwk\nhyGdxZKMMMBeFMWIj1zZJogsRyALiUuea1I6drWhJgsSUKuzO+nbPYsi4fHgBWRf/RQCoMyVF8j0\nZZXNQEgDwnf3tjrPylJPQNqdbv+1557klGlHsBmQPD7sgka/f3tXH9794AhXDs0MsDZDwvoELKZh\n3HeDoi7yiC4MBNgMRPimqbTHDoWNU0Kg1QTHIYKC6oiSCcUs068mSMs7Vco9xx7/Z4b6NqnFSORN\nUFbcvwQYrpogM1maEUgt3j2O1C4nNgNBBoRw6LchNcH0pHIxN/yTR18yOM6Aojgp6GRPfn//8M8g\n3TIMM0DgZvUj6iDTcHdqgbtmulximJhKC+IMBN/vMgOSyTTItVB22jTYeP+xmIlxQ8sxa2IdgBDC\nAPd/FAGJRsK1GXDqYpkGJo6qApCJYGp7roWqlNZBWQuDwAuDt/wfNiYCQwxQagJpoh+FIObcF1wn\n+vt89JQRqK8qwtihFdLrVcakIhCWU+SyaaejqR1ow1uxd4L8Xm1AOAAhovJjliFQE8j1cUEd3jQN\nGJmvy+Rkz/TGoLCmyrKppEQeM0BfoR48MpfB3NkMBEwGhoGhg4INmAjbcd+/LcK8k+oDr++h4gwY\nhjwTmgimaUhbjV5g+MWGFipJ4BoZyI6lTSUMcP2CvAOdWZOExw7SpzPlEjZBsFMMM9m6YaSzVRNI\n7uOZgbhl4suXzsLKj4wHEN2bQOXaqQJvM0AzS+TdrDDMgMJmoK4qmA1TReMD+Pf1bDHkwoD3vUXJ\njMKwZ7SAOqiyCLd9Zh5ObpCrF3q4bxC0ybAU6peoNgN00KGo4cg1MzAA4agJ2GMWFVmMVxMIw/wG\n6GtNSu1AT2hk5yCzOQgFwxtALjMg6LgTR1aiQDAByOLn50ZNYAe2jQGE8nwg71SYiAmpSl7o6HNT\nlzrUQJS0Ciq6VKUmoCcq1Y7RqZfzt7VToSaQMANE+LRMz+AuiqU9HdyHVxOEmWqDmYHsIhCaptiA\n0BV2Be+4eOZwnDLJYQ74d+GNhcMi7sYZID7vhq8OpItkY0Bo27Y0m+dnPn6S+1skkMvSMtO7frUB\noXNNUYFfWA2jJhAJKKqNA7/ZCLKDCFYTBFbRu54SdtNpG//5xA689tYB97xaGNA2AwMOIj2UZXre\nBHzULqWaQPIMk4qNnxQwA9kYfxEQ10KAoo+pOpL+HouZKOYmgHTalu6eggZtGAR5EwDOICtMBCfs\npCcq/hMY8FP27kJgR884ZpmGVLGbZNQEcgPCYGEgwwwo4kHw4XiJVyutJiC0ahRmgEzetIEVX6/r\nLpmJs+aOVNZdNjFn7VoIVk1AWA9LIfCMrCtF4+TBmXqxwlq2zADp+yJmwBUGMh+DVvGNGVKO//jU\nKa5NhooZSKXTwvmCXmxFY/CKO17G3qZ2AH7XQlswRy2aNgTTxw/KPNdT0RQLmKswC55o4ZfZtgB+\nmyTVtYCnJiBtSMMJvhV+rqSZr2TKxs6/tuC+p3a551UkAy/Qam+C4xSFCQvnLxoLgBi5sR8+xngT\nIPNXvuCnPH5O+DzT9LsqAl4Mgmx1m84jDZ9roSHoSQYM36KrCpebK2YgjM5QZDnMg17Q/a1sCII7\nZRLs2JnzEeQtFV2qZAaoVy0IaL9wNgOsQCGiql0DwgjMABEykum0jwog9Zo1qR61lWIqO5AZCFAT\nSG0GTN6AMJgZcHbxRqZeNmMg/M8Ad1UZiCBHMwOmWwenfNIfaRfUr1w2CyPqSnFBZm4h7TNmSDlT\nPoktIRIYLYUBJcG2PzshmJncBNTz6O5bUVKAaz4xFUUFsYyfvnMNvzFw3il4yRN5U6lCCPOxU4KZ\nAaesC08bh9GDy5hzkQ0IU+rrVcxAH5dESqsJjlMUJCx3MNu27dtVxSxPx+w3IPSXF6gmMAzh7nTr\nrv041NYTOjCPDGQC8VwLxR23sICdfFQ+7rmwGUiHYgaCU8ECHIUpYme4NnTDEcMJRxzFkMlS2AyE\ndS1UxawHnBz2tq0OPMMLZCbPAFHCQDY2A3QIawIyQapS9AbFGVAzA/Ids2EYzM6YeMm4RpKCd4xb\nFjO2aIPY3XuP+K4PA9LuZFyZhpiVARy3PP97sP9fff5knD1vlPs/2YCIBG7m/SU2A6Rd6GakDQjp\n8U9+OmSXt1MWqglCLHhCZkAxV/RyAlwgM0C16/oLpjDnogYdSqfVrs2qqclvMxD+ubmAFgZyDNmO\nuyBuuYt92vYv5nScgcdf+gvefLdZONAIgozk6MBANPY0tePWR1/rFzMAwI2GRnZOIilWRMfzngQ0\ncsYMhJDkw7grMROc4Dwf6ZHOWggjmpuZ2maAVhNwCyn1v0wnTLD9nSbs2N2i3NHHucXA5HbIFuNN\nEP79SHuL+l2ScluUfZd3P1C77iljS6jiDBi8moAwA3I1QSJuuh0ibasF3LAgdSBCkwHDpyZwF63S\nAt/9/PizLBNVZd51tm0jmbaFY4y+V7bIurtzqhmdOSpThqD/mpkopbSwt+68yfjKZbOoZwsfx0AU\neyHKxoHv06qyhKHjI0gD6QCbpSieCaKgRfmEFgZyDD7AEIEjDDi/nQ7DSa8mm+Xuniff9Ca+bJgB\nyoCQR0trT79sBgBvcuCNmwCWBeYNCPOvJgjekRtGOG8Klhnwl8EzA0zQIcOIFHrYMg3pDkTpTUDd\nVBBgMwAA7+1rRV8yLd0B8osx2RF6BoRmdswAlfNAaszHRQOk8d1fOAlspHEGFP35W0/8r9Ro0jTB\nGRBmduamMxWLSo1bprdocGqCbEEEOTppjuORQtsMhGcG+DgXJP6GqN/Tt8p20aRd6MXs4WfeYiIQ\n0vObc8xgVDSGYWDWxDpGhREqzoCgXwd5PTD3h7QZcOrInssmVbdqXEQpSzMDH3LIKNhE3PMWsEXC\ngGWCT0GQtjMDWtCByOQn6y+WqXZtixpXnocoHLEIPDUocysEjh4zYCCYUgfUzIBIl5jKUIS2bcNA\ntDwEpmlg2vga4bk+RhjgbAaof8PYQViWgb6kmC4G/N+AuIP1Ubv3rGwGaNpd0iyWaQT2AZmLoKql\nD7fLbSQMg41ASO8SRbpqwGkj15YibSvZrrDwMQOZ8k3DoARu51ilgBngx59psBEwnfgbaSHzwggD\nEmHMFQa44/RC73lDZeqQYQaeffXvALyslap6izBmiKPHnzHBcyeMxgyE8yYABONcEBMmCKJ8L15Y\n5gjMwFGWBoJNqjUiQUa/W6a3m7AFaoKYZbrUO0HatmGaYj0psSpX0Z9hqedsYHHCgIgmBPzMgCiX\nO0GubAYC380wAil1AIxwxlN2fX1p4Xfp7Uu7gY2iMgOXfrQBVWWF+M2WvzHn6F0vL8TRE1WQNwF5\nTl8qnWlr/7fgd1ykzGTKryaIwgyQCfepV96TMhhmCGEgqyybCvBsBC0AWKaJZMrfRvGY6bZLe1cf\nuhV9OiwSnM0AmQos03AFaDI+RPEk+HWDYS+QEQZStnhHzagJxOOYzCX+lM0eM2CZBsP8mIYjGDz/\nh/cBQJh7I8x6N7i6GPdffxpTNyvCXBHWZsCpDz8HR891wNssAM4msbQoHsmoWDMDH3LI6Epnp+78\nFjEDluVfvNNpWyo5k+fIOpchMSAk6LfNgM+1UHwdbzPQ2ePsDmh9JkHumAE5DQ5kmIEwagK67bni\nZLESeikbiqjMQDxm4cRM1DkaTJyIzHffvecIPnX7/2Ws1wtCCDgxy3SZgUs/2uA/z7UDwFCgAAAg\nAElEQVRLQZxlAUyDMiDMghkAxKoi0taq7xJVfxu6bjQzQEmAMov1eMxEeSacd2tHb07UBDEJM2CY\nhss8EDbLMAxceOpYXH7WRPd+fhHjXUTJBkQkcNNXynbRsoRDdG4C3jXaMk0k02kMHeRE+zx/4Vhf\nuWGYgaqyQsRjrHATSU0QxAyo1AQKTxQZRMwAYUWCBAuVYJJvaGEgx5AtALQOP237KVY6HDFBbzIt\n3d2THaI8mIra/SZXwgAxImMGNVUlPuoYsak4f+FYbFw9k4nsFzXOQL0gohrRjSrjCBjeIqeCSk0g\nU3eQicDgDAjvWteofBZpT9H4TwlsBjZt3u27LoyawDAcZiBumTjt5GE4p3E0c57/BqQdyZswBoRR\n4gwECF9u3H1FH0im0lmlgA6CyLUQkNc5EbNQWhyHASeAk8oOJixIX6NtBgDHUJcIXbS+/+x5o7Fo\n2lD3f7rfWKbhS3vupkEWzAn0vTJ2jnxrvzDglUGrTgCHVerNMGilRXHUV/sDfYWxGagWbByisIiB\nfc+QL8CqGBUyiJiB9m4iDKjvVcU2yTe0MJBjyHTxlunt1IllLw3egBAAjrT3wDTEhmVkhyjTodZV\nFUupe8Cj0s9fOMYNvRoFpK5kIhTRdgb8zABJi1tUEMP44RWMDjNo0PK46ZOnYM6JbJhgJ1EIUFQg\n3yUbMEJNJvT34BchmZ64xxUGDLcvJOImqssL1c9Sxhmg1QTO738e8if34dUEIuGgL5lCkrIZ4LsI\n/w34MiwrS2aAN4jhQE6rmIHeZDpSYqawoIPN0P1CZmQaj5mwTBMlRfEMM9B/mwH++aQ/0H1Q5QFD\n9x/ROCKLedCOOlgY4Oxk3HK9zQzZoBQkTPT2pZBKpaUbkzALXmU/hYGgTQY9tvlqRg1HDIiZgfaM\nAWtQACNGGIj01P5DCwM5hlpN4A0WnhmwLL/1f0d3UhqznggTso46fmi50PfXq6dDpX9s/hjMbKhT\nvZIQZOdBOj7tvkN3eJ4ZaMvQZcUFbJAVp8xo3b8gYfmC1BBKXcUMEEvtINADk9/9yahhOgKdF6gn\nhGGfywz46yXyJmgVRBHkFy+Rbr4vmWYMCPk+V1wQw3UXTZeWYVK7zkg2EQGLUBg1QV8yHZmyDYMT\nR3uqGfqby2wbSB0rShJo6+ztt/0NjRjHDND1UXnA0P1GtPi57okioZ0RJNRqSf5NyTiImaZPTZCI\nWUilbfQqvFfo/nfq9KHCa0TfIYoBdNAmg2befK6FWRgQdgg8yvZkIjgGFRVjmAGtJvhQQ6UmoLyR\nBDYDpnAxNA0IuSXSgWWdawwnDPAGc929KZ+xUhSQunZzxk00DMNAIedNQBax0kxIVfq+aCl/CdgG\nIGqLIkFOhKig68MLAzJqmBw3DWBIjUOLThxZGfwshZqAj0Aom5x4Zkk0ifYSYUDy7U3TwEljqr0y\nuHa0DANxyYKhQpCgFyYJT18ynXWKYBWGDRJnsJSpXUgdy4rj6OhOKj1kwuDfVkxzf7vhiDP7QrrZ\nlMKAoH40aANQFaTMQDrtLsANIyrdcMPdGabPohKtkTmQ9L+O7j6pQEz32cuWTvSdv3b5NN8xIGqM\nC/UyRwtzftfC8JlBicAjEtR373GCUQX1X9ZmINxzcwXtTZBDvPX3Q/jPJ3YIzzHMQFoUZ8BvMwA4\nBkSi7sNHKaRx3oIxKEzEGGv4eMxkFrD2rj5XCs1GAiU7PVKmTPrmmQFXGMhQs3Tnj0gMAPDLSaRd\neSGERtjH0PXxCQOSBcC9zjCwaPpQlBTFMWWs2GWQhssMCGrHBx3q6Bb7zPN3CpNE9SRhw/tefJ/j\nBTIhM5CF10cQrUv6YFBkuXwYEBqGgQ2XzEA75/om8ji5+IwT3DqWZ/z9D7X3ZP3seMzEZKp/8EIa\noyZQeIvQny0qM0BDriaw8e5eJ/DTkJpid/fbRW0GXDUoEQYy/a+3Ly1lhlRzz6CKQkwdJ3O39Y+/\nO9bOw5d+sNV3PFhNIGcG0mk7tDrMssTeJ8UFMezee8SJPBtQFv19dNChDzHu/OkbyuxoXpwBkWuh\nOEiQzGYg6TID/pMfXzDGfSYBP6m3dfZR+knZG8nBMwPMgGMMCNlF+QgvDNDMQDYV4UDUBIm4hZkT\nanHhqX4L5rDCD21zwSegERkJOddlbAbgqAdOmVQvDMPKw333QGYg7Vu03Ppy7yXaSZI4GLzVugy8\nHYJlGsKIcAAwbmg5bvn0HOGzg3TVpD+RfjplbA2++dlGxh0tmSdhAAAmjKhk/NgBsavmGbNGuL/L\nipy6HW7LXhjgX4csmq7NAMPuhVQTCK4j40L07VgDQvF3SqbS2LG7GQAwbfwgd+4gNkB0OHXXZoBi\nVmSMhGrIqz41H8cfEKdIBoKZAVq1S1fHMJx36QuZiVI2LkbWl6KjO6l0qyZQqXbzDS0MHCVYRpBr\noUxNYAitWf/0t0NoPtylHDC0qxm/IKVtG3RSlKggkwExnpIyAwV+IaQgYbkDlB5AMmGgITNRL5g6\nJLBeRPKOWyauvmAKzpo7KvAeGVRqAhloA8IoUHkTMMxAykZHl8RgzXevv7CDrc7CRdo/qJoFMZMp\nxbJM6bdunDwYQ2pK8MMvnoYvrGDp3SC7CfLtTdPAgzecjmuXT0VNRSFjjLX9naasswJmgyDvDOLq\nJ3MzDQN+bKuYAVUcCWZBF6kJXGbA/8Fp+xcZM5BK2djT1AEAOGF4pdt/yL30/EXISrq+UjWBsgPK\nJ7fZGcNhmjmQCQP0O40fVuH+HjfUiYRIuznT45ZEUAzLDIja3TINFBc6Gx8Zo8dcr3BzzDe0MHCU\nwDADcCR1xgJYEGfAuU9e5r//8FWlDoqmiYsF1vX9sRkgO/62jJUszQzYgusI2rv6UEZZb9OdXzYx\nFCQsrL9gijt4afDCkGvQKDGQiwKTYQbCTfhksYr6WFOpJvAmo7/sOYxb/+t1YRljBvvbhwdJpEPa\nRxTvgUY8xqqvTMOQegYQJkXkJhtsQEj9plRq9EL16y1/U5aRawQFpiLCdH9sBvzMAMvY0BsE1Q43\nLDMgWpRbO3px21Vz8aWLT5bu4JOptLtDLizwhHmaGeCzpNJspIxxUHk8qTig6vJC/OhLp+NMiqlx\nVBX+8uj2OHO2d/3nLpyKS5c2oHHKYK8+XD9M27aUBeQhivNRELdchiSUMGDSa8LRXZ61MHCUYFmm\nF7s77UQDozuprCPzaoKrz5/s/lbFeQdYYUBEVYelikUgwgWhrGWDXaS3lrlyyZgBOrAJD95Vp4cT\nBkQI+7r0wAzLDNBqgigIa0Ao8mJoGFGJb1w5B+OHV/jOyUDa55SJ9Vi1+ATFdRZTJzrOAA+T21XR\nCJrYZN8+T1qBUAiKRcGzYzKoGAa+//q8CUKqCejmE9sMZDxbBN9u6KAS1FcXo2FklUIY8LwC6ORO\nXYQZFHgTFDDMQG7VBICXu4H+XzTfyPpeeUkCp00fxghIfB9Op8O70IqYm3jci1YpZfQoMMKfFgaO\nT1hUhC6SwpjuuIYhnhDTtjddGIDPDVApDFCds1gQwpQPcBIFvIGeiCIzDLEQUlpMMQNhrGcjLAhk\nZ56LaIZ0fejdnygcrHtdP9UEIgRNisWFMTfKGw26Cv++egZzLm45fcM0DWa3xIPOqUGul6kJ6Dfw\nMQMB9iD9YXDyhaDwzmSRCRIUCxXlDOYC8fBxBgxGGFCpCdTMgBtngFr4PrlsIm69aq4ycdDimcMB\nOEZ2vX1ebgOyUJFQzDHLcMOpC4UBycKm+u5hgv3w44wIcLQAQLdHUKAslhkgNgPePaMGl0nvLUj4\n3zFumYxXRRBowSQXc1gUaGHgKIGmPtO2YwiWiJlYe+5JGFRRiHFDK4SUYE9fGmQ1FO6MFWoCehIS\nLcq8G1MU8OXJpFiRHk/KDEgmBlcYEp2WqQkUUnXQQi0y3iJU4dI5I5XeAT1UBMIoED0zLOhFiw5R\nS4PfHfETzXevXYR7r1ngu4+PcR+3FGoCBTMQBBkzsOGSGcLjRwNBNgMeM6AWBkS7VQCYPKbaZ1sR\n41R34dUECHUdzQwUxC2fMMKrEcj4TaYcQzo3oRLHDFiW6VL+XtChYGYgWzUBAX97QUYtSbMo9FwQ\nLAxwzEAIDwACkbDm5LHIqAkEhr8j60tRR8VKofucVhMcp7BMb8lN2zb6UjYsy7E2v/OzjZgwopKZ\nEMmC2dOX8nKGC8aNym01SE0QU1DTQeDLozsuLdAXCIL/0PcyNgNSqjgjDAmEFv71e5LBzAAp5dwF\nY1BeHPclUDlxTBVmTqjFxJFeMBo6JOyIulJp2UQnL8Ly08ZJz0UNuESDnvgWTRuKyVScAAKeQeKD\nyxQXxlBW7E8kE4+z2TSLCmOMmmD2RI+p4vWtUSC7fsKISlx5zqRQZeSaWwhrM0Ca9tKl/lwPAFAQ\nFzNJ5y4Yg0EVbNAs3qiXbnuVcBLEDBCwrrz+FuP7IZ2oqi+zgaGfwTADnM1AIha8sCkXoBDSAC/Y\nkw0Qo4Kl+nqUAFGGYfg8WFR9TBTXI0YxA+2CYEQfnT0Sl1ECPC3Ya2bgOAXNDNiZ3ARxTn9HD86y\nDJXeG7DrUBkQFjIGhCI1QfZGdnxQn7BxBgDW0CbG6etE9VQJQ1JmgKrPZ8+bjKVzRnoXZco5d8EY\n3HPNQh+NW1tZhKsvmIKaCi+E8PkLxwBw0qiqhAHiiy0KPHLW3FGoLhcb7KlsBghkuvow2Qr7fFb4\n4b55nLNlKUrEmG/9MSq3AWtoGKp46nr5DaowvEwZOXBNpRFWTUAwf7JniDaS6iMyK3dRfXlmwAzJ\nDNBnVKwYk6I5wM0QcLxJAODNd1twsLXHxwy43kRWljYD/WQGeAGJbICYfBPUHBMl7bZpGpE8RUS7\n+njMdIVKwgyYnOBGf1fW6FILA8clTNNwpfynf/ceOnuSPj0avQsgFvc21IuhSq9GdyaVYU02zIAT\nn11m7OLVKWaZvkWM7vw8M/Cfn1uA731hEXO9ywwI6jk242FA3oUIA/SuZPbEOsyibC34YnyBdwQL\n5cfmj8EPrjsVI+vLlMIAwcJp4tCqMpVMGGaAXhRpVUuYBEW9nK90WO8IOvU24LA69ORaRyWLygcz\nAIQ3pMq9MMA+lw+Aw/drmmK/+MwJ7m+ZmkAkAHlj0q826o/NgFdHNRPnz34oVi+Rb0J85y3TExrJ\neE3QaoIsgg6FsRkYVV+GpaeMdNVJnlrDW/Tpd05GCGNsGv5xopor6fZ05yXTM2okNgMlRd6GJxYz\nmf5NG61qZuA4RYxiBkjgFx50py2lKFtVcgtVfHh6oIkpLL+R0pmzRrishAqGYTB0v6jjknJHcy5v\nCSYYCc0MOOXIgvSIFtKZDbX4ymWzcFmGoiW6fV8qXnpC5ka0b1KUDHiyU6wo9e/u6d3ftHE1TEY5\n9lnisl0/e8VsQws438gE9wH831bUI3j//LBpdw2T3eUXFcSYiZ3ePfOGhlGgZAZCCDuA2to+G9AM\n1qeWTcI1F05lztPCNm8ATI9lmQGh6JXdMSkoJxc2A0HMAABm/PsDWbE0/N/3t7n1JsVF8yZQCQPS\nU0z9VnxkPCaMqGSeSRt10nYJkZmBKG6jVH2JasGyTLdf7ny3BQBQUui1r2YGBiCcOAPsMZ5KFtkM\nAHA7mUiKfveD1lDPFwkDojgDhhFe90ovgKoIcxtWz8CK073MiPQOJxYizoAr7whOG4aBMUPK3UVJ\npCYA2AmZL8binpvN/pL+NnzyJNl1TB2IlKB4ODNpUG0o2zEagBuBkUyWBGGZAdMwmPgBNCM0mrOs\n7p8BofwcvXP6+PzRUhuCccPCu1aGAS20VpQmfAIOu7Ca0nMyZkAEnhlgvAlybDMgM96753OeISl/\nBa8moOvt2gzYAmFAsrDl2omkJDNv0os43Rf7UsT+KBii6K+GYeBLF5+MUyb5k7vRlxKByDQNtx1a\nO/3MQJwSFoBjazOgcxPkCUtPGYmykjiefPldACSFMdsF+TCmjM0AJQzwa2E8ZkZKHwuI9Z9EH8jQ\nu4YReoTSO3iVFGsaBkt/xcWSsGxy8gwI5SDnXNdCi31f3o2TqR/33DBugYMqCtF8pJuuJQw430q1\nK5Ytkl7QITmYiYJpQ7btietjcWEcZ88bjWVzR8EwDHzyrIl4+Nm3MmWFm2gKE5ZbZ5IW2jAM/PCL\np/mupeseVRjgBTIa9KR43sKxGT31n33XNYyoxJuZ3VcuIGM9CGhB1q8yoFg5iTAg2vnyIcJZtiEk\nM6AYi0HBn5yy6N0Be04mDFimJzR6zACtt5eMbUU9wqgJeNQIbHIYNQEJvhQmhTnVDlPH1aCzJ4nL\nPtqAYbWlaBhZhdffflnIzMYswz1umYZv7lUxA8wYD/GtcgnNDOQAm/93L6669UXm2MyGWpw1xwuF\nSxsQEvDdiD5fQgkDYzN+wMRy+z/XL5Am8JBBZMREOh793CjMAOMVQA040RCmOzktCdNlBLkWqipG\n3kEWdEhmxAX4Kcww6xgfGjlte9HNJo6qEt0CAFh77klCOtutg+LhBZSlNKNL5iabVYtPwIKpQ1zV\nCWmbhdOG4q51jVg4dQjOXyT3bACAr10+G6sWn4AhNSXuwsQLf7wAmC+bAd4dTJZaOOqYCAL9ncSU\nfjg3MFWcAR4Wp7pThammwTID8udFpZ75x8pUMTHLREOGfWrIeOGwagLJcxXrfTYBp6rLC33H6K5F\nPIQ+MmNYYFn05mRYbQk2rp6JYbVyeyGbUg2kKWGA76+MMGBxwgDtEhnScDZX0MxADlBZUoB9LR3M\nMV4Cp1MYhwEdJIjoxYnhWnFhTNjpVRDtBMkxulr8Lmb8sAqpu1wRs9v2vxxTblxMaxdR7ymdLxSu\nhe69mVPEUE5EY8rq6mcGpI9x8bHG0Rg3tAL/u7sZL72+B7CB5aePQ+PkwRhZLw9MMrK+DHd9fhGu\nuXszV39iMyB/ZnlGl8t7kPDCQEVpAT61TEylV5cX4pOSczRGDS5zA6yQSSko4RI9eUcVBlRszJgh\n5Zh7Yj3mTxniXnv31fPxxl+a8NLre3DVx05CVVmBm0VQhEuXNqCkMI7vP7UrdJ2qqDGmMvYDBC55\n1NiQCS+igGGmYWDiyEqMzmwAyHOD3BxFNgMizxVGTaAskZTLXkX6Ar8htiwDS+eMxOgh5Zgw3BEK\nmNwEWexyswk+WSMSBqh3njquBneunYfqiuD5c2hNMfYf7AQQLRpg3DJdZsA0Dd/cy6gJeGaAEQa0\nzcCHDtNPGOQbeLwkbAmYgUmKHSQd5Y7oxenJpzNENCsaooWUTDCMtXgi5k4sC6ndJQDMmliHk08Y\n5P5fJpt8BaOYHhD07+IQzIBnMyE+7ZxzThLr5jBxBgj4iZxMZioYhoGTxlS7k4Rt27BMUykI8HVV\n1YFgSI0XFIbEAeCpyXxPGvUZj4EgOwO6XqLXIXYw1y6fhls+PYdha1TeFDHLxFUfPwknUfETqsoK\n8JEZw3HLp+di1OAypSAAAKdNH+a+R1jUBiwYLDPg1P/uq+djwyUzUFpIe3uEVxMAwA0XezY2ZCEL\n+sZ8nhMAOGl0Na762ImcwW5UIY39n9Rj6rgaJleIYzNg4qTR1e41BSGEAd44ej6VJyAbcYCeh7/9\n+YW455oFPsF0UGVRKDUWY+ck+IaTRrPzN3lOIm4yagJeGCzl1ARMtMQQ+RzyBc0M5AiiVK80eAPC\nO9fOEwZ5IaCpJBE6BAEsALD+9Ez95MwAjcKExRqCUZVed95k5trKUvUETEPGDNALQpABoWr36Ju0\nBJI80enz0gB5x8KEhS+vmSkM7Rv03CjTlmg+9uIMsCfrKouwr8XZnci8PPIdypcExmlhbCT8oPPC\ni5iBu9Y1ojeZdoWCOz/biGvufUV6fX8w76TBqCorwDOv/l1Yp5UfGc/EkRDBMAyUFMbQ0Z10jeJo\n0JM1Ef6rygpQVVbAhK+WLeRhvB9IlYOEAboL0Oq/uScNxq9+9x72H+pizoUFv4lw4x8YBs5dMAbf\nemIHAPHCZZoGYpaJZCotVRPwzXrF2SeiMB7DS9v3KAOqyVBJefqQftaUefewOGvOSJQVJxi3WdF8\nsvbjk/Hz376Ll9/YC8CJW3KwtQcrF4/Hfb90GCihzQAdgTXGuu4eS2ZACwM5Aq/f4YUBnhkYpLA4\nBxwDNQAYXitemKoF2eauXT7Npzf92uWz8c6ewxhSU4LLljagpbUHv9nyNwBi6pHOOWAL3oNGRYk6\n4x0NmfFbmERFbjhmRfl+OlMg6BTE0NWTlMYZMAwodYLiB2dqGEHBKXpPmW6YFhhlwmOO11EfyKIZ\nlL2NZQYETFTckrsi5ligufjME7B11z+ZY3QfWXKKWGjm8Y0r5+C1t5twooDFo43QRGpBAn7Rv+YT\nU/FBcweGSca2qM5BggO9aPPjmnExplV7gU/398cUFcGPVQOI61cQd4QBmQGhCG5bZiEMxCwTi2cO\nZzYqUQXN5RQjQCByby0ujOGUSXWuMFBbUeTGOyAqINM0fHMR703APCdE1MZ8QasJcgTeolskDESZ\n8EqK4vjW+vn4ymWzhOdXLj7BF61PlGVt1OAyN83nqdOH4YxM4hFAzgy4sNUDKZAZEOxWALn+k26f\n61ZOd3+H2SHw1RRNnkSfyLMqXoKV4Of4n+vcG8XYSdQPyCH+DJ3UScYMqOK75wIzGmoBsNEGRaBt\nGcJMwEEBcPoDA37bimweUVFagMUzhwtZqTjjTSAf//xCMn5YhevhEQRiPBmNGZAbdsrsF8KCFvgY\nn3hJ4xLhQ6omEAwcj23LLmXlJWdOwNnzRrv/50LQ9EfwdCBjUWk1QUlhDHNPrHfP8WoCGvTcqG0G\nPqTwqQl80QWjdUjLNFBZWiC1KC0qiOFj80czx8IsSPSkJaIMHTUBXQ95F6kUBN8BxAJ9gcRmgIZB\nHT5pdDWmEZYjlJogmBkgOuMDHG3ohlHNwnyZPDbKvcrIb9x70C6mvPBHFhz6mnygrrII919/Gs7L\nhGSWgV57w0zA/QlfHAa8EJlr9kFlQMi6+qlZQxX6QuTaAPhIhab0XBTPBnLvvdcscOtM93M2zoiM\nGcgIA6pAEhwMTxrICfojaJK2O9zRozzPw/MmcNQAV338JPdccaE4ayugExUdFwiyGbBM083wFQZh\ndg38oA8zduIxetIQCQO0msBWDiQ+wQ8P+s6ozADgtQHZIagNCNn/RZNnbUYYaDrMCgPuRJeFktKl\nZyPcqhRquP9p/SLv6fGNK+fgk8smhjJa7C/inG5ThFSKthkILjOfzEDa9oIikQAxuTatULkWGobD\nBDox+9n7ouz4PGEgvDcBPxcx5xKWGyq3VmFQuSDjuTF2WDmjP6e/cSKEsRu5RsYMEA8pmrEkV2Zj\nMyBCf7rW+YscAXjyaH/yL0Dep4g6RdSv6Y2RLMIjoG0GPrTgFzifDtEwhCks+wPfBBFid0ozFiK1\nQlHCYha4bGwGRNQfTSnKOjm/GLsbBMIMSGsSjhkgqUJ5a/z+MAMnjanGr7f8DWdkVDFhoNqh8qfo\nSJREd0+O1VcXo55LQXsskVbYDIjyOfQnLoEMdVVFOHCoCwVxCxNHVeHrnzoFgzMeGblnBgzhbwLH\ngI5VD25cMzPSjq83JDMgM0LjzxXGLXzp4pNxsK3HlzGRxieXTcRFi8e7hsx8RkKAZQbkNgOZxEGS\n71tcGMeDN5zOfn/3Z26kgTAbKxmWzR2F+VOGSFlQWb8lBqfC+TNkgK3+ZDLNBloYyBF46ltkMzA+\nI12u/IjfQCUXzwyX/5uaNERqgoIYaJZOnU3OxJqPNgS6YJFrCURCCABphjA7hDTAjxvRhEtcOWdM\nqGWOk2+VTZCTCSMq8a3181ER4NpGQ7Vr5q23aWGgvqoY16+cjiE14b0djiZoi3t6Av7GlXOEHhr9\nCV8sw81XzEFXT9Ltb8MpIaQ/i4IIQXH+rYw1Pf3c8RFDJtOps1Vg1BLcuKbbtiBuIR6zUF+lFiId\nTwqv7w0dVII9TR1MfJOCEMyAqyZQRSjlVSzIfjyK0J/PbhiGVBBQlU2YAVG/UBlTJhSsQb6hhYEc\ngU+M44szYBmoKEngR186PWcfmd8tRB08QQaEth0cLOT0k4MjeQG8H3S4nRFvnKcKOsS3qaiN66uL\ncde6Rp8hXn93parJQoQozAAdfAoATpTQlccS686bjJ+8+A7mnjhYeD6Mq2aumAEniItYMMunmkC0\n2LnMQD/Y3j5JEC3fs+gFX5GkK2zSJx6rlzRgeG0pPjLDo/NZmw+ZMOA8L8ou9yivgf2C7L2Jmy3d\nRjd9cjbefv8w6quLcdr0ocJQxmHCJOcLeRUG3nnnHaxbtw6XX345Vq9ejX379uGGG25AKpVCbW0t\nvvnNbyKRSODpp5/GI488AtM0sWLFCixfvhx9fX3YsGEDPvjgA1iWhdtuuw0jRozAW2+9hZtuugkA\n0NDQgP/4j/8AADz44IN47rnnYBgG1q9fj1NPPTWfr+YD3ylkrkZBgsC1y6f6MszJwKsmouxORfcD\n/EJt94+qkrwr3wZfu3w2tv1pPyaN5Ny3OHU8vzDKHvXpc06UXieK3NiTaW9RXPN8IMrCl+8YArnA\nrIl1mDXRn7glCj4M78lDlqWQPhazzH69W19IbwJaTubVh+WU8JttXUqL4jhH4U0im9cKAmwGxGU5\nf7NR24nLy1/fkpVNqk73i5H1Za59z6VLJ4rLy231IiFvYkhnZyduvvlmzJs3zz327W9/GxdffDEe\ne+wxjBo1Cps2bUJnZye+973v4cc//jEeffRRPPLIIzh8+DB+85vfoLy8HD/96U+xdu1a3H333QCA\nW265BRs3bsTjjz+O9vZ2/Pa3v8X777+PZ555Bo899hjuv/9+3HbbbUilIqSezAF8QYZ44SBkh5w6\nblDoiZWeIK75xFSGEg0DqVV/HnS5KowaXIYVHxkvTRhE1AQnDK/AitPH4+YrTjPc1RsAABDLSURB\nVPGVQQ/KeZPFO1QZ9ja1AwBG1OXfEA9Qt6locjlt+lDGwOp4xNHoZ/mEiO0qLoyhpCjeL4E6vAEh\nrf5j66IKbpZvJFybgShLTXSjXGVpeexaQZ827Lc/p3E0asoLUSWIH3O0kDdmIJFI4IEHHsADDzzg\nHtu2bZu7kz/99NPx0EMPYcyYMZgyZQrKypyJeMaMGdi+fTu2bt2K8847DwDQ2NiIjRs3ore3F3v3\n7sXUqVPdMrZu3YqmpiYsXLgQiUQC1dXVGDZsGHbv3o2GhgYcLQRNZvmY7OhBP338IMWVsvvVE0yQ\nzUAQ+DsXzxiO7r4IHhWkHpRroSzCYn9AIvxFFaayhWqnwhtfGoZ8F/GvjivOnhR6IQorLP+rQqQz\nv+bCqbAsA4MqCjGzoRaNEYVUgDIgDKCP6bO8YCKLT3E04LkWRmHDnL85kgXyutsOYh3CzvsXLBqL\nCxaNzUWVskbehIFYLIZYjC2+q6sLiYQzOdTU1KCpqQnNzc2orvb0oNXV1b7jZsZXs7m5GeXlXjxs\nUkZlZaWwjH8lYSAflqH9zWpVQN2/YMoQd+AOry1F0+FupbWxChefOQHf2fQmls0dxRy/ZMmESOVE\ncTfuC4ibr8JlSxvwyHNvY9G0IcEX5wAf7mUvPEhioTDoSR5dJi/XEPnR07YSV58/Jatyk8SAMEDX\nr1qU8skM3PTJ2W6mUBFIvbNJVJQz5FHQlM37U8fV4M13WzAqC7ffW6+ae9Q9CYBjaEAoC98a5XjU\nMmhUVRUjlsMUkfzOpraW7QQ1NSW+Y/1FipqAsil76JAKtzN/6XKPer9+zWxsfv19fHTeaMZiOOwz\nTqstw2mzPUEg2/ceM7wSf/jzAYwZWh5YxnsHvKyRUZ/3iTMn4hNnHr3dt8jFlNTZ5vrkhLGDmNgP\nxxsuXtKAx154G2MzyaFyPUZoGHGvHXP9nNLSgrzUffaJ9Xh11z8xdUKdsnzVuw2rL5ee6y+Cyltw\n8gj8ZW8rZpw4hMkCqcLZC8fh6d//DZ9bMV1Zfth3qa4pxQkjKrFg2rCcv3/SEM/BX7liLt7dewQn\njqmObLPQ3zpme/9RnWWKi4vR3d2NwsJC7N+/H3V1dairq0Nzc7N7zYEDBzB9+nTU1dWhqakJEydO\nRF9fH2zbRm1tLQ4fPuxeS5fx3nvv+Y6rcOhQZ07fzeQk36amNub/1iNdaFIYwGWDtnYvKhb/vDBo\naWmXnps3qQ6th702qihJZPWM2tqyrO4DgNOnDoFp25h30uDAMvY3e+ezfd7RQkmZf1IkdW454gVE\neuCG09B2pAv/2m/TP5wxYximjqlyYyjk89vZto35kwfjpLHVOXvOrIl1eO2tA6goiuWl7pcumYBz\n5o/FkMoCZfmH2uRzQV9vn/RcvjGoNI4vrpyOZE8fmprCxVmJA67Xlay+UeeVf8/kDMj1+7dQ6whf\ndl1ZAs3N8jk2HwhqF5WgcFT9GBobG/H8888DAF544QUsXLgQ06ZNw86dO9Ha2oqOjg5s374ds2bN\nwvz58/Hcc88BAF5++WXMmTMH8XgcY8eOxWuvvcaUMXfuXGzevBm9vb3Yv38/Dhw4gPHjc+PLHxZB\n4TbzYjOQZYSqu9Y14uuf8hvhyfD9fzsV31zXmNWz+oNE3MKZs0YwvvYyTB5Tg5LCGNZ89OiphrJF\nUUEMC6YOwSeXOWwEna6a1olECeH6YUZdVfFReVfDMHDFOSdKXSCzwbrzJuN7X1iEJbPDB52KgsJE\nDNMm1AbrphWns50njiWOto99tsgmaum/KvLGDOzatQt33HEH9u7di1gshueffx533XUXNmzYgJ/9\n7GcYOnQozjvvPMTjcVx33XW44oorYBgGrr76apSVlWHZsmXYsmULVq1ahUQigdtvvx0AsHHjRnz1\nq19FOp3GtGnT0NjoLFIrVqzA6tWrYRgGbrrpJphHeSKlB+N9/7bIdz4fXTvbcJXV5YWoLg++joAP\ng/uviNKiOL5zrb/d/xVhGAY+tWwSAOCUifWMPvX4mVoGDooKjr0aR7V4kkycJCyzRu5wHMkC+RMG\nJk+ejEcffdR3/OGHH/YdW7p0KZYuXcocI7EFeIwfPx6PPfaY7/iaNWuwZs2aftS4fyA7f9MwxDre\nPEi6McvE1HE1mDCiMudlaxwd8ILWh2M/pPEvB0XHKS2K4/vXnRrokaARHfZxJA0ce5H2OAGhOXMV\nKCMMDMPAtcunHbXnaeQfNRWFmDWxDtPH1xzrqmh8iEDC38rQ39TFGmLUVxejqqwAp04feqyr0m9o\nYSBHGFrruBGNHy6OPa53fBphYBgG1p03+VhXQ+NDBrLYh7Gv0cgd4jETd189/1hXIyfQwkCOcOrJ\nw3HkSBemjhPv6D4k9jAaGhofQhQXxnDzFaeg8hhGsNP4cEMrkXIE0zQwf8oQX4CPOSfWAwCqBe5k\nGhoaGrnCsNpSJtOghkYUaGYgz7jqYyfiirMnRcphrqGhoaGhcTShhYE8wzAMaa5vDQ0NDQ2NfwXo\n7aqGhoaGhsYAhxYGNDQ0NDQ0Bji0MKChoaGhoTHAoYUBDQ0NDQ2NAQ4tDGhoaGhoaAxwaGFAQ0ND\nQ0NjgEMLAxoaGhoaGgMcWhjQ0NDQ0NAY4NDCgIaGhoaGxgCHFgY0NDQ0NDQGOLQwoKGhoaGhMcBh\n2LZtH+tKaGhoaGhoaBw7aGZAQ0NDQ0NjgEMLAxoaGhoaGgMcWhjQ0NDQ0NAY4NDCgIaGhoaGxgCH\nFgY0NDQ0NDQGOLQwoKGhoaGhMcARO9YVOB5w6623YseOHTAMAxs3bsTUqVOPdZWOKt555x2sW7cO\nl19+OVavXo19+/bhhhtuQCqVQm1tLb75zW8ikUjg6aefxiOPPALTNLFixQosX778WFc9r7jzzjvx\n+uuvI5lM4jOf+QymTJkyoNulq6sLGzZsQEtLC3p6erBu3TpMnDhxQLcJQXd3N8455xysW7cO8+bN\nG/Btsm3bNnz+85/HCSecAACYMGECrrzyygHfLgDw9NNP48EHH0QsFsM111yDhoaG3LSLrdEvbNu2\nzb7qqqts27bt3bt32ytWrDjGNTq66OjosFevXm3feOON9qOPPmrbtm1v2LDBfuaZZ2zbtu27777b\n/slPfmJ3dHTYS5YssVtbW+2uri777LPPtg8dOnQsq55XbN261b7yyitt27btgwcP2qeeeuqAb5f/\n/u//tn/4wx/atm3be/bssZcsWTLg24TgW9/6ln3BBRfYP//5z3Wb2Lb96quv2p/73OeYY7pdnLlk\nyZIldltbm71//377xhtvzFm7aDVBP7F161acccYZAIBx48bhyJEjaG9vP8a1OnpIJBJ44IEHUFdX\n5x7btm0bFi9eDAA4/fTTsXXrVuzYsQNTpkxBWVkZCgsLMWPGDGzfvv1YVTvvmD17Nu69914AQHl5\nObq6ugZ8uyxbtgyf/vSnAQD79u1DfX39gG8TAHj33Xexe/dunHbaaQD0+JFBt4uz3sybNw+lpaWo\nq6vDzTffnLN20cJAP9Hc3Iyqqir3/+rqajQ1NR3DGh1dxGIxFBYWMse6urqQSCQAADU1NWhqakJz\nczOqq6vda473drIsC8XFxQCATZs2YdGiRbpdMli5ciWuv/56bNy4UbcJgDvuuAMbNmxw/9dt4mD3\n7t1Yu3YtVq1ahd///ve6XQDs2bMH3d3dWLt2LS6++GJs3bo1Z+2ibQZyDFtHd2Yga4+B0k4vvvgi\nNm3ahIceeghLlixxjw/kdnn88cfx5z//GV/84heZ9x2IbfLUU09h+vTpGDFihPD8QGwTABg9ejTW\nr1+Ps846C++//z4uvfRSpFIp9/xAbRcAOHz4ML773e/igw8+wKWXXpqzMaSZgX6irq4Ozc3N7v8H\nDhxAbW3tMazRsUdxcTG6u7sBAPv370ddXZ2wnWjVwvGIV155BT/4wQ/wwAMPoKysbMC3y65du7Bv\n3z4AwKRJk5BKpVBSUjKg22Tz5s146aWXsGLFCjz55JO47777Bnw/AYD6+nosW7YMhmFg5MiRGDRo\nEI4cOTLg26WmpgYnn3wyYrEYRo4ciZKSkpyNIS0M9BPz58/H888/DwD44x//iLq6OpSWlh7jWh1b\nNDY2um3ywgsvYOHChZg2bRp27tyJ1tZWdHR0YPv27Zg1a9Yxrmn+0NbWhjvvvBP3338/KisrAeh2\nee211/DQQw8BcNRrnZ2dA75N7rnnHvz85z/HE088geXLl2PdunUDvk0Ax2L+Rz/6EQCgqakJLS0t\nuOCCCwZ8uyxYsACvvvoq0uk0Dh06lNMxpLMW5gB33XUXXnvtNRiGga997WuYOHHisa7SUcOuXbtw\nxx13YO/evYjFYqivr8ddd92FDRs2oKenB0OHDsVtt92GeDyO5557Dj/60Y9gGAZWr16Nj3/848e6\n+nnDz372M3znO9/BmDFj3GO33347brzxxgHbLt3d3fjyl7+Mffv2obu7G+vXr8fkyZPxpS99acC2\nCY3vfOc7GDZsGBYsWDDg26S9vR3XX389Wltb0dfXh/Xr12PSpEkDvl0AR822adMmAMBnP/tZTJky\nJSftooUBDQ0NDQ2NAQ6tJtDQ0NDQ0Bjg0MKAhoaGhobGAIcWBjQ0NDQ0NAY4tDCgoaGhoaExwKGF\nAQ0NDQ0NjQEOLQxoaGj4sGfPHixatMh3vKGhAclk8qjWZdu2bVi1ahUA4Be/+AUaGxuxZs0arF69\nGpdccgmeeOKJo1ofDY3jETocsYaGxocKjY2NuOuuuwA4kdW+8IUvoLOzE5dffvmxrZiGxocYmhnQ\n0NCIjFQqhZtvvhkrV67EypUrcc899wBgd/EAsGHDBjz55JPo6Ohwk6usWLEC3//+9wEAR44cwbXX\nXotLL70UF1xwAX79619HqkddXR1uueUWPPDAAwMiLr2GRr6gmQENDY3IePbZZ7Fnzx789Kc/RTqd\nxsqVK9HY2Ci9fsuWLUgmk3jssceQTqfx6KOPIp1O45577sHChQtx4YUXorOzE+eeey7mz5/PZFwL\nwujRo5FMJtHS0oJBgwbl4vU0NAYctDCgoaEhxMGDB7FmzRrhuR07dmDevHkwDAOWZWHWrFnYuXMn\nJk+eLLx+xowZ+Pa3v43Pf/7zOPXUU7F8+XKYpolt27Zh586deOqppwA4KbH37NkTSRhIp9Po7OyE\naWqiU0MjW2hhQENDQ4jq6mo8+uijzLGGhgYAgGEYzHHbtmEYhu94X18fACfb2q9+9Su88cYbeOml\nl3DhhRfil7/8JRKJBL72ta9hypQpWddz165dGDRoUCQBQkNDg4UWpTU0NCJj+vTp2LJlC2zbRjKZ\nxB/+8AdMmzYNpaWl2L9/P2zbRldXF3bs2AEA+N3vfofNmzdj5syZuOGGG1BcXIyWlhbMnDkTzz77\nLAAnkdFNN90UyVuhubkZX//617F27dq8vKeGxkCBZgY0NDQiY+nSpdi+fTtWrVqFdDqNM844AzNn\nzkQ6nUZDQwPOP/98jBw5EieffDIAYMyYMdiwYQMefPBBWJaFBQsWYNiwYVi/fj1uvPFGrFq1Cr29\nvbjooosQi6mnpS1btmDNmjXo7e1Fd3c3Vq1ahYsuuuhovLaGxnELnbVQQ0NDQ0NjgEOrCTQ0NDQ0\nNAY4tDCgoaGhoaExwKGFAQ0NDQ0NjQEOLQxoaGhoaGgMcGhhQENDQ0NDY4BDCwMaGhoaGhoDHFoY\n0NDQ0NDQGODQwoCGhoaGhsYAx/8HHKda6z5chtQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa6f89f6c>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Since random forest is our best performing regressor, we're going to tune it \n",
    "rf = RandomForestRegressor(n_estimators = 500, max_features = int(len(variables)*0.5), max_depth = 5, bootstrap=False)\n",
    "print(rf)\n",
    "rf.fit(X_train, y_train)\n",
    "y_hat = rf.predict(X_test)\n",
    "print(np.sqrt(mean_squared_error(y_hat, y_test))) # our RMSE for the predictions of sale prices\n",
    "\n",
    "plt.plot(y_hat)\n",
    "plt.title(\"Random Forest House Sale Price Predictions\")\n",
    "plt.ylabel('Sale Price $')\n",
    "plt.xlabel(\"House ID\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}