Regression_Analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Import all the required libraries "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import datetime as dt\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "#inline statement - displays the graphs in the current notebook\n",
    "% matplotlib inline\n",
    "from sklearn.model_selection import train_test_split, LeaveOneOut, GridSearchCV\n",
    "from sklearn.preprocessing import LabelEncoder, OneHotEncoder, scale, StandardScaler\n",
    "from sklearn.linear_model import LinearRegression, RidgeCV, LassoCV, Ridge, Lasso\n",
    "from sklearn import preprocessing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us load the modified csv file from the previous notebook **house_prices_cleaned.csv**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "house_prices_new = pd.read_csv(\"E:\\Data Science\\Capstone Project - House prices\\Regression\\\\house_prices_cleaned.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "<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>No alley access</td>\n",
       "      <td>Reg</td>\n",
       "      <td>Lvl</td>\n",
       "      <td>AllPub</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>No Pool</td>\n",
       "      <td>No Fence</td>\n",
       "      <td>None</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>No alley access</td>\n",
       "      <td>Reg</td>\n",
       "      <td>Lvl</td>\n",
       "      <td>AllPub</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>No Pool</td>\n",
       "      <td>No Fence</td>\n",
       "      <td>None</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>No alley access</td>\n",
       "      <td>IR1</td>\n",
       "      <td>Lvl</td>\n",
       "      <td>AllPub</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>No Pool</td>\n",
       "      <td>No Fence</td>\n",
       "      <td>None</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>No alley access</td>\n",
       "      <td>IR1</td>\n",
       "      <td>Lvl</td>\n",
       "      <td>AllPub</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>No Pool</td>\n",
       "      <td>No Fence</td>\n",
       "      <td>None</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>No alley access</td>\n",
       "      <td>IR1</td>\n",
       "      <td>Lvl</td>\n",
       "      <td>AllPub</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>No Pool</td>\n",
       "      <td>No Fence</td>\n",
       "      <td>None</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  \\\n",
       "0   1          60       RL         65.0     8450   Pave  No alley access   \n",
       "1   2          20       RL         80.0     9600   Pave  No alley access   \n",
       "2   3          60       RL         68.0    11250   Pave  No alley access   \n",
       "3   4          70       RL         60.0     9550   Pave  No alley access   \n",
       "4   5          60       RL         84.0    14260   Pave  No alley access   \n",
       "\n",
       "  LotShape LandContour Utilities    ...     PoolArea   PoolQC     Fence  \\\n",
       "0      Reg         Lvl    AllPub    ...            0  No Pool  No Fence   \n",
       "1      Reg         Lvl    AllPub    ...            0  No Pool  No Fence   \n",
       "2      IR1         Lvl    AllPub    ...            0  No Pool  No Fence   \n",
       "3      IR1         Lvl    AllPub    ...            0  No Pool  No Fence   \n",
       "4      IR1         Lvl    AllPub    ...            0  No Pool  No Fence   \n",
       "\n",
       "  MiscFeature MiscVal MoSold YrSold  SaleType  SaleCondition  SalePrice  \n",
       "0        None       0      2   2008        WD         Normal     208500  \n",
       "1        None       0      5   2007        WD         Normal     181500  \n",
       "2        None       0      9   2008        WD         Normal     223500  \n",
       "3        None       0      2   2006        WD        Abnorml     140000  \n",
       "4        None       0     12   2008        WD         Normal     250000  \n",
       "\n",
       "[5 rows x 81 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "house_prices_new.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data Standardization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Standardization is very important when we are comparing measurements that have different units. Standardization should be performed to make sure that all the features are on the same scale so that they can be compared for analyzing results.\n",
    "\n",
    "**Data Standardization:** Standardization (or Z-score normalization) is the process where the features are rescaled so that they’ll have the properties of a standard normal distribution with μ=0 and σ=1, where μ is the mean (average) and σ is the standard deviation from the mean.\n",
    "\n",
    "- Standardization can be done using scale() function or StandardScaler class.\n",
    "- StandardScaler is preferred over sacle() as it implements the Transformer API to compute the mean and standard deviation on a training set so as to be able to later reapply the same transformation on the testing set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "house_prices_new[['MSSubClass','LotFrontage','LotArea','OverallQual','OverallCond','YearBuilt','YearRemodAdd','MasVnrArea','BsmtFinSF1',\n",
    "     'BsmtFinSF2','BsmtUnfSF','TotalBsmtSF','1stFlrSF','2ndFlrSF','LowQualFinSF','GrLivArea','BsmtFullBath','BsmtHalfBath',\n",
    "     'FullBath','HalfBath','BedroomAbvGr','KitchenAbvGr','TotRmsAbvGrd','Fireplaces','GarageYrBlt','GarageCars','GarageArea',\n",
    "     'WoodDeckSF','OpenPorchSF','EnclosedPorch','3SsnPorch','ScreenPorch','PoolArea','MiscVal','MoSold','YrSold']] = StandardScaler().fit_transform(house_prices_new[['MSSubClass','LotFrontage','LotArea','OverallQual','OverallCond','YearBuilt',\n",
    "                                       'YearRemodAdd','MasVnrArea','BsmtFinSF1','BsmtFinSF2','BsmtUnfSF','TotalBsmtSF',\n",
    "                                       '1stFlrSF','2ndFlrSF','LowQualFinSF','GrLivArea','BsmtFullBath','BsmtHalfBath',\n",
    "                                       'FullBath','HalfBath','BedroomAbvGr','KitchenAbvGr','TotRmsAbvGrd','Fireplaces',\n",
    "                                       'GarageYrBlt','GarageCars','GarageArea','WoodDeckSF','OpenPorchSF','EnclosedPorch',\n",
    "                                       '3SsnPorch','ScreenPorch','PoolArea','MiscVal','MoSold','YrSold']])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1460, 81)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "house_prices_new.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Encode the categorical data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To perform Regression Analysis all the data should be in numerical form. Since our data frame contains categorical data too, this should be converted into numerical for further analysis. A good way to convert categorical data into numerical is One Hot Encoding. \n",
    "\n",
    "**One Hot Encoding -** One Hot Encoding is a representation of categorical variables as binary vectors. This first requires that the categorical values be mapped to integer values. Then, each integer value is represented as a binary vector that is all zero values except the index of the integer, which is marked with a 1.\n",
    "\n",
    "get_dummies function is used to produce a resultant binary matrix "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Used get_dummies to produce binary matrix dummy variables \n",
    "new_house_prices = pd.get_dummies(house_prices_new, columns=['MSZoning','Street','Alley','LotShape','LandContour','Utilities','LotConfig',\n",
    "                                                'LandSlope','Neighborhood','Condition1','Condition2','BldgType','HouseStyle',\n",
    "                                                'RoofStyle','RoofMatl','Exterior1st','Exterior2nd','MasVnrType','ExterQual',\n",
    "                                                'ExterCond','Foundation','BsmtQual','BsmtCond','BsmtExposure','BsmtFinType1',\n",
    "                                                'BsmtFinType2','Heating','HeatingQC','CentralAir','Electrical','KitchenQual',\n",
    "                                                'Functional','FireplaceQu','GarageType','GarageFinish','GarageQual','GarageCond',\n",
    "                                                'PavedDrive','PoolQC', 'Fence', 'MiscFeature','SaleType','SaleCondition'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After One hot encoding the number of variables have increased because dummy variables have been introduced to the resultant matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1460, 306)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_house_prices.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_house_prices.isnull().values.any()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Id</th>\n",
       "      <th>MSSubClass</th>\n",
       "      <th>LotFrontage</th>\n",
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       "      <th>SaleType_Oth</th>\n",
       "      <th>SaleType_WD</th>\n",
       "      <th>SaleCondition_Abnorml</th>\n",
       "      <th>SaleCondition_AdjLand</th>\n",
       "      <th>SaleCondition_Alloca</th>\n",
       "      <th>SaleCondition_Family</th>\n",
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       "<p>5 rows × 306 columns</p>\n",
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      ],
      "text/plain": [
       "   Id  MSSubClass  LotFrontage   LotArea  OverallQual  OverallCond  YearBuilt  \\\n",
       "0   1    0.073375    -0.225902 -0.207142     0.651479    -0.517200   1.050994   \n",
       "1   2   -0.872563     0.425052 -0.091886    -0.071836     2.179628   0.156734   \n",
       "2   3    0.073375    -0.095711  0.073480     0.651479    -0.517200   0.984752   \n",
       "3   4    0.309859    -0.442886 -0.096897     0.651479    -0.517200  -1.863632   \n",
       "4   5    0.073375     0.598640  0.375148     1.374795    -0.517200   0.951632   \n",
       "\n",
       "   YearRemodAdd  MasVnrArea  BsmtFinSF1          ...            \\\n",
       "0      0.878668    0.511514    0.575425          ...             \n",
       "1     -0.429577   -0.573359    1.171992          ...             \n",
       "2      0.830215    0.323322    0.092907          ...             \n",
       "3     -0.720298   -0.573359   -0.499274          ...             \n",
       "4      0.733308    1.363915    0.463568          ...             \n",
       "\n",
       "   SaleType_ConLw  SaleType_New  SaleType_Oth  SaleType_WD  \\\n",
       "0               0             0             0            1   \n",
       "1               0             0             0            1   \n",
       "2               0             0             0            1   \n",
       "3               0             0             0            1   \n",
       "4               0             0             0            1   \n",
       "\n",
       "   SaleCondition_Abnorml  SaleCondition_AdjLand  SaleCondition_Alloca  \\\n",
       "0                      0                      0                     0   \n",
       "1                      0                      0                     0   \n",
       "2                      0                      0                     0   \n",
       "3                      1                      0                     0   \n",
       "4                      0                      0                     0   \n",
       "\n",
       "   SaleCondition_Family  SaleCondition_Normal  SaleCondition_Partial  \n",
       "0                     0                     1                      0  \n",
       "1                     0                     1                      0  \n",
       "2                     0                     1                      0  \n",
       "3                     0                     0                      0  \n",
       "4                     0                     1                      0  \n",
       "\n",
       "[5 rows x 306 columns]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_house_prices.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Make csv copy of new_house_prices\n",
    "#new_house_prices.to_csv('E:\\Data Science\\Capstone Project - House prices\\Regularization\\\\final_house_prices.csv', index=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Create a new data frame house_prices_new_numerical which contains columns that are of type numerical \n",
    "house_prices_new_numerical = house_prices_new.select_dtypes(include = [np.number])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is worthwhile to check if the number of columns that result from introducing the dummy variables is correct wrt the number of unique values per categorical variables.\n",
    "\n",
    "In the code below I compute the aggregation of the no. of unique values per categorical variable to check that the no. of columns is equals to the no. of columns for non-categorical variables plus the number computed below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# No of columns produced only by categorical variables\n",
    "s = 0\n",
    "for col in house_prices_new:\n",
    "    if house_prices_new[col].dtype == 'object':\n",
    "        s  = s + house_prices_new[col].nunique()  \n",
    "\n",
    "# No of numerical columns \n",
    "n = len(house_prices_new_numerical.columns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Column numbers match: 306\n"
     ]
    }
   ],
   "source": [
    "# The total number of columns produced after One Hot Encoding will be the sum of 's' and 'n'\n",
    "total_cols = s+n\n",
    "total_cols\n",
    "if len(new_house_prices.columns) == total_cols:\n",
    "    print(\"Column numbers match: %s\" % total_cols)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Split the data into test and train data sets\n",
    "\n",
    "It is extremely important to split the data into train and test sets. Train set is used to train the model and Test set is used to test the performance of the model.\n",
    "\n",
    "Problems encountered if train test split not performed:\n",
    "- It does not make sense to talk about the performance of the model by testing it on same data. The model learns the data pretty well and when tested on same data will produce the best score.\n",
    "- The model becomes very specific to the training data, so far as they even get trained on the ocassional erroneous labels present in the training data. This results in **Overfitting** and the model might not work well outside the training data.\n",
    "\n",
    "Therefore it is advised to keep a certian portion of the data aside (test set) untouched and test our model on this data to evaluate the true performance of the model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- X_train - all the predictors\n",
    "- Y_train - target variable (SalePrice)\n",
    "- X_test - all the predictors\n",
    "- Y_test - target variable (SalePrice)\n",
    "\n",
    "Let's define X and Y before splitting the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X = new_house_prices.drop('SalePrice', axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1022, 305)\n",
      "(438, 305)\n",
      "(1022,)\n",
      "(438,)\n"
     ]
    }
   ],
   "source": [
    "X_train, X_test, Y_train, Y_test  = train_test_split(X, new_house_prices.SalePrice, test_size=0.3, random_state=10)\n",
    "print(X_train.shape)\n",
    "print(X_test.shape)\n",
    "print(Y_train.shape)\n",
    "print(Y_test.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regression Analysis\n",
    "\n",
    "Let us perform Multiple Linear Regression to analyze the relationship between independent and target variables. \n",
    "\n",
    "**Multiple linear regression -** It is a predictive analysis tool which is used to explain the relationship between one continuous dependent variable and two or more continuous/ categorical independent variables.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "** Multiple Linear Regression**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create an object lm for the LinearRegression model\n",
    "lm = LinearRegression()\n",
    "# Fit the model on the training data\n",
    "lm.fit(X_train, Y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is very uselful table which gives out $R^2$, adjusted $R^2$, coefficients of all the numerical variables along with p-values, standard errors, t-statistic and confidence interval for 2 standard deviations. Let us concentrate on coefficients, some are negative and others are positive. The positive correlation signifies a stronger correlation of the feature with the predictor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\nikhi_000\\Anaconda3\\lib\\site-packages\\statsmodels\\compat\\pandas.py:56: FutureWarning: The pandas.core.datetools module is deprecated and will be removed in a future version. Please use the pandas.tseries module instead.\n",
      "  from pandas.core import datetools\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>        <td>SalePrice</td>    <th>  R-squared:         </th> <td>   0.131</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.111</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   6.343</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Mon, 04 Dec 2017</td> <th>  Prob (F-statistic):</th> <td>5.86e-26</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>16:24:43</td>     <th>  Log-Likelihood:    </th> <td> -19772.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  1460</td>      <th>  AIC:               </th> <td>3.961e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>  1426</td>      <th>  BIC:               </th> <td>3.979e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>    34</td>      <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "        <td></td>           <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MSSubClass</th>    <td>-7751.6575</td> <td> 6255.474</td> <td>   -1.239</td> <td> 0.215</td> <td>   -2e+04</td> <td> 4519.262</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>LotFrontage</th>   <td>-1534.7682</td> <td> 5948.077</td> <td>   -0.258</td> <td> 0.796</td> <td>-1.32e+04</td> <td> 1.01e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>LotArea</th>       <td> 4309.4956</td> <td> 5442.596</td> <td>    0.792</td> <td> 0.429</td> <td>-6366.859</td> <td>  1.5e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>OverallQual</th>   <td> 2.404e+04</td> <td> 8801.436</td> <td>    2.732</td> <td> 0.006</td> <td> 6776.092</td> <td> 4.13e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>OverallCond</th>   <td> 5186.2497</td> <td> 6161.811</td> <td>    0.842</td> <td> 0.400</td> <td>-6900.937</td> <td> 1.73e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>YearBuilt</th>     <td> 8378.9476</td> <td> 1.08e+04</td> <td>    0.775</td> <td> 0.438</td> <td>-1.28e+04</td> <td> 2.96e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>YearRemodAdd</th>  <td> 2823.7228</td> <td> 7593.014</td> <td>    0.372</td> <td> 0.710</td> <td>-1.21e+04</td> <td> 1.77e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MasVnrArea</th>    <td> 5626.2114</td> <td> 5755.739</td> <td>    0.977</td> <td> 0.328</td> <td>-5664.412</td> <td> 1.69e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>BsmtFinSF1</th>    <td> 4328.7757</td> <td> 5429.140</td> <td>    0.797</td> <td> 0.425</td> <td>-6321.182</td> <td>  1.5e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>BsmtFinSF2</th>    <td> -228.5180</td> <td> 4970.623</td> <td>   -0.046</td> <td> 0.963</td> <td>-9979.036</td> <td> 9522.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>BsmtUnfSF</th>     <td> -199.8616</td> <td> 4702.380</td> <td>   -0.043</td> <td> 0.966</td> <td>-9424.185</td> <td> 9024.462</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>TotalBsmtSF</th>   <td> 4215.0611</td> <td> 6698.308</td> <td>    0.629</td> <td> 0.529</td> <td>-8924.534</td> <td> 1.74e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>1stFlrSF</th>      <td> 8564.0716</td> <td> 7957.913</td> <td>    1.076</td> <td> 0.282</td> <td>-7046.401</td> <td> 2.42e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>2ndFlrSF</th>      <td> 9559.1067</td> <td> 6935.754</td> <td>    1.378</td> <td> 0.168</td> <td>-4046.270</td> <td> 2.32e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>LowQualFinSF</th>  <td>   -7.3055</td> <td> 5164.098</td> <td>   -0.001</td> <td> 0.999</td> <td>-1.01e+04</td> <td> 1.01e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>GrLivArea</th>     <td> 1.424e+04</td> <td> 7239.642</td> <td>    1.967</td> <td> 0.049</td> <td>   39.253</td> <td> 2.84e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>BsmtFullBath</th>  <td> 4793.3480</td> <td> 7264.324</td> <td>    0.660</td> <td> 0.509</td> <td>-9456.561</td> <td>  1.9e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>BsmtHalfBath</th>  <td>  457.6175</td> <td> 5239.316</td> <td>    0.087</td> <td> 0.930</td> <td>-9819.977</td> <td> 1.07e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>FullBath</th>      <td> 1887.1767</td> <td> 8375.684</td> <td>    0.225</td> <td> 0.822</td> <td>-1.45e+04</td> <td> 1.83e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>HalfBath</th>      <td> -943.8989</td> <td> 7178.262</td> <td>   -0.131</td> <td> 0.895</td> <td> -1.5e+04</td> <td> 1.31e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>BedroomAbvGr</th>  <td>-8200.3334</td> <td> 7444.890</td> <td>   -1.101</td> <td> 0.271</td> <td>-2.28e+04</td> <td> 6403.777</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>KitchenAbvGr</th>  <td>-2636.0392</td> <td> 6153.485</td> <td>   -0.428</td> <td> 0.668</td> <td>-1.47e+04</td> <td> 9434.814</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>TotRmsAbvGrd</th>  <td> 8220.8485</td> <td> 1.08e+04</td> <td>    0.763</td> <td> 0.446</td> <td>-1.29e+04</td> <td> 2.94e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Fireplaces</th>    <td> 2519.7661</td> <td> 6138.898</td> <td>    0.410</td> <td> 0.682</td> <td>-9522.474</td> <td> 1.46e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>GarageYrBlt</th>   <td> 2710.9325</td> <td> 8818.667</td> <td>    0.307</td> <td> 0.759</td> <td>-1.46e+04</td> <td>    2e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>GarageCars</th>    <td> 8312.3492</td> <td> 1.15e+04</td> <td>    0.723</td> <td> 0.470</td> <td>-1.42e+04</td> <td> 3.09e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>GarageArea</th>    <td> -820.5652</td> <td> 1.14e+04</td> <td>   -0.072</td> <td> 0.943</td> <td>-2.32e+04</td> <td> 2.15e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>WoodDeckSF</th>    <td> 2994.1661</td> <td> 5381.681</td> <td>    0.556</td> <td> 0.578</td> <td>-7562.696</td> <td> 1.36e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>OpenPorchSF</th>   <td> -179.1728</td> <td> 5386.176</td> <td>   -0.033</td> <td> 0.973</td> <td>-1.07e+04</td> <td> 1.04e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>EnclosedPorch</th> <td>  701.9129</td> <td> 5522.835</td> <td>    0.127</td> <td> 0.899</td> <td>-1.01e+04</td> <td> 1.15e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>3SsnPorch</th>     <td>  595.4686</td> <td> 4931.294</td> <td>    0.121</td> <td> 0.904</td> <td>-9077.901</td> <td> 1.03e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ScreenPorch</th>   <td> 3111.9090</td> <td> 5137.736</td> <td>    0.606</td> <td> 0.545</td> <td>-6966.422</td> <td> 1.32e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>PoolArea</th>      <td>-1163.2670</td> <td> 5116.441</td> <td>   -0.227</td> <td> 0.820</td> <td>-1.12e+04</td> <td> 8873.292</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MiscVal</th>       <td> -392.3765</td> <td> 4934.544</td> <td>   -0.080</td> <td> 0.937</td> <td>-1.01e+04</td> <td> 9287.367</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MoSold</th>        <td> -117.1390</td> <td> 4997.339</td> <td>   -0.023</td> <td> 0.981</td> <td>-9920.064</td> <td> 9685.786</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>YrSold</th>        <td>-1024.0617</td> <td> 5001.590</td> <td>   -0.205</td> <td> 0.838</td> <td>-1.08e+04</td> <td> 8787.203</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>585.003</td> <th>  Durbin-Watson:     </th>  <td>   0.068</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>100362.814</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.732</td>  <th>  Prob(JB):          </th>  <td>    0.00</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td>43.591</td>  <th>  Cond. No.          </th>  <td>1.87e+16</td> \n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:              SalePrice   R-squared:                       0.131\n",
       "Model:                            OLS   Adj. R-squared:                  0.111\n",
       "Method:                 Least Squares   F-statistic:                     6.343\n",
       "Date:                Mon, 04 Dec 2017   Prob (F-statistic):           5.86e-26\n",
       "Time:                        16:24:43   Log-Likelihood:                -19772.\n",
       "No. Observations:                1460   AIC:                         3.961e+04\n",
       "Df Residuals:                    1426   BIC:                         3.979e+04\n",
       "Df Model:                          34                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "=================================================================================\n",
       "                    coef    std err          t      P>|t|      [0.025      0.975]\n",
       "---------------------------------------------------------------------------------\n",
       "MSSubClass    -7751.6575   6255.474     -1.239      0.215      -2e+04    4519.262\n",
       "LotFrontage   -1534.7682   5948.077     -0.258      0.796   -1.32e+04    1.01e+04\n",
       "LotArea        4309.4956   5442.596      0.792      0.429   -6366.859     1.5e+04\n",
       "OverallQual    2.404e+04   8801.436      2.732      0.006    6776.092    4.13e+04\n",
       "OverallCond    5186.2497   6161.811      0.842      0.400   -6900.937    1.73e+04\n",
       "YearBuilt      8378.9476   1.08e+04      0.775      0.438   -1.28e+04    2.96e+04\n",
       "YearRemodAdd   2823.7228   7593.014      0.372      0.710   -1.21e+04    1.77e+04\n",
       "MasVnrArea     5626.2114   5755.739      0.977      0.328   -5664.412    1.69e+04\n",
       "BsmtFinSF1     4328.7757   5429.140      0.797      0.425   -6321.182     1.5e+04\n",
       "BsmtFinSF2     -228.5180   4970.623     -0.046      0.963   -9979.036    9522.000\n",
       "BsmtUnfSF      -199.8616   4702.380     -0.043      0.966   -9424.185    9024.462\n",
       "TotalBsmtSF    4215.0611   6698.308      0.629      0.529   -8924.534    1.74e+04\n",
       "1stFlrSF       8564.0716   7957.913      1.076      0.282   -7046.401    2.42e+04\n",
       "2ndFlrSF       9559.1067   6935.754      1.378      0.168   -4046.270    2.32e+04\n",
       "LowQualFinSF     -7.3055   5164.098     -0.001      0.999   -1.01e+04    1.01e+04\n",
       "GrLivArea      1.424e+04   7239.642      1.967      0.049      39.253    2.84e+04\n",
       "BsmtFullBath   4793.3480   7264.324      0.660      0.509   -9456.561     1.9e+04\n",
       "BsmtHalfBath    457.6175   5239.316      0.087      0.930   -9819.977    1.07e+04\n",
       "FullBath       1887.1767   8375.684      0.225      0.822   -1.45e+04    1.83e+04\n",
       "HalfBath       -943.8989   7178.262     -0.131      0.895    -1.5e+04    1.31e+04\n",
       "BedroomAbvGr  -8200.3334   7444.890     -1.101      0.271   -2.28e+04    6403.777\n",
       "KitchenAbvGr  -2636.0392   6153.485     -0.428      0.668   -1.47e+04    9434.814\n",
       "TotRmsAbvGrd   8220.8485   1.08e+04      0.763      0.446   -1.29e+04    2.94e+04\n",
       "Fireplaces     2519.7661   6138.898      0.410      0.682   -9522.474    1.46e+04\n",
       "GarageYrBlt    2710.9325   8818.667      0.307      0.759   -1.46e+04       2e+04\n",
       "GarageCars     8312.3492   1.15e+04      0.723      0.470   -1.42e+04    3.09e+04\n",
       "GarageArea     -820.5652   1.14e+04     -0.072      0.943   -2.32e+04    2.15e+04\n",
       "WoodDeckSF     2994.1661   5381.681      0.556      0.578   -7562.696    1.36e+04\n",
       "OpenPorchSF    -179.1728   5386.176     -0.033      0.973   -1.07e+04    1.04e+04\n",
       "EnclosedPorch   701.9129   5522.835      0.127      0.899   -1.01e+04    1.15e+04\n",
       "3SsnPorch       595.4686   4931.294      0.121      0.904   -9077.901    1.03e+04\n",
       "ScreenPorch    3111.9090   5137.736      0.606      0.545   -6966.422    1.32e+04\n",
       "PoolArea      -1163.2670   5116.441     -0.227      0.820   -1.12e+04    8873.292\n",
       "MiscVal        -392.3765   4934.544     -0.080      0.937   -1.01e+04    9287.367\n",
       "MoSold         -117.1390   4997.339     -0.023      0.981   -9920.064    9685.786\n",
       "YrSold        -1024.0617   5001.590     -0.205      0.838   -1.08e+04    8787.203\n",
       "==============================================================================\n",
       "Omnibus:                      585.003   Durbin-Watson:                   0.068\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):           100362.814\n",
       "Skew:                          -0.732   Prob(JB):                         0.00\n",
       "Kurtosis:                      43.591   Cond. No.                     1.87e+16\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The smallest eigenvalue is 2.97e-29. This might indicate that there are\n",
       "strong multicollinearity problems or that the design matrix is singular.\n",
       "\"\"\""
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "X = house_prices_new[['MSSubClass','LotFrontage','LotArea','OverallQual','OverallCond','YearBuilt','YearRemodAdd','MasVnrArea',\n",
    "        'BsmtFinSF1','BsmtFinSF2','BsmtUnfSF','TotalBsmtSF','1stFlrSF','2ndFlrSF','LowQualFinSF','GrLivArea','BsmtFullBath',\n",
    "        'BsmtHalfBath','FullBath','HalfBath','BedroomAbvGr','KitchenAbvGr','TotRmsAbvGrd','Fireplaces','GarageYrBlt',\n",
    "        'GarageCars','GarageArea','WoodDeckSF','OpenPorchSF','EnclosedPorch','3SsnPorch','ScreenPorch','PoolArea','MiscVal',\n",
    "        'MoSold','YrSold']]\n",
    "Y = house_prices_new['SalePrice']\n",
    "model = sm.OLS(Y, X).fit()\n",
    "predictions = model.predict(X)\n",
    "model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us look at all the features and thier respective coefficients."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Features</th>\n",
       "      <th>Estimated_Coefficients</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>MiscVal</td>\n",
       "      <td>21298.626224</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>BsmtFullBath</td>\n",
       "      <td>15327.722992</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>LowQualFinSF</td>\n",
       "      <td>14026.806738</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>OverallCond</td>\n",
       "      <td>10836.631181</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>YearRemodAdd</td>\n",
       "      <td>10465.033786</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>OverallQual</td>\n",
       "      <td>8831.872085</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1stFlrSF</td>\n",
       "      <td>8304.026483</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>BsmtFinSF2</td>\n",
       "      <td>6891.937360</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>YearBuilt</td>\n",
       "      <td>6805.543499</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>2ndFlrSF</td>\n",
       "      <td>5140.709475</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>WoodDeckSF</td>\n",
       "      <td>4823.832482</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>BsmtFinSF1</td>\n",
       "      <td>3535.074438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>OpenPorchSF</td>\n",
       "      <td>3125.151412</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>GarageArea</td>\n",
       "      <td>2897.478249</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>GarageYrBlt</td>\n",
       "      <td>2809.293658</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>Fireplaces</td>\n",
       "      <td>2693.727114</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>HalfBath</td>\n",
       "      <td>2075.125328</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>BsmtUnfSF</td>\n",
       "      <td>1647.806470</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>PoolArea</td>\n",
       "      <td>1643.702738</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>MasVnrArea</td>\n",
       "      <td>1369.656190</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>ScreenPorch</td>\n",
       "      <td>1037.556490</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>BsmtHalfBath</td>\n",
       "      <td>941.567474</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>LotArea</td>\n",
       "      <td>755.553479</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>TotalBsmtSF</td>\n",
       "      <td>529.114514</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>FullBath</td>\n",
       "      <td>372.492401</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>EnclosedPorch</td>\n",
       "      <td>225.677087</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>MSSubClass</td>\n",
       "      <td>2.323880</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>MoSold</td>\n",
       "      <td>-81.729301</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>3SsnPorch</td>\n",
       "      <td>-158.479333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>BedroomAbvGr</td>\n",
       "      <td>-217.771808</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>LotFrontage</td>\n",
       "      <td>-626.091765</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>YrSold</td>\n",
       "      <td>-1136.824685</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>GrLivArea</td>\n",
       "      <td>-1152.076289</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>GarageCars</td>\n",
       "      <td>-1489.893249</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>KitchenAbvGr</td>\n",
       "      <td>-2904.693587</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>TotRmsAbvGrd</td>\n",
       "      <td>-3429.718480</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Features  Estimated_Coefficients\n",
       "33        MiscVal            21298.626224\n",
       "16   BsmtFullBath            15327.722992\n",
       "14   LowQualFinSF            14026.806738\n",
       "4     OverallCond            10836.631181\n",
       "6    YearRemodAdd            10465.033786\n",
       "3     OverallQual             8831.872085\n",
       "12       1stFlrSF             8304.026483\n",
       "9      BsmtFinSF2             6891.937360\n",
       "5       YearBuilt             6805.543499\n",
       "13       2ndFlrSF             5140.709475\n",
       "27     WoodDeckSF             4823.832482\n",
       "8      BsmtFinSF1             3535.074438\n",
       "28    OpenPorchSF             3125.151412\n",
       "26     GarageArea             2897.478249\n",
       "24    GarageYrBlt             2809.293658\n",
       "23     Fireplaces             2693.727114\n",
       "19       HalfBath             2075.125328\n",
       "10      BsmtUnfSF             1647.806470\n",
       "32       PoolArea             1643.702738\n",
       "7      MasVnrArea             1369.656190\n",
       "31    ScreenPorch             1037.556490\n",
       "17   BsmtHalfBath              941.567474\n",
       "2         LotArea              755.553479\n",
       "11    TotalBsmtSF              529.114514\n",
       "18       FullBath              372.492401\n",
       "29  EnclosedPorch              225.677087\n",
       "0      MSSubClass                2.323880\n",
       "34         MoSold              -81.729301\n",
       "30      3SsnPorch             -158.479333\n",
       "20   BedroomAbvGr             -217.771808\n",
       "1     LotFrontage             -626.091765\n",
       "35         YrSold            -1136.824685\n",
       "15      GrLivArea            -1152.076289\n",
       "25     GarageCars            -1489.893249\n",
       "21   KitchenAbvGr            -2904.693587\n",
       "22   TotRmsAbvGrd            -3429.718480"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Features and their respective coefficients\n",
    "coeffs_df = pd.DataFrame(list(zip(X.columns, lm.coef_)), columns = ['Features', 'Estimated_Coefficients'])\n",
    "coeffs_df.sort_values(by='Estimated_Coefficients', ascending=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- From the Exploratory analysis the top five features highly correlated with Sale Price are OverallQual, GrLivArea, GarageCars, GarageArea, TotalBsmtSF.\n",
    "- After performing Regression the features with higher postive coefficients are MiscVal, BsmtFullBath, LowQualFinSF, OverallCond, YearRemodAdd. \n",
    "- We can clearly observe that results are quite different. The OverallQual/ OverallCond which is simply the present condition of the house seems to influence the price the house.\n",
    "- Miscellaneous value (highest coefficient) is the value of miscellaneous features like Elevator, Garage, Shed, Tennis court etc., therefore having these aminities bumps up the price of the house.\n",
    "- According to Regression analysis other features such as Full bath in basement, Low quality finished square foot, Remodel date of the house, and square footage increases/ decreases the price of a house."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us have a closer look at the coefficients to explore the linear and non-linear relationship of the features with the target variable 'Sale Price'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Features</th>\n",
       "      <th>Estimated_Coefficients</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>MiscVal</td>\n",
       "      <td>21298.626224</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>BsmtFullBath</td>\n",
       "      <td>15327.722992</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>LowQualFinSF</td>\n",
       "      <td>14026.806738</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>OverallCond</td>\n",
       "      <td>10836.631181</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>YearRemodAdd</td>\n",
       "      <td>10465.033786</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>OverallQual</td>\n",
       "      <td>8831.872085</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1stFlrSF</td>\n",
       "      <td>8304.026483</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>BsmtFinSF2</td>\n",
       "      <td>6891.937360</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>YearBuilt</td>\n",
       "      <td>6805.543499</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>2ndFlrSF</td>\n",
       "      <td>5140.709475</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>WoodDeckSF</td>\n",
       "      <td>4823.832482</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>BsmtFinSF1</td>\n",
       "      <td>3535.074438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>OpenPorchSF</td>\n",
       "      <td>3125.151412</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>GarageArea</td>\n",
       "      <td>2897.478249</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>GarageYrBlt</td>\n",
       "      <td>2809.293658</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>Fireplaces</td>\n",
       "      <td>2693.727114</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>HalfBath</td>\n",
       "      <td>2075.125328</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>BsmtUnfSF</td>\n",
       "      <td>1647.806470</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>PoolArea</td>\n",
       "      <td>1643.702738</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>MasVnrArea</td>\n",
       "      <td>1369.656190</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>ScreenPorch</td>\n",
       "      <td>1037.556490</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>BsmtHalfBath</td>\n",
       "      <td>941.567474</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>LotArea</td>\n",
       "      <td>755.553479</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>TotalBsmtSF</td>\n",
       "      <td>529.114514</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>FullBath</td>\n",
       "      <td>372.492401</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>EnclosedPorch</td>\n",
       "      <td>225.677087</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>MSSubClass</td>\n",
       "      <td>2.323880</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Features  Estimated_Coefficients\n",
       "33        MiscVal            21298.626224\n",
       "16   BsmtFullBath            15327.722992\n",
       "14   LowQualFinSF            14026.806738\n",
       "4     OverallCond            10836.631181\n",
       "6    YearRemodAdd            10465.033786\n",
       "3     OverallQual             8831.872085\n",
       "12       1stFlrSF             8304.026483\n",
       "9      BsmtFinSF2             6891.937360\n",
       "5       YearBuilt             6805.543499\n",
       "13       2ndFlrSF             5140.709475\n",
       "27     WoodDeckSF             4823.832482\n",
       "8      BsmtFinSF1             3535.074438\n",
       "28    OpenPorchSF             3125.151412\n",
       "26     GarageArea             2897.478249\n",
       "24    GarageYrBlt             2809.293658\n",
       "23     Fireplaces             2693.727114\n",
       "19       HalfBath             2075.125328\n",
       "10      BsmtUnfSF             1647.806470\n",
       "32       PoolArea             1643.702738\n",
       "7      MasVnrArea             1369.656190\n",
       "31    ScreenPorch             1037.556490\n",
       "17   BsmtHalfBath              941.567474\n",
       "2         LotArea              755.553479\n",
       "11    TotalBsmtSF              529.114514\n",
       "18       FullBath              372.492401\n",
       "29  EnclosedPorch              225.677087\n",
       "0      MSSubClass                2.323880"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pos_coeffs_df= coeffs_df[(coeffs_df['Estimated_Coefficients'] >= 0)].sort_values(by='Estimated_Coefficients', ascending=False)\n",
    "#pos_coeffs_df.sort_values(by='Estimated_Coefficients', ascending=False)\n",
    "pos_coeffs_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Features</th>\n",
       "      <th>Estimated_Coefficients</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>TotRmsAbvGrd</td>\n",
       "      <td>-3429.718480</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>KitchenAbvGr</td>\n",
       "      <td>-2904.693587</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>GarageCars</td>\n",
       "      <td>-1489.893249</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>GrLivArea</td>\n",
       "      <td>-1152.076289</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>YrSold</td>\n",
       "      <td>-1136.824685</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>LotFrontage</td>\n",
       "      <td>-626.091765</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>BedroomAbvGr</td>\n",
       "      <td>-217.771808</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>3SsnPorch</td>\n",
       "      <td>-158.479333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>MoSold</td>\n",
       "      <td>-81.729301</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Features  Estimated_Coefficients\n",
       "22  TotRmsAbvGrd            -3429.718480\n",
       "21  KitchenAbvGr            -2904.693587\n",
       "25    GarageCars            -1489.893249\n",
       "15     GrLivArea            -1152.076289\n",
       "35        YrSold            -1136.824685\n",
       "1    LotFrontage             -626.091765\n",
       "20  BedroomAbvGr             -217.771808\n",
       "30     3SsnPorch             -158.479333\n",
       "34        MoSold              -81.729301"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "neg_coeffs_df = coeffs_df[(coeffs_df['Estimated_Coefficients'] < 0)].sort_values(by='Estimated_Coefficients', ascending = True)\n",
    "neg_coeffs_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Features like MiscVal, BsmtFullBath, LowQualFinSF, OverallCond, YearRemodAdd have linear correlation with Sale Price\n",
    "- According to the analysis above total number of rooms and kitchen above grade (above basement), garage area and year sold have negative correlation with Sale Price. \n",
    "- This is quite surprising as to why would total number of rooms above ground and garage area have negative correlation with the Sale Price"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Regression Plot**\n",
    "\n",
    "Let us draw a regression plot between the test target values and predicted test values to assess how the model is performing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x175d3c0bda0>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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0gX3EgROPWsyp0sVhS9rK2kcORnLGqaZWo/xnReQPMNHoaeAbqvqTho7MYrHM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\nJhQWUIwxxoTi/wFAdpWRieTdugAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x175d3184358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "g = sns.regplot(x=lm.predict(X_test), y=Y_test, fit_reg=True)\n",
    "g.set(xlabel='Predicted House Prices($)', ylabel='Actual House Prices($)', title='Model Predictions')\n",
    "plt.title('Regression Plot for Actual vs Predicted Values')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the graph above the model seems to be a good fit for the data, except for a few outliers in the houses highly priced."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us calcualte $R^2$ and RMSE (Root Mean Square Error) for the train and test sets to further assess the model.\n",
    "\n",
    "$R^2$: It is the percentage of the response variable variation that is explained by a linear model\n",
    "\n",
    "RMSE: It is the square root of the mean of squared errors. Squared errors are the difference of actual and predicted values sqaured."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R squared for train data is: 0.936\n",
      "R squared for test data is: 0.843\n"
     ]
    }
   ],
   "source": [
    "# R2 for train and test data\n",
    "R2_reg_train = lm.score(X_train,Y_train)\n",
    "R2_reg_test = lm.score(X_test,Y_test)\n",
    "print('R squared for train data is: %.3f' %(R2_reg_train))\n",
    "print('R squared for test data is: %.3f' %(R2_reg_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- The train set explains more varaince (93.6%) than the test set (84.3%). This is quite common because the model is trained on training data, training set's $R^2$ is always greater than the test set's $R^2$.\n",
    "- An $R^2$ of 0.843 is a good score to start with. \n",
    "- Since the train score is more than test score, let us see if it is a case of Overfitting by plotting a Residual Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Root mean squared error for train data is: 20426.160\n",
      "Root mean sqaured error for test data is: 30352.931\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt\n",
    "RMSE_reg_train = sqrt(np.mean((Y_train - lm.predict(X_train))**2))\n",
    "RMSE_reg_test = sqrt(np.mean((Y_test - lm.predict(X_test))**2))\n",
    "print('Root mean squared error for train data is: %.3f' %(RMSE_reg_train))\n",
    "print('Root mean sqaured error for test data is: %.3f' %(RMSE_reg_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Residual Plots**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x175d3cf0c18>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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yDvv64zzbO4qFRTQSyK8n81m9vDVvobRGQ/QNJehNZrBti3AoQGs0NGlo+8uO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\n2lxvVgUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x175d3c03f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.residplot(x=lm.predict(X_train), y=Y_train, lowess=True)\n",
    "plt.title('Residual Plot using train data')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Residual plot for the training data shows that the data points lie between \\$-50,000 to \\$50,000. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x175d3da3278>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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q2CRT1XRwnd89x0e9PQHmNEJx3dVN8Yo85iQgvP/RA5MmQSj0CRw4HueZlwZY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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x175d3d43c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.residplot(x=lm.predict(X_test), y=Y_test, lowess=True)\n",
    "plt.title('Residual Plot using test data')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Test data is also showing the same range from the reference line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x175d3e257f0>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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fGzbaQtauNB+1bNvfavmkBvGzvPI31D/8GqCzezfIpk3sm/6fBJOsXWH19j1s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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x175d3c7aa58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(lm.predict(X_train), lm.predict(X_train) - Y_train, c='b', s=40, alpha=0.5)\n",
    "plt.scatter(lm.predict(X_test), lm.predict(X_test) - Y_test, c='g', s=40)\n",
    "plt.hlines(y = 0, xmin=0, xmax = 50)\n",
    "plt.title('Residual Plot using training (blue) and test (green) data')\n",
    "plt.ylabel('Residuals')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The blue dots represent train data and grren dots represent test data. From the residual plot above it is evident that the model is a good fit for test data as well. The data lies between +/- \\$50,000 from the reference line. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Analysis:** \n",
    "- The regression line appears to be a **good fit for the data**.\n",
    "- The train and test scores not being too different form each other, indiactes that there is **no Overfitting**.\n",
    "- The distribution of test and train data looks similar in the residual plot, which says that there is **no big difference in residuals**. And the data is spread around -50,000 and 50,000. \n",
    "- In terms of the actual problem we can infer that there might be a difference of \\$50,000 for every house if important features like Aminities, Full bath in basement, Quality of finished square footage, Overall condition and quality of the house, Remodel date etc. \n",
    "- This seems to be relevant in the real world scenario in real estate market. For example the difference between a basement house and a non-basement house is \\$50,000. Similarly an increase in number of bedrooms/ bathrooms/ square footage can increase the price of the house by \\$30,000 - \\$40,000.\n",
    "- Clearly the **important features** that control the house price are the **Condition, Square footage(basement, 1st & 2nd floors), Garage area, Year built/remodeled**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regularization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With as many as 306 features in the model it is natural for the model to get quite complex. The model sticks too much to the data and the model has probably learned the background noise which results in high variance while being fit, which leads to **Overfitting**. This results in poor prediction and generalization power when applied o data outside the training set. To overcome this problem **regularization technique** is used. \n",
    "\n",
    "To find the best model, the common method in machine learning is to define a loss or cost function that describes how well the model fits the data. The goal is to find the model that minimzes this loss function. The idea is to penalize this loss function by adding a complexity term that would give a bigger loss for more complex models. \n",
    "\n",
    "**Regularization** allows to shrink the coefficients to zero by introducing a tuning parameter **'lambda'** or **'alpha'**. This ensures:\n",
    "- Shrinking of parameters, therefore it is mostly used to prevent multicollinearity.\n",
    "- Reduces the model complexity by coefficient shrinkage."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The two popular methods used to regularize parameters are:\n",
    "- Ridge Regression\n",
    "- Lasso Regression\n",
    "\n",
    "**Ridge Regression:** Ridge regression uses L2 penalty to penalize coefficients. L2 penalty is the penalty equivalent to **square of the magnitude of coefficients** \n",
    "\n",
    "**Lasso Regression:** Lasso regression uses L1 penalty which is the **absolute value of the magnitude of coefficients**\n",
    "\n",
    "Let us apply Ridge and Lasso models to our data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**1. Ridge Regression**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RidgeCV(alphas=[1e-15, 1e-10, 1e-08, 1e-05, 0.0001, 0.001, 0.01, 1, 5, 10],\n",
       "    cv=None, fit_intercept=True, gcv_mode=None, normalize=False,\n",
       "    scoring=None, store_cv_values=True)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Define the alphas \n",
    "alphas = [1e-15, 1e-10, 1e-8, 1e-5,1e-4, 1e-3,1e-2, 1, 5, 10]\n",
    "# Create an object for RidgeCV\n",
    "ridge_reg = RidgeCV(alphas=alphas, cv=None, store_cv_values=True)\n",
    "# Fit the model to our training data\n",
    "ridge_reg.fit(X_train,Y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us calculate the $R^2$ on both train and test sets to assess the performance of our model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R squared for train data is: 0.898\n",
      "R squared for test data is: 0.887\n"
     ]
    }
   ],
   "source": [
    "# R2 for train and test data respectively\n",
    "R2_ridge_train = (ridge_reg.score(X_train, Y_train))\n",
    "R2_ridge_test = (ridge_reg.score(X_test,Y_test))\n",
    "print('R squared for train data is: %.3f' %(R2_ridge_train))\n",
    "print('R squared for test data is: %.3f' %(R2_ridge_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- The **train set** explains obtained an $R^2$ of **0.898** and **test set** got an $R^2$ of **0.887**.\n",
    "- There is very little difference between train and test set, this signifies that the **model is a good fit for data**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us calculate the RMSE values for train and test data sets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Root mean squared error for train data is: 25725.420\n",
      "Root mean sqaured error for test data is: 25777.429\n"
     ]
    }
   ],
   "source": [
    "RMSE_ridge_train = sqrt(np.mean((Y_train - ridge_reg.predict(X_train))**2))\n",
    "RMSE_ridge_test = sqrt(np.mean((Y_test - ridge_reg.predict(X_test))**2))\n",
    "print('Root mean squared error for train data is: %.3f' %(RMSE_ridge_train))\n",
    "print('Root mean sqaured error for test data is: %.3f' %(RMSE_ridge_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us see the best alpha parameter for Ridge Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The estimated best regularization parameter is: 10.0\n"
     ]
    }
   ],
   "source": [
    "alpha_ridge_cv = ridge_reg.alpha_\n",
    "print('The estimated best regularization parameter is: %.1f' %(alpha_ridge_cv))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Regression Plot**\n",
    "\n",
    "Let us draw a regression plot between the actual and predicted house prices to see how well the regresssion line fits tha data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x175d3eef390>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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H6z1Bi8Vy6NSjnEit6drRx91rXyqIhNrRPcyP1r7Eh644ser5V+MzKlUEctVp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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x175d3d857b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Regression plot between actual and predicted prices \n",
    "g = sns.regplot(x=ridge_reg.predict(X_test), y=Y_test, fit_reg=True)\n",
    "g.set(xlabel='Predicted House Prices($)', ylabel='Actual House Prices($)', title='Model Predictions')\n",
    "plt.title('Regression Plot for Actual vs Predicted Values')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The regression line looks like a good fit to the data, except for a few outliers in the higher house price range."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Residual Plots**\n",
    "\n",
    "To drill down further let us plot some residual plots which helps giving better idea about the data. I decided to plot residual plots for train and test data seperately and another plot depicting train and test data points to get a better visual on data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_Residual Plot - Train data_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x175d4c6a4a8>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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3JGMMjGTMujnXDC8UTIWKSAVLNeh286yflkSUSDpvivNi+u4xXSZhNVZgpQXK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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x175d3cd9a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.residplot(x=ridge_reg.predict(X_train), y=Y_train, lowess=True)\n",
    "plt.title('Residual Plot for train data')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The data seems to be close to the reference line (at 0). The data is spread around $-50,000 to $50,000 which is quite normal in real estate market."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_Residual Plot - Test data_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x175d4d01ac8>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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HASylIrIttVnO5YtEwzOvV8uJoHJ72r/2QlUcvV0x9h1MMJbMks2XltHN5gqY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\nzMwsF04oZmaWCycUMzPLhROKmZnl4j+3WX/FNe8LMQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x175d3191080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.residplot(x=ridge_reg.predict(X_test), y=Y_test, lowess=True)\n",
    "plt.title('Residual Plot for test data')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The residual plot for test data looks similar to the train data which is a good sign. We can see that the major percent of data lies within teh $-50,000 and $50,000 range which is the same as train data. Except for that there are a few outliers which is natural when the model is exposed to data outside the training data set."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_Residual Plot - Train and Test data_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x175d4d7ab00>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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PpdSXMIF4w0IMQSxEQRAEQQAOn6AaQRAEQRhURBAFQRAEARlD7EZ1dUO/fch5eenU1CQK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\niTFvXg/xeGzAhSSDLc568KX7+fxTf04P3eFfe20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      "text/plain": [
       "<matplotlib.figure.Figure at 0x175d3ee3470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(ridge_reg.predict(X_train), ridge_reg.predict(X_train) - Y_train, c='b', s=40, alpha=0.5)\n",
    "plt.scatter(ridge_reg.predict(X_test), ridge_reg.predict(X_test) - Y_test, c='g', s=40)\n",
    "plt.hlines(y = 0, xmin=0, xmax = 50)\n",
    "plt.title(\"Linear regression with Ridge regularization for train (blue) and test (green) data\")\n",
    "plt.xlabel(\"Predicted values\")\n",
    "plt.ylabel('Residuals')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The residual plot clearly explians how similar the train and test data are in the graph. This tells that the model provides good results on the test data too."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us look at the features and thier respective coefficients to know which features have positive and negative correlation with the target variable 'Sale Price'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Features</th>\n",
       "      <th>Estimated_Coefficients</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>BsmtFullBath</td>\n",
       "      <td>15120.595840</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>OverallCond</td>\n",
       "      <td>14442.505839</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>LowQualFinSF</td>\n",
       "      <td>12992.951015</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>GarageArea</td>\n",
       "      <td>11016.749147</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>2ndFlrSF</td>\n",
       "      <td>5919.494230</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>YearBuilt</td>\n",
       "      <td>5738.125302</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>Fireplaces</td>\n",
       "      <td>5154.235404</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>YearRemodAdd</td>\n",
       "      <td>5140.174280</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>OverallQual</td>\n",
       "      <td>4739.258703</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>HalfBath</td>\n",
       "      <td>4460.987753</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>BsmtHalfBath</td>\n",
       "      <td>4258.125461</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>OpenPorchSF</td>\n",
       "      <td>3331.289186</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>BsmtFinSF1</td>\n",
       "      <td>3279.457636</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>PoolArea</td>\n",
       "      <td>2241.548791</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>MiscVal</td>\n",
       "      <td>2237.119868</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>GarageYrBlt</td>\n",
       "      <td>1690.313745</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>ScreenPorch</td>\n",
       "      <td>1380.682623</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>3SsnPorch</td>\n",
       "      <td>713.788881</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>MasVnrArea</td>\n",
       "      <td>677.913643</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>BsmtUnfSF</td>\n",
       "      <td>632.540829</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>FullBath</td>\n",
       "      <td>555.760891</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>BedroomAbvGr</td>\n",
       "      <td>474.263996</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>TotalBsmtSF</td>\n",
       "      <td>29.327799</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>MSSubClass</td>\n",
       "      <td>0.184199</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>MoSold</td>\n",
       "      <td>-74.194003</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>GrLivArea</td>\n",
       "      <td>-300.679614</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>EnclosedPorch</td>\n",
       "      <td>-306.981433</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>YrSold</td>\n",
       "      <td>-527.354429</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>WoodDeckSF</td>\n",
       "      <td>-593.196962</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>GarageCars</td>\n",
       "      <td>-972.311277</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1stFlrSF</td>\n",
       "      <td>-1609.154838</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>BsmtFinSF2</td>\n",
       "      <td>-1799.930374</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>KitchenAbvGr</td>\n",
       "      <td>-2447.693972</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>TotRmsAbvGrd</td>\n",
       "      <td>-2784.507511</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>LotArea</td>\n",
       "      <td>-3161.394589</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>LotFrontage</td>\n",
       "      <td>-6482.443966</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Features  Estimated_Coefficients\n",
       "16   BsmtFullBath            15120.595840\n",
       "4     OverallCond            14442.505839\n",
       "14   LowQualFinSF            12992.951015\n",
       "26     GarageArea            11016.749147\n",
       "13       2ndFlrSF             5919.494230\n",
       "5       YearBuilt             5738.125302\n",
       "23     Fireplaces             5154.235404\n",
       "6    YearRemodAdd             5140.174280\n",
       "3     OverallQual             4739.258703\n",
       "19       HalfBath             4460.987753\n",
       "17   BsmtHalfBath             4258.125461\n",
       "28    OpenPorchSF             3331.289186\n",
       "8      BsmtFinSF1             3279.457636\n",
       "32       PoolArea             2241.548791\n",
       "33        MiscVal             2237.119868\n",
       "24    GarageYrBlt             1690.313745\n",
       "31    ScreenPorch             1380.682623\n",
       "30      3SsnPorch              713.788881\n",
       "7      MasVnrArea              677.913643\n",
       "10      BsmtUnfSF              632.540829\n",
       "18       FullBath              555.760891\n",
       "20   BedroomAbvGr              474.263996\n",
       "11    TotalBsmtSF               29.327799\n",
       "0      MSSubClass                0.184199\n",
       "34         MoSold              -74.194003\n",
       "15      GrLivArea             -300.679614\n",
       "29  EnclosedPorch             -306.981433\n",
       "35         YrSold             -527.354429\n",
       "27     WoodDeckSF             -593.196962\n",
       "25     GarageCars             -972.311277\n",
       "12       1stFlrSF            -1609.154838\n",
       "9      BsmtFinSF2            -1799.930374\n",
       "21   KitchenAbvGr            -2447.693972\n",
       "22   TotRmsAbvGrd            -2784.507511\n",
       "2         LotArea            -3161.394589\n",
       "1     LotFrontage            -6482.443966"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Features and thier respective coefficients\n",
    "ridge_coeffs_df = pd.DataFrame(list(zip(X.columns, ridge_reg.coef_)), columns = ['Features', 'Estimated_Coefficients'])\n",
    "ridge_coeffs_df.sort_values(by='Estimated_Coefficients', ascending=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us look a the positive and negative coefficients seperately"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Features</th>\n",
       "      <th>Estimated_Coefficients</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>BsmtFullBath</td>\n",
       "      <td>15120.595840</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>OverallCond</td>\n",
       "      <td>14442.505839</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>LowQualFinSF</td>\n",
       "      <td>12992.951015</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>GarageArea</td>\n",
       "      <td>11016.749147</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>2ndFlrSF</td>\n",
       "      <td>5919.494230</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>YearBuilt</td>\n",
       "      <td>5738.125302</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>Fireplaces</td>\n",
       "      <td>5154.235404</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>YearRemodAdd</td>\n",
       "      <td>5140.174280</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>OverallQual</td>\n",
       "      <td>4739.258703</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>HalfBath</td>\n",
       "      <td>4460.987753</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>BsmtHalfBath</td>\n",
       "      <td>4258.125461</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>OpenPorchSF</td>\n",
       "      <td>3331.289186</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>BsmtFinSF1</td>\n",
       "      <td>3279.457636</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>PoolArea</td>\n",
       "      <td>2241.548791</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>MiscVal</td>\n",
       "      <td>2237.119868</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>GarageYrBlt</td>\n",
       "      <td>1690.313745</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>ScreenPorch</td>\n",
       "      <td>1380.682623</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>3SsnPorch</td>\n",
       "      <td>713.788881</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>MasVnrArea</td>\n",
       "      <td>677.913643</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>BsmtUnfSF</td>\n",
       "      <td>632.540829</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>FullBath</td>\n",
       "      <td>555.760891</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>BedroomAbvGr</td>\n",
       "      <td>474.263996</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>TotalBsmtSF</td>\n",
       "      <td>29.327799</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>MSSubClass</td>\n",
       "      <td>0.184199</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Features  Estimated_Coefficients\n",
       "16  BsmtFullBath            15120.595840\n",
       "4    OverallCond            14442.505839\n",
       "14  LowQualFinSF            12992.951015\n",
       "26    GarageArea            11016.749147\n",
       "13      2ndFlrSF             5919.494230\n",
       "5      YearBuilt             5738.125302\n",
       "23    Fireplaces             5154.235404\n",
       "6   YearRemodAdd             5140.174280\n",
       "3    OverallQual             4739.258703\n",
       "19      HalfBath             4460.987753\n",
       "17  BsmtHalfBath             4258.125461\n",
       "28   OpenPorchSF             3331.289186\n",
       "8     BsmtFinSF1             3279.457636\n",
       "32      PoolArea             2241.548791\n",
       "33       MiscVal             2237.119868\n",
       "24   GarageYrBlt             1690.313745\n",
       "31   ScreenPorch             1380.682623\n",
       "30     3SsnPorch              713.788881\n",
       "7     MasVnrArea              677.913643\n",
       "10     BsmtUnfSF              632.540829\n",
       "18      FullBath              555.760891\n",
       "20  BedroomAbvGr              474.263996\n",
       "11   TotalBsmtSF               29.327799\n",
       "0     MSSubClass                0.184199"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ridge_pos_coeffs_df = ridge_coeffs_df[(ridge_coeffs_df['Estimated_Coefficients'])>=0].sort_values(by='Estimated_Coefficients', ascending=False)\n",
    "ridge_pos_coeffs_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Let us look at the top five important coefficients having linear correlation with the target variable 'Sale Price'. \n",
    "- **BsmtFullBath, OverallCond, LowQualFinSF, GarageArea, 2ndFlrSF** in Ridge Regression are different from the positive coefficients (MiscVal, BsmtFullBath, LowQualFinSF, OverallCond, YearRemodAdd) produced in Multiple Linear Regression.\n",
    "- This analysis says that aminities and year remodeled are not very important anymore.\n",
    "- Therefore we can conclude that a full bath in basement, overall condition of the house and low quality square footage are the most consistent correalted features to boast the Sale price of the house."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Features</th>\n",
       "      <th>Estimated_Coefficients</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>LotFrontage</td>\n",
       "      <td>-6482.443966</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>LotArea</td>\n",
       "      <td>-3161.394589</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>TotRmsAbvGrd</td>\n",
       "      <td>-2784.507511</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>KitchenAbvGr</td>\n",
       "      <td>-2447.693972</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>BsmtFinSF2</td>\n",
       "      <td>-1799.930374</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1stFlrSF</td>\n",
       "      <td>-1609.154838</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>GarageCars</td>\n",
       "      <td>-972.311277</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>WoodDeckSF</td>\n",
       "      <td>-593.196962</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>YrSold</td>\n",
       "      <td>-527.354429</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>EnclosedPorch</td>\n",
       "      <td>-306.981433</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>GrLivArea</td>\n",
       "      <td>-300.679614</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>MoSold</td>\n",
       "      <td>-74.194003</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Features  Estimated_Coefficients\n",
       "1     LotFrontage            -6482.443966\n",
       "2         LotArea            -3161.394589\n",
       "22   TotRmsAbvGrd            -2784.507511\n",
       "21   KitchenAbvGr            -2447.693972\n",
       "9      BsmtFinSF2            -1799.930374\n",
       "12       1stFlrSF            -1609.154838\n",
       "25     GarageCars             -972.311277\n",
       "27     WoodDeckSF             -593.196962\n",
       "35         YrSold             -527.354429\n",
       "29  EnclosedPorch             -306.981433\n",
       "15      GrLivArea             -300.679614\n",
       "34         MoSold              -74.194003"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ridge_neg_coeffs_df = ridge_coeffs_df[(ridge_coeffs_df['Estimated_Coefficients'])<0].sort_values(by='Estimated_Coefficients',ascending = True)\n",
    "ridge_neg_coeffs_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let us look at the negative coefficients. We can clearly see that Lot Frontage (front yard of the house) is now the most negatively correlated feature to the Sale Price.\n",
    "\n",
    "Therefore we can say that if the front yard is more (probably more than back yard), number of rooms above ground is more then the Sale Price will decrease.\n",
    "\n",
    "I strongly believe that Kitchen above ground (according to our data above basement) might not really mean above basement because everyone prefers kitchen in the ground floor. This will hold right for houses without basement and the kitchen is above the ground i.e. on the 1st floor. This ideally would decrease the house price.\n",
    "\n",
    "The other features that decrease house price are Lot area, total rooms above ground and Basement (type 2) finished area. \n",
    "\n",
    "Note: Basement (type 2) - If a house has more than one basement."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Cross Validation**\n",
    "\n",
    "When evaluating different hyperparameters for estimators, such as the alpha is this setting that must be manually set for an Ridge, there is still a risk of overfitting on the test set because the parameters can be tweaked until the estimator performs optimally. This way, knowledge about the test set can “leak” into the model and evaluation metrics no longer report on generalization performance. To solve this problem, yet another part of the dataset can be held out as a so-called “validation set”: training proceeds on the training set, after which evaluation is done on the validation set, and when the experiment seems to be successful, final evaluation can be done on the test set.Even though the model is trained exclusively on the training data, we are optimizing hyperparameters based on the test set. As such, estimate of performance can be optimistic, because we are essentially reporting best-case results.\n",
    "\n",
    "Another way to deal with this is through cross-validation (CV). In CV a test set should still be held out for final evaluation, but the validation set is no longer needed when doing CV. In the basic approach, called k-fold CV, the training set is split into k smaller sets. A model is trained using k-1 of the folds as training data; the resulting model is validated on the remaining part of the data (i.e., it is used as a test set to compute a performance measure such as accuracy)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**GridSearchCV**\n",
    "\n",
    "Let us explore the **best hyper parameter (alpha)** and it's respective **score** using **GridSearchCV**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ridge(alpha=1.0, copy_X=True, fit_intercept=True, max_iter=None,\n",
       "   normalize=False, random_state=None, solver='auto', tol=0.001)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create an object of type Ridge()\n",
    "ridge = Ridge()\n",
    "# Fit the model on the trainng data.\n",
    "ridge.fit(X_train, Y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Apply GridSearchCV to Ridge Regression find out the alpha value and respective R square**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best alpha value is: 10\n",
      "Accuracy from alpha = 10: 0.872876954748 \n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Import library to find out score (R2)\n",
    "from sklearn.metrics import r2_score\n",
    "\n",
    "# Define an array of alpha values\n",
    "alphas = [1e-15, 1e-10, 1e-8, 1e-5,1e-4, 1e-3,1e-2, 1, 5, 10]\n",
    "\n",
    "# Define GridSearchCV \n",
    "ridge_grid = GridSearchCV(estimator=ridge, param_grid = dict(alpha=alphas), scoring = 'r2')\n",
    "\n",
    "# Fit the training model \n",
    "ridge_grid.fit(X_train, Y_train)\n",
    "\n",
    "# Get the best alpha value and it's respective R2 score\n",
    "print(\"Best alpha value is: %s\" % ridge_grid.best_params_[\"alpha\"])\n",
    "print(\"Accuracy from alpha = %s: %s \\n\" % (ridge_grid.best_params_[\"alpha\"],r2_score(ridge_grid.predict(X_test), Y_test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us compare the R2 scores for train and test data using GridSearchCV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R squared for train data is: 0.882\n",
      "R squared for test data is: 0.873\n"
     ]
    }
   ],
   "source": [
    "R2_ridge_grid_train = r2_score(ridge_grid.predict(X_train), Y_train)\n",
    "R2_ridge_grid_test = r2_score(ridge_grid.predict(X_test), Y_test)\n",
    "print('R squared for train data is: %.3f' %(R2_ridge_grid_train))\n",
    "print('R squared for test data is: %.3f' %(R2_ridge_grid_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Let us repeat the same process to find out RMSE values for train and test data sets**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best alpha value is: 10\n",
      "Accuracy from alpha = 10: 25777.428925228076 \n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Import library to find out score MSE\n",
    "from sklearn.metrics import mean_squared_error\n",
    "\n",
    "# Define an array of alpha values\n",
    "alphas = [1e-15, 1e-10, 1e-8, 1e-5,1e-4, 1e-3,1e-2, 1, 5, 10]\n",
    "\n",
    "# Define GridSearchCV \n",
    "ridge_grid = GridSearchCV(estimator=ridge, param_grid = dict(alpha=alphas), scoring = 'neg_mean_squared_error')\n",
    "\n",
    "# Fit the training model \n",
    "ridge_grid.fit(X_train, Y_train)\n",
    "\n",
    "# Get the best alpha value and it's respective RMSE score\n",
    "print(\"Best alpha value is: %s\" % ridge_grid.best_params_[\"alpha\"])\n",
    "print(\"Accuracy from alpha = %s: %s \\n\" % (ridge_grid.best_params_[\"alpha\"],\n",
    "                                           sqrt(mean_squared_error(ridge_grid.predict(X_test), Y_test))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us compare the RMSE scores for train and test data using GridSearchCV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Root mean squared error for train data is: 25725.420\n",
      "Root mean sqaured error for test data is: 25777.429\n"
     ]
    }
   ],
   "source": [
    "RMSE_ridge_grid_train = sqrt(mean_squared_error(ridge_grid.predict(X_train), Y_train))\n",
    "RMSE_ridge_grid_test = sqrt(mean_squared_error(ridge_grid.predict(X_test), Y_test))\n",
    "print('Root mean squared error for train data is: %.3f' %(RMSE_ridge_grid_train))\n",
    "print('Root mean sqaured error for test data is: %.3f' %(RMSE_ridge_grid_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**We can conclude that the best alpha value is 10 for Ridge Regression**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**2. Lasso Regression**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LassoCV(alphas=[1e-15, 1e-10, 1e-08, 1e-05, 0.0001, 0.001, 0.01, 1, 5, 10],\n",
       "    copy_X=True, cv=None, eps=0.001, fit_intercept=True, max_iter=50000,\n",
       "    n_alphas=100, n_jobs=1, normalize=False, positive=False,\n",
       "    precompute='auto', random_state=None, selection='random', tol=0.1,\n",
       "    verbose=False)"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Define the alphas \n",
    "alphas = [1e-15, 1e-10, 1e-8, 1e-5,1e-4, 1e-3,1e-2, 1, 5, 10]\n",
    "# Create an object for LassoCV\n",
    "lasso_reg = LassoCV(alphas=alphas, cv=None, max_iter=50000, tol=0.1,selection='random')\n",
    "# Fit the model to our training data\n",
    "lasso_reg.fit(X_train,Y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us calculate the $R^2$ on both train and test sets to assess the performance of our model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R squared for train data is: 0.921\n",
      "R squared for test data is: 0.867\n"
     ]
    }
   ],
   "source": [
    "# R2 for train and test data respectively\n",
    "R2_train = (lasso_reg.score(X_train, Y_train))\n",
    "R2_test = (lasso_reg.score(X_test,Y_test))\n",
    "print('R squared for train data is: %.3f' %(R2_train))\n",
    "print('R squared for test data is: %.3f' %(R2_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- The train set explains obtained an $R^2$ of 0.91 and test set got an $R^2$ of 0.86.\n",
    "- There is not a huge difference between train and test set, this signifies that the model is a good fit for data, because it performed well when exposed outside of the training data ."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let us calculate the RMSE scores for train and test data sets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Root mean squared error for train data is: 22601.017\n",
      "Root mean sqaured error for test data is: 27918.355\n"
     ]
    }
   ],
   "source": [
    "RMSE_train = sqrt(np.mean((Y_train - lasso_reg.predict(X_train))**2))\n",
    "RMSE_test = sqrt(np.mean((Y_test - lasso_reg.predict(X_test))**2))\n",
    "print('Root mean squared error for train data is: %.3f' %(RMSE_train))\n",
    "print('Root mean sqaured error for test data is: %.3f' %(RMSE_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us see the best alpha parameter for Lasso Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The estimated best regularization parameter is: 1.0\n"
     ]
    }
   ],
   "source": [
    "alpha_lasso_cv = lasso_reg.alpha_\n",
    "print('The estimated best regularization parameter is: %.1f' %(alpha_lasso_cv))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Regression Plot**\n",
    "\n",
    "Let us plot a regression plot to see how good of a fit is our regression line on the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x175d4e50e10>"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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xWOrOeCPRKh0fT2YYjKdH9CE5kB7twYBDUyRELDL5fdmnM7UKlFdE5DeYJlsF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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x175d3e91cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Regression plot\n",
    "g = sns.regplot(x=lasso_reg.predict(X_test), y=Y_test, fit_reg=True)\n",
    "g.set(xlabel='Predicted House Prices($)', ylabel='Actual House Prices($)', title='Model Predictions')\n",
    "plt.title('Regression Plot for Actual vs Predicted Values')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is quite evident that the regression line is a good fit to our data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Residual Plots**\n",
    "\n",
    "I plotted residual graphs for train, test seperatley and together using lasso regression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x175d4ef0208>"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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xyvELsxA2ieRDwsMwYWh0CsM0cF2XnUOT5PMOpmkUijSWMxs1G8s0SWfzTGXy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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x175d4e1dac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.residplot(x=lasso_reg.predict(X_train), y=Y_train, lowess=True)\n",
    "plt.title('Residual Plot for train data')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The graph looks very much similar to what was produced by Linear Regression and Ridge Regression. The data lies within the -50,000 to +50,000 range where most of the data lies close to the reference line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x175d4f8b748>"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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GBgZl23bfi5hB6LFd5ZYxDDANSE8WiEetmk7vWkrXf74Hj6dJZ4u8eGqSPftP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\nQYmIiCJ+B+8tzW8axVnMAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x175d4d91518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.residplot(x=lasso_reg.predict(X_test), y=Y_test, lowess=True)\n",
    "plt.title('Residual Plot for test data')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The data points are scattered around the reference line. There are few outliers, but most of the data lies with the expected -50,000 to +50,000 range."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x175d500d668>"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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qi1Gj0SSGVogazTCgutq+SEis7RqNJhqtEDWaYUBOjr1bNNZ2jUYTjVaIGs0wYM6cAIYR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\nqsHT/zHvAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x175d4f09be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(lasso_reg.predict(X_train), lasso_reg.predict(X_train) - Y_train, c='b', s=40, alpha=0.5)\n",
    "plt.scatter(lasso_reg.predict(X_test), lasso_reg.predict(X_test) - Y_test, c='g', s=40)\n",
    "plt.hlines(y = 0, xmin=0, xmax = 50)\n",
    "plt.title(\"Linear regression with Lasso regularization for train (blue) and test (green) data\")\n",
    "plt.xlabel(\"Predicted values\")\n",
    "plt.ylabel('Residuals')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the graph the train and test data points are close to each other indicating that the model is performing well on the test data too."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us see what coefficients does lasso regression produce and what are the top features that influence Sale price."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Features</th>\n",
       "      <th>Estimated_Coefficients</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>HalfBath</td>\n",
       "      <td>12257.749663</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>GarageArea</td>\n",
       "      <td>9637.046639</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>BsmtFullBath</td>\n",
       "      <td>8347.376447</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>2ndFlrSF</td>\n",
       "      <td>7509.885582</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>LowQualFinSF</td>\n",
       "      <td>6219.155272</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>YearBuilt</td>\n",
       "      <td>5698.332002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>OverallCond</td>\n",
       "      <td>5376.383932</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>BsmtHalfBath</td>\n",
       "      <td>5058.892694</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>BedroomAbvGr</td>\n",
       "      <td>4574.551094</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>BsmtFinSF2</td>\n",
       "      <td>4085.738278</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>OverallQual</td>\n",
       "      <td>3970.225522</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>TotalBsmtSF</td>\n",
       "      <td>3772.358902</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>GarageYrBlt</td>\n",
       "      <td>3228.225300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>BsmtFinSF1</td>\n",
       "      <td>2978.065283</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>OpenPorchSF</td>\n",
       "      <td>2636.816178</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>BsmtUnfSF</td>\n",
       "      <td>2317.302220</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>WoodDeckSF</td>\n",
       "      <td>2299.773118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>YearRemodAdd</td>\n",
       "      <td>2287.650942</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>MasVnrArea</td>\n",
       "      <td>2038.752834</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1stFlrSF</td>\n",
       "      <td>1894.039212</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>Fireplaces</td>\n",
       "      <td>1551.596928</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>FullBath</td>\n",
       "      <td>1353.617090</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>PoolArea</td>\n",
       "      <td>1311.010698</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>ScreenPorch</td>\n",
       "      <td>1277.153378</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>MiscVal</td>\n",
       "      <td>1022.521461</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>EnclosedPorch</td>\n",
       "      <td>642.996536</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>KitchenAbvGr</td>\n",
       "      <td>101.026281</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>MSSubClass</td>\n",
       "      <td>0.896198</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>MoSold</td>\n",
       "      <td>-149.921255</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>LotArea</td>\n",
       "      <td>-434.246254</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>LotFrontage</td>\n",
       "      <td>-756.093902</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>3SsnPorch</td>\n",
       "      <td>-779.645607</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>GrLivArea</td>\n",
       "      <td>-876.877432</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>YrSold</td>\n",
       "      <td>-1609.666610</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>GarageCars</td>\n",
       "      <td>-2887.161782</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>TotRmsAbvGrd</td>\n",
       "      <td>-5632.808442</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Features  Estimated_Coefficients\n",
       "19       HalfBath            12257.749663\n",
       "26     GarageArea             9637.046639\n",
       "16   BsmtFullBath             8347.376447\n",
       "13       2ndFlrSF             7509.885582\n",
       "14   LowQualFinSF             6219.155272\n",
       "5       YearBuilt             5698.332002\n",
       "4     OverallCond             5376.383932\n",
       "17   BsmtHalfBath             5058.892694\n",
       "20   BedroomAbvGr             4574.551094\n",
       "9      BsmtFinSF2             4085.738278\n",
       "3     OverallQual             3970.225522\n",
       "11    TotalBsmtSF             3772.358902\n",
       "24    GarageYrBlt             3228.225300\n",
       "8      BsmtFinSF1             2978.065283\n",
       "28    OpenPorchSF             2636.816178\n",
       "10      BsmtUnfSF             2317.302220\n",
       "27     WoodDeckSF             2299.773118\n",
       "6    YearRemodAdd             2287.650942\n",
       "7      MasVnrArea             2038.752834\n",
       "12       1stFlrSF             1894.039212\n",
       "23     Fireplaces             1551.596928\n",
       "18       FullBath             1353.617090\n",
       "32       PoolArea             1311.010698\n",
       "31    ScreenPorch             1277.153378\n",
       "33        MiscVal             1022.521461\n",
       "29  EnclosedPorch              642.996536\n",
       "21   KitchenAbvGr              101.026281\n",
       "0      MSSubClass                0.896198\n",
       "34         MoSold             -149.921255\n",
       "2         LotArea             -434.246254\n",
       "1     LotFrontage             -756.093902\n",
       "30      3SsnPorch             -779.645607\n",
       "15      GrLivArea             -876.877432\n",
       "35         YrSold            -1609.666610\n",
       "25     GarageCars            -2887.161782\n",
       "22   TotRmsAbvGrd            -5632.808442"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Features and thier respective coefficients\n",
    "lasso_coeffs_df = pd.DataFrame(list(zip(X.columns, lasso_reg.coef_)), columns = ['Features', 'Estimated_Coefficients'])\n",
    "lasso_coeffs_df.sort_values(by='Estimated_Coefficients', ascending=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Features</th>\n",
       "      <th>Estimated_Coefficients</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>HalfBath</td>\n",
       "      <td>12257.749663</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>GarageArea</td>\n",
       "      <td>9637.046639</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>BsmtFullBath</td>\n",
       "      <td>8347.376447</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>2ndFlrSF</td>\n",
       "      <td>7509.885582</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>LowQualFinSF</td>\n",
       "      <td>6219.155272</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>YearBuilt</td>\n",
       "      <td>5698.332002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>OverallCond</td>\n",
       "      <td>5376.383932</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>BsmtHalfBath</td>\n",
       "      <td>5058.892694</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>BedroomAbvGr</td>\n",
       "      <td>4574.551094</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>BsmtFinSF2</td>\n",
       "      <td>4085.738278</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>OverallQual</td>\n",
       "      <td>3970.225522</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>TotalBsmtSF</td>\n",
       "      <td>3772.358902</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>GarageYrBlt</td>\n",
       "      <td>3228.225300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>BsmtFinSF1</td>\n",
       "      <td>2978.065283</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>OpenPorchSF</td>\n",
       "      <td>2636.816178</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>BsmtUnfSF</td>\n",
       "      <td>2317.302220</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>WoodDeckSF</td>\n",
       "      <td>2299.773118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>YearRemodAdd</td>\n",
       "      <td>2287.650942</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>MasVnrArea</td>\n",
       "      <td>2038.752834</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1stFlrSF</td>\n",
       "      <td>1894.039212</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>Fireplaces</td>\n",
       "      <td>1551.596928</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>FullBath</td>\n",
       "      <td>1353.617090</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>PoolArea</td>\n",
       "      <td>1311.010698</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>ScreenPorch</td>\n",
       "      <td>1277.153378</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>MiscVal</td>\n",
       "      <td>1022.521461</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>EnclosedPorch</td>\n",
       "      <td>642.996536</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>KitchenAbvGr</td>\n",
       "      <td>101.026281</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>MSSubClass</td>\n",
       "      <td>0.896198</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Features  Estimated_Coefficients\n",
       "19       HalfBath            12257.749663\n",
       "26     GarageArea             9637.046639\n",
       "16   BsmtFullBath             8347.376447\n",
       "13       2ndFlrSF             7509.885582\n",
       "14   LowQualFinSF             6219.155272\n",
       "5       YearBuilt             5698.332002\n",
       "4     OverallCond             5376.383932\n",
       "17   BsmtHalfBath             5058.892694\n",
       "20   BedroomAbvGr             4574.551094\n",
       "9      BsmtFinSF2             4085.738278\n",
       "3     OverallQual             3970.225522\n",
       "11    TotalBsmtSF             3772.358902\n",
       "24    GarageYrBlt             3228.225300\n",
       "8      BsmtFinSF1             2978.065283\n",
       "28    OpenPorchSF             2636.816178\n",
       "10      BsmtUnfSF             2317.302220\n",
       "27     WoodDeckSF             2299.773118\n",
       "6    YearRemodAdd             2287.650942\n",
       "7      MasVnrArea             2038.752834\n",
       "12       1stFlrSF             1894.039212\n",
       "23     Fireplaces             1551.596928\n",
       "18       FullBath             1353.617090\n",
       "32       PoolArea             1311.010698\n",
       "31    ScreenPorch             1277.153378\n",
       "33        MiscVal             1022.521461\n",
       "29  EnclosedPorch              642.996536\n",
       "21   KitchenAbvGr              101.026281\n",
       "0      MSSubClass                0.896198"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lasso_pos_coeffs_df = lasso_coeffs_df[(lasso_coeffs_df['Estimated_Coefficients'])>=0].sort_values(by='Estimated_Coefficients', ascending=False)\n",
    "lasso_pos_coeffs_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see the features changed from what we saw in Ridge rgression, Lasso results show added new features such as MasVnrArea - type of material used in external of  the house (brick/ stone etc.),  GarageYrBlt - garage biult year. The other features remain same as the other regression models i.e. 2ndFlrSF  LowQualFinSF OverallCond.\n",
    "\n",
    "The results of Lasso regression (MasVnrArea and GarageYrBlt) seem to be unrealistic in real estate market. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Features</th>\n",
       "      <th>Estimated_Coefficients</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>TotRmsAbvGrd</td>\n",
       "      <td>-5632.808442</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>GarageCars</td>\n",
       "      <td>-2887.161782</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>YrSold</td>\n",
       "      <td>-1609.666610</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>GrLivArea</td>\n",
       "      <td>-876.877432</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>3SsnPorch</td>\n",
       "      <td>-779.645607</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>LotFrontage</td>\n",
       "      <td>-756.093902</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>LotArea</td>\n",
       "      <td>-434.246254</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>MoSold</td>\n",
       "      <td>-149.921255</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Features  Estimated_Coefficients\n",
       "22  TotRmsAbvGrd            -5632.808442\n",
       "25    GarageCars            -2887.161782\n",
       "35        YrSold            -1609.666610\n",
       "15     GrLivArea             -876.877432\n",
       "30     3SsnPorch             -779.645607\n",
       "1    LotFrontage             -756.093902\n",
       "2        LotArea             -434.246254\n",
       "34        MoSold             -149.921255"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lasso_neg_coeffs_df = lasso_coeffs_df[(lasso_coeffs_df['Estimated_Coefficients'])<0].sort_values(by='Estimated_Coefficients', ascending=True)\n",
    "lasso_neg_coeffs_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lasso produced slightly differnt results from Ridge with order of features changed and adding features like Fireplaces and Year built."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**GridSearchCV**\n",
    "\n",
    "Let us explore the **best hyper parameter (alpha)** and it's respective **score** using **GridSearchCV**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Lasso(alpha=1.0, copy_X=True, fit_intercept=True, max_iter=50000,\n",
       "   normalize=False, positive=False, precompute=False, random_state=None,\n",
       "   selection='cyclic', tol=0.1, warm_start=False)"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create an object \n",
    "lasso = Lasso(max_iter = 50000, tol=0.1)\n",
    "\n",
    "# Fit the model on the trainng data\n",
    "lasso.fit(X_train, Y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Apply GridSearchCV to Ridge Regression find out the alpha value and respective R square**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best alpha value is: 10\n",
      "Score when alpha = 10: is 0.819865195821 \n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Import library to find out score (R2)\n",
    "from sklearn.metrics import r2_score\n",
    "\n",
    "# Define an array of alpha values\n",
    "alphas = [1e-15, 1e-10, 1e-8, 1e-5,1e-4, 1e-3,1e-2, 1, 5, 10]\n",
    "\n",
    "# Define GridSearchCV \n",
    "lasso_grid = GridSearchCV(estimator = lasso, param_grid = dict(alpha=alphas), scoring='r2')\n",
    "\n",
    "# Fit the training model \n",
    "lasso_grid.fit(X_train, Y_train)\n",
    "\n",
    "# Get the best alpha value and it's respective R2 score\n",
    "print('Best alpha value is: %s' % lasso_grid.best_params_['alpha'])\n",
    "print('Score when alpha = %s: is %s \\n' % (lasso_grid.best_params_['alpha'],r2_score(lasso_grid.predict(X_test), Y_test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us compare the R2 scores for train and test data using GridSearchCV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R squared for train data is: 0.898\n",
      "R squared for test data is: 0.820\n"
     ]
    }
   ],
   "source": [
    "R2_lasso_grid_train = r2_score(lasso_grid.predict(X_train), Y_train)\n",
    "R2_lasso_grid_test = r2_score(lasso_grid.predict(X_test), Y_test)\n",
    "print('R squared for train data is: %.3f' %(R2_lasso_grid_train))\n",
    "print('R squared for test data is: %.3f' %(R2_lasso_grid_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Let's repeat the same using Lasso & GridSearchCV process to find out RMSE values for train and test data sets**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best alpha value is: 10\n",
      "Accuracy from alpha = 10: 33835.537049658975 \n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Import library to find out score MSE\n",
    "from sklearn.metrics import mean_squared_error\n",
    "\n",
    "# Define an array of alpha values\n",
    "alphas = [1e-15, 1e-10, 1e-8, 1e-5,1e-4, 1e-3,1e-2, 1, 5, 10]\n",
    "\n",
    "# Define GridSearchCV \n",
    "lasso_grid = GridSearchCV(estimator = lasso, param_grid = dict(alpha=alphas), scoring='neg_mean_squared_error')\n",
    "\n",
    "# Fit the training model\n",
    "lasso_grid.fit(X_train, Y_train)\n",
    "\n",
    "# Get the best alpha value and it's respective RMSE score\n",
    "print(\"Best alpha value is: %s\" % lasso_grid.best_params_[\"alpha\"])\n",
    "print(\"Accuracy from alpha = %s: %s \\n\" % (lasso_grid.best_params_[\"alpha\"],\n",
    "                                           sqrt(mean_squared_error(lasso_grid.predict(X_test), Y_test))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us compare the RMSE scores for train and test data using GridSearchCV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Root mean squared error for train data is: 25386.622\n",
      "Root mean sqaured error for test data is: 33835.537\n"
     ]
    }
   ],
   "source": [
    "RMSE_lasso_grid_train = sqrt(mean_squared_error(lasso_grid.predict(X_train), Y_train))\n",
    "RMSE_lasso_grid_test = sqrt(mean_squared_error(lasso_grid.predict(X_test), Y_test))\n",
    "print('Root mean squared error for train data is: %.3f' %(RMSE_lasso_grid_train))\n",
    "print('Root mean sqaured error for test data is: %.3f' %(RMSE_lasso_grid_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**We can conclude that the best alpha value is 10 for Lasso Regression**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Comparing the models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us compare all the models and evaluate one model that is best suited to the data, this can be acheived by comparing the scores of train and test sets for each model. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Index</th>\n",
       "      <th>RMSE_train</th>\n",
       "      <th>RMSE_test</th>\n",
       "      <th>R2_train</th>\n",
       "      <th>R2_test</th>\n",
       "      <th>Best_alpha</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Linear Reg</td>\n",
       "      <td>20426.160</td>\n",
       "      <td>30352.931</td>\n",
       "      <td>0.936</td>\n",
       "      <td>0.843</td>\n",
       "      <td>N/A</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>RidgeCV Reg</td>\n",
       "      <td>25725.420</td>\n",
       "      <td>25777.429</td>\n",
       "      <td>0.898</td>\n",
       "      <td>0.887</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>LassoCV Reg</td>\n",
       "      <td>26498.918</td>\n",
       "      <td>25777.429</td>\n",
       "      <td>0.927</td>\n",
       "      <td>0.880</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Ridge_GridSearchCV</td>\n",
       "      <td>25725.420</td>\n",
       "      <td>25777.429</td>\n",
       "      <td>0.882</td>\n",
       "      <td>0.873</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Lasso_GridSearchCV</td>\n",
       "      <td>25386.622</td>\n",
       "      <td>33835.537</td>\n",
       "      <td>0.898</td>\n",
       "      <td>0.820</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                Index  RMSE_train  RMSE_test  R2_train  R2_test Best_alpha\n",
       "0          Linear Reg   20426.160  30352.931     0.936    0.843        N/A\n",
       "1         RidgeCV Reg   25725.420  25777.429     0.898    0.887         10\n",
       "2         LassoCV Reg   26498.918  25777.429     0.927    0.880          1\n",
       "3  Ridge_GridSearchCV   25725.420  25777.429     0.882    0.873         10\n",
       "4  Lasso_GridSearchCV   25386.622  33835.537     0.898    0.820         10"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from collections import OrderedDict\n",
    "# Create a dictionary to store the train and test scores, best alpha values\n",
    "scores = {'Index': ['Linear Reg','RidgeCV Reg','LassoCV Reg', 'Ridge_GridSearchCV', 'Lasso_GridSearchCV'],\n",
    "         'RMSE_train': [20426.160, 25725.420, 26498.918, 25725.420, 25386.622],\n",
    "         'RMSE_test': [30352.931, 25777.429, 25777.429, 25777.429, 33835.537],\n",
    "         'R2_train': [0.936, 0.898, 0.927, 0.882,0.898 ],\n",
    "         'R2_test': [0.843, 0.887, 0.880, 0.873, 0.820],\n",
    "         'Best_alpha': ['N/A', 10.0, 1.0, 10.0, 10.0]}\n",
    "scores = OrderedDict(scores)\n",
    "\n",
    "# Create a dataframe from the dictionary\n",
    "reg_models_scores = pd.DataFrame.from_dict(scores)\n",
    "reg_models_scores"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The scores produced by Ridge Regression doesn't vary much, both RMSE and R2 of train and test data sets are not far from each other. The same is the case with Ridge using GridSearch Cross Validation. \n",
    "\n",
    "Therefore by lookig at the scores, regression plots and residual plots I feel that Ridge Regression using Cross Validation is the best model for the data. Having said that let us look at the features that are positively and negatively correlated with the Sale Price using Ridge Cross Validation method. \n",
    "\n",
    "The top ten important features that are positively correlated with Sale Price are:\n",
    "1. A full bath in Basement\n",
    "2. Overall Condition of the house\n",
    "3. Low quality finished area of the house (sqft)\n",
    "4. Area of Garage (sqft)\n",
    "5. Square footage of 2nd floor\n",
    "6. Built year of the house\n",
    "7. No. of Fireplaces\t\n",
    "8. Year remodeled\n",
    "9. Overall quality of the house\n",
    "10. No. of Half baths above basement/ ground floor (for houses without basement)\n",
    "\n",
    "The presence/ increase of the above features increases the Sale Price of a house\n",
    "\n",
    "The top ten important features that are negatively correlated with the Sale Price are:\n",
    "1. Front yard of the house (if more than back yard)\n",
    "2. Area of the lot\n",
    "3. Total rooms above basement/ ground floor (for houses without basement)\n",
    "4. Kitchen above ground floor\n",
    "5. Second basement finished square footage\n",
    "6. Area of 1st floor (sqft)\n",
    "7. Garage capacity (no. of cars it can accommodate)\n",
    "8. Area of Wooden Deck\n",
    "9. Year Sold\t\n",
    "10. Enclosed Porch\t\n",
    "\n",
    "The absence/ decrease of the above features increases the Sale Price of a house."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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