Price_Prediction_Model.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "**Reema Jain**\n",
    "\n",
    "Predict Housing Prices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Index\n",
    "\n",
    "- [Abstract](#Abstract)\n",
    "- [1. Introduction](#1.-Introduction)\n",
    "- [2. The Data](#2.-The-Data)\n",
    "    - [2.1 Import the Data](#2.1-Import-the-Data)\n",
    "    - [2.2 Data Exploration](#2.2-Data-Exploration)\n",
    "    - [2.3 Data Preparation](#2.3-Data-Preparation)\n",
    "    - [2.4 Correlation](#2.4-Correlation)\n",
    "- [3. Project Description](#3.-Project-Description)\n",
    "    - [3.1 Linear Regression](#3.1-Linear-Regression)\n",
    "    - [3.2 Analysis](#3.2-Analysis)\n",
    "    - [3.3 Results](#3.3-Results)\n",
    "    - [3.4 Verify Your Model Against Test Data](#3.4-Verify-Your-Model-Against-Test-Data)\n",
    "- [Conclusion](#Conclusion)\n",
    "- [References](#References)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Back to top](#Index)\n",
    "\n",
    "\n",
    "##  Abstract\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Created price prediction model for three group of variables. \n",
    "First Group consisted of 3 independent variables selected based on correlation of 69% or more with sale price. Second Group consisted of 7 independent variables selected based on correlation of 60% or more with sale price. Third Group consisted of 13 independent variables selected based on correlation of 50% or more with sale price.\n",
    "\n",
    "To check accuracy of models, I calculated R² values. R² shows how much variability in the target variable(i.e. Y) is explained by independent variables. R² is 79%,85% & 88% for first, second and third group respectively. This shows effectiveness of model improved when more independent variables with higher correlation are added to the analysis. \n",
    "\n",
    "Histogram for residuals depicted a normal distribution around zero for all three groups.Scatter plot for predicted vs actual value of Y also showed a straight line for all above three groups.\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Back to top](#Index)\n",
    "\n",
    "\n",
    "## 1. Introduction\n",
    "\n",
    "\n",
    "Data analysis can be used for predicting various outcomes based on the past data. In this project we will perform necessary analysis & create an effective price prediction model which can accurately predict the sale price of a house based on data about similar houses. In order to perform the analysis I started with importing data and necessary libraries, understand and explore the data, perform data cleaning and find correlation, create linear regression model and check effectiveness of model using R² and finally test price prediction model against test data.\n",
    "\n",
    "In order to perform analysis, I imported numpy, pandas & matplotlib libraries. In order to understand data & target variable, I looked at statistical data (i.e. mean, min, max, etc.), plotted scatter plots on the variables which I considered to be the most important in predicting the house prices. Next, I cleaned the dat & calculated correlation. I created linear regression price prediction models & assessed their accuracy using R² and residual plots. Finally I tested the model against test data.\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Back to top](#Index)\n",
    "\n",
    "## 2. The Data\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Back to top](#Index)\n",
    "\n",
    "### 2.1 Import the Data\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I started with importing necessary libraries & data needed for analysis."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data Description\n",
    "  Below is the description of each column in the data to better understand what the column name means:\n",
    "\n",
    "- SalePrice: Property's sale price in dollars. This is the target variable we are trying to predict\n",
    "- MSSubClass: Identifies the type of dwelling involved in the sale.  \n",
    "- MSZoning: Identifies the general zoning classification of the sale.  \n",
    "- LotFrontage: Linear feet of street connected to property  \n",
    "- LotArea: Lot size in square feet\n",
    "- Street: Type of road access to property\n",
    "- Alley: Type of alley access to property  \n",
    "- LotShape: General shape of property  \n",
    "- LandContour: Flatness of the property  \n",
    "- Utilities: Type of utilities available  \n",
    "- LotConfig: Lot configuration  \n",
    "- LandSlope: Slope of property  \n",
    "- Neighborhood: Physical locations within Ames city limits\n",
    "- Condition1: Proximity to various conditions  \n",
    "- Condition2: Proximity to various conditions (if more than one is present)  \n",
    "- BldgType: Type of dwelling  \n",
    "- HouseStyle: Style of dwelling  \n",
    "- OverallQual: Rates the overall material and finish of the house   \n",
    "- OverallCond: Rates the overall condition of the house  \n",
    "- YearBuilt: Original construction date    \n",
    "- YearRemodAdd: Remodel date (same as construction date if no remodeling or additions)    \n",
    "- RoofStyle: Type of roof  \n",
    "- RoofMatl: Roof material  \n",
    "- Exterior1st: Exterior covering on house  \n",
    "- Exterior2nd: Exterior covering on house (if more than one material)  \n",
    "- MasVnrType: Masonry veneer type  \n",
    "- MasVnrArea: Masonry veneer area in square feet   \n",
    "- ExterQual: Evaluates the quality of the material on the exterior  \n",
    "- ExterCond: Evaluates the present condition of the material on the exterior  \n",
    "- Foundation: Type of foundation  \n",
    "- BsmtQual: Evaluates the height of the basement  \n",
    "- BsmtCond: Evaluates the general condition of the basement  \n",
    "- BsmtExposure: Refers to walkout or garden level walls  \n",
    "- BsmtFinType1: Rating of basement finished area  \n",
    "- BsmtFinSF1: Type 1 finished square feet  \n",
    "- BsmtFinType2: Rating of basement finished area (if multiple types)  \n",
    "- BsmtFinSF2: Type 2 finished square feet  \n",
    "- BsmtUnfSF: Unfinished square feet of basement area  \n",
    "- TotalBsmtSF: Total square feet of basement area   \n",
    "- Heating: Type of heating  \n",
    "- HeatingQC: Heating quality and condition  \n",
    "- CentralAir: Central air conditioning  \n",
    "- Electrical: Electrical system  \n",
    "- 1stFlrSF: First Floor square feet   \n",
    "- 2ndFlrSF: Second floor square feet  \n",
    "- LowQualFinSF: Low quality finished square feet (all floors)  \n",
    "- GrLivArea: Above grade (ground) living area square feet   \n",
    "- BsmtFullBath: Basement full bathrooms      \n",
    "- BsmtHalfBath: Basement half bathrooms     \n",
    "- FullBath: Full bathrooms above grade      \n",
    "- HalfBath: Half baths above grade     \n",
    "- Bedroom: Bedrooms above grade (does NOT include basement bedrooms)     \n",
    "- Kitchen: Kitchens above grade     \n",
    "- KitchenQual: Kitchen quality     \n",
    "- TotRmsAbvGrd: Total rooms above grade (does not include bathrooms)       \n",
    "- Functional: Home functionality (Assume typical unless deductions are warranted)     \n",
    "- Fireplaces: Number of fireplaces     \n",
    "- FireplaceQu: Fireplace quality \n",
    "- GarageType: Garage location  \n",
    "- GarageYrBlt: Year garage was built    \n",
    "- GarageFinish: Interior finish of the garage  \n",
    "- GarageCars: Size of garage in car capacity      \n",
    "- GarageArea: Size of garage in square feet   \n",
    "- GarageQual: Garage quality  \n",
    "- GarageCond: Garage condition  \n",
    "- PavedDrive: Paved driveway  \n",
    "- WoodDeckSF: Wood deck area in square feet   \n",
    "- OpenPorchSF: Open porch area in square feet    \n",
    "- EnclosedPorch: Enclosed porch area in square feet   \n",
    "- 3SsnPorch: Three season porch area in square feet    \n",
    "- ScreenPorch: Screen porch area in square feet      \n",
    "- PoolArea: Pool area in square feet    \n",
    "- PoolQC: Pool quality    \n",
    "- Fence: Fence quality    \n",
    "- MiscFeature: Miscellaneous feature not covered in other categories    \n",
    "- MiscVal: Value of miscellaneous feature    \n",
    "- MoSold: Month Sold (MM)    \n",
    "- YrSold: Year Sold (YYYY)      \n",
    "- SaleType: Type of sale                  \n",
    "- SaleCondition: Condition of sale        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# imported necessary libraries\n",
    "import numpy as np   \n",
    "import matplotlib.pyplot as plt   \n",
    "import pandas as pd    \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 82)"
      ]
     },
     "execution_count": 613,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# reading the data\n",
    "\n",
    "data=pd.read_csv('houseSmallData.csv')\n",
    "data.shape \n"
   ]
  },
  {
   "cell_type": "code",
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       "      <th>Id</th>\n",
       "      <th>MSSubClass</th>\n",
       "      <th>MSZoning</th>\n",
       "      <th>LotFrontage</th>\n",
       "      <th>LotArea</th>\n",
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       "      <th>SaleType</th>\n",
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       "      <td>5</td>\n",
       "      <td>2007</td>\n",
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       "      <td>0</td>\n",
       "      <td>9</td>\n",
       "      <td>2008</td>\n",
       "      <td>WD</td>\n",
       "      <td>Normal</td>\n",
       "      <td>223500</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>70</td>\n",
       "      <td>RL</td>\n",
       "      <td>60.0</td>\n",
       "      <td>9550</td>\n",
       "      <td>Pave</td>\n",
       "      <td>NaN</td>\n",
       "      <td>IR1</td>\n",
       "      <td>Lvl</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>2006</td>\n",
       "      <td>WD</td>\n",
       "      <td>Abnorml</td>\n",
       "      <td>140000</td>\n",
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       "      <th>4</th>\n",
       "      <td>4</td>\n",
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       "      <td>60</td>\n",
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       "      <td>84.0</td>\n",
       "      <td>14260</td>\n",
       "      <td>Pave</td>\n",
       "      <td>NaN</td>\n",
       "      <td>IR1</td>\n",
       "      <td>Lvl</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0</td>\n",
       "      <td>12</td>\n",
       "      <td>2008</td>\n",
       "      <td>WD</td>\n",
       "      <td>Normal</td>\n",
       "      <td>250000</td>\n",
       "    </tr>\n",
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      ],
      "text/plain": [
       "   Unnamed: 0  Id  MSSubClass MSZoning  LotFrontage  LotArea Street Alley  \\\n",
       "0           0   1          60       RL         65.0     8450   Pave   NaN   \n",
       "1           1   2          20       RL         80.0     9600   Pave   NaN   \n",
       "2           2   3          60       RL         68.0    11250   Pave   NaN   \n",
       "3           3   4          70       RL         60.0     9550   Pave   NaN   \n",
       "4           4   5          60       RL         84.0    14260   Pave   NaN   \n",
       "\n",
       "  LotShape LandContour  ... PoolArea PoolQC Fence MiscFeature MiscVal MoSold  \\\n",
       "0      Reg         Lvl  ...        0    NaN   NaN         NaN       0      2   \n",
       "1      Reg         Lvl  ...        0    NaN   NaN         NaN       0      5   \n",
       "2      IR1         Lvl  ...        0    NaN   NaN         NaN       0      9   \n",
       "3      IR1         Lvl  ...        0    NaN   NaN         NaN       0      2   \n",
       "4      IR1         Lvl  ...        0    NaN   NaN         NaN       0     12   \n",
       "\n",
       "  YrSold SaleType  SaleCondition  SalePrice  \n",
       "0   2008       WD         Normal     208500  \n",
       "1   2007       WD         Normal     181500  \n",
       "2   2008       WD         Normal     223500  \n",
       "3   2006       WD        Abnorml     140000  \n",
       "4   2008       WD         Normal     250000  \n",
       "\n",
       "[5 rows x 82 columns]"
      ]
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     "execution_count": 614,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Looking at the head of data\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
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       "      <th>SalePrice</th>\n",
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       "      <td>325300</td>\n",
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      "text/plain": [
       "    SalePrice\n",
       "58     438780\n",
       "53     385000\n",
       "11     345000\n",
       "20     325300\n",
       "45     319900\n",
       "..        ...\n",
       "98      83000\n",
       "39      82000\n",
       "68      80000\n",
       "29      68500\n",
       "30      40000\n",
       "\n",
       "[100 rows x 1 columns]"
      ]
     },
     "execution_count": 615,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Investigate Sales Price \n",
    "pd.DataFrame(data['SalePrice'].sort_values(ascending=False))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
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       "      <td>72236.552886</td>\n",
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       "      <td>40000.000000</td>\n",
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       "      <td>129362.500000</td>\n",
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       "      <th>50%</th>\n",
       "      <td>153750.000000</td>\n",
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       "      <th>75%</th>\n",
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      "text/plain": [
       "           SalePrice\n",
       "count     100.000000\n",
       "mean   173820.660000\n",
       "std     72236.552886\n",
       "min     40000.000000\n",
       "25%    129362.500000\n",
       "50%    153750.000000\n",
       "75%    207750.000000\n",
       "max    438780.000000"
      ]
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     "execution_count": 616,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Investigate Sales Price \n",
    "\n",
    "pd.DataFrame(data['SalePrice'].describe())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above table shows mean is 173K, std deviation is 72K. 75% of data lie below 207K with min at 40K & max at  438K "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 2., 17., 35., 17., 11.,  8.,  5.,  3.,  1.,  1.]),\n",
       " array([ 40000.,  79878., 119756., 159634., 199512., 239390., 279268.,\n",
       "        319146., 359024., 398902., 438780.]),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "execution_count": 617,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plot Histogram of Sales Price\n",
    "plt.hist(data['SalePrice'])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above graph depicts majority of SalePrice falls b/w 79K to 240K with maximum 35 datapoints at ~120K.     \n",
    "SalePrice is not evenly distributed. It looks like log normal distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.1783462304851948"
      ]
     },
     "execution_count": 618,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plot log of SalePrice & checking skew\n",
    "\n",
    "plt.hist(np.log(data['SalePrice']))\n",
    "data['SalePrice'].skew()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.09632240207755555"
      ]
     },
     "execution_count": 619,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(np.log(data['SalePrice']))\n",
    "np.log(data['SalePrice']).skew()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Saving log of SalePrice in new variable 'target'\n",
    "target=np.log(data['SalePrice'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see original data has skew of 1.17 & log of SalePrice has skew of -0.096. This shows that skewness has been reduced from 1 to .1. Value of -0.096 indicates that the distribution is fairly symmetrical"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Back to top](#Index)\n",
    "\n",
    "### 2.2 Data Exploration\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After getting sense of my target variable(i.e. SalePrice), I started exploring the data. I used scatter plots to understand the relationship between SalePrice & the variables I consider the most important. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### First assumption\n",
    "My first assumption is houses with higher 'grade living area in square feet' will have higher sale price. Hence, I started looking at SalePrice(dependent variable Y) with respect to GrLivArea(independent variable)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x2b10ce63850>"
      ]
     },
     "execution_count": 622,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Scatter plot\n",
    "\n",
    "plt.scatter(data['GrLivArea'],y=target)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Result\n",
    "From the above graph, we see that there is strong positive relationship between GrLivArea & SalePrice i.e. SalePrice is increasing with the increase in the GrLivArea. However, there are some outliers showing some houses with similar GrLivArea were sold at lesser price. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Second assumption\n",
    "Next, I explored relationship between TotalBsmtSF and SalePrice. I assumed that houses with higher 'total square feet of basement area' will sell for higher price."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x2b10cec1970>"
      ]
     },
     "execution_count": 623,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Scatter plot\n",
    "\n",
    "plt.scatter(data['TotalBsmtSF'],y=target)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Result\n",
    "Above graph displays strong positive relationship between TotalBsmtSF & SalePrice. We can see that houses with higher 'total square feet of basement area' sell for higher prices. As TotalBsmtSF increases, SalePrice also increases with few outliers.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Third assumption\n",
    "I looked at the relationship between OverallQual and SalePrice. I assumed that houses with higher rates for 'overall material and finish of the house' will sold for higher price. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x2b10cf25580>"
      ]
     },
     "execution_count": 624,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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oqNJVJKWZ6QP9fU3bNAMl3LpqZs119Yg+IsZqHw8DO4HV3fx+KUhtTHFKW1fNrLmuFXpJZ0o6a/o28B6mFnFPaamNKU5t37+ZzdbO9sodwNuBsyUdAj4FHAH+HlgK7Jb0UESslbQM+HJEXAmcC+ysLdieBtwWEfd058dIR0rjGqZ566pZ2trZdbMx41M7mzx2DLiydvsp4NIFZVdB/Wf08kKTAWb9Z5RzTLGZpa8SIxBS8uuGtk2ruJnZQrnQ5+zFicbrNc0dNzNbKBd6M7OKc6HPWX/GJQOz4mZmC1WZQp/KNWM/ffUb6V1SPz6gd4n49NVvLCgjM6u6SowpTumasamNVDaz9FWi0Kc2Sje1fekpjWwws9kqUehTOwkppcKZ0rslM2uuEj36lK4Zm9qsm9RGNpjZbJUo9CkN3kqtcKb2bsnMZqtEoU9p8FZqV2xK6d2SmTVXiR49pLPAmdoVmzavHazr0UN53y2ZWXOVKfSpSO2KTd4OapY+F/qcpXjFplTeLZlZc5Xo0ackpYVjM6sGH9HnzK0QM8ubC30B3Aoxszy5dWNmVnEu9GZmFedCb2ZWcS70ZmYV50JvZlZx3nVTgJTGFJtZ+lzoc+b57maWN7ducpbamGIzS58Lfc48393M8uZCnzPPdzezvLnQ58xDzcwsb16MzZmHmplZ3lzoC+ChZmaWJ7duzMwqzoXezKziWhZ6STdLOizpwIzY+yU9JumEpKE5nrtO0kFJT0raslhJm5lZ+9o5or8FWNcQOwBsAPZlPUlSD/AF4ArgImCjpIs6S9PMzDrVstBHxD7gSEPs8YhodSrnauDJiHgqIn4D3A5c03GmZmbWkW726AeA52bcP1SLmZlZjrpZ6NUkFpkPljZJGpY0PD4+3sW0zMxOLd0s9IeA5TPunweMZT04IrZHxFBEDC1durSLaZmZnVq6Wei/D1wo6QJJpwPXAt/o4vczM7Mm2tleuQO4HxiUdEjS9ZLeK+kQ8FZgt6Q9tccuk3Q3QEQcB24A9gCPA1+PiMe69YOYmVlzishsmxdmaGgohoeHi07DzCwZkkYioul5TT4z1sys4lzozcwqzoXezKziXOjNzCrOhd7MrOJc6M3MKs6F3sys4lzozcwqzoXezKziXOjNzCrOhd7MrOJc6M3MKs6F3sys4lzozcwqzoXezKziXOjNzCrOhd7MrOJc6M3MKs6F3sys4lzozcwqzoXezKziXOjNzCrOhd7MrOJc6M3MKs6F3sys4k4rOoFT0a79o2zbc5Cxo8dY1t/H5rWDrF81UHRaZlZRLvQ527V/lBvvepRjE5MAjB49xo13PQrgYm9mXeHWTc627Tl4sshPOzYxybY9BwvKyMyqzoU+Z2NHj80rbma2UC70OVvW3zevuJnZQrnQ52zz2kH6envqYn29PWxeO1hQRmZWdV6Mzdn0gqt33ZhZXlzoC7B+1YALu5nlpmXrRtLNkg5LOjAj9ipJ90n6ce3jKzOe+7SkRyU9JGl4MRM3M7P2tNOjvwVY1xDbAnw7Ii4Evl27n+UdEXFZRAx1lqKZmS1Ey0IfEfuAIw3ha4Cv1m5/FVi/uGmZmdli6XTXzbkR8TxA7eM5GY8L4F5JI5I2zfUFJW2SNCxpeHx8vMO0zMysUbe3V66JiDcBVwAfkfS2rAdGxPaIGIqIoaVLl3Y5LTOzU0enu25+Kuk1EfG8pNcAh5s9KCLGah8PS9oJrAb2tfriIyMjP5P0TIe5nQ38rMPn5i2lXCGtfFPKFdLKN6VcIa18F5Lra7M+0Wmh/wbwQWBr7eO/Nj5A0pnAkoj4Re32e4C/bOeLR0THh/SShlNZ+E0pV0gr35RyhbTyTSlXSCvfbuXazvbKHcD9wKCkQ5KuZ6rAv1vSj4F31+4jaZmku2tPPRf4jqSHge8BuyPinsX+AczMbG4tj+gjYmPGp97V5LFjwJW1208Bly4oOzMzW7AqzrrZXnQC85BSrpBWvinlCmnlm1KukFa+XclVEdGNr2tmZiVRxSN6MzObwYXezKziKlHoJb1c0vckPSzpMUmfKTqndkjqkbRf0reKzmUuqQ2nk9Qv6Q5JT0h6XNJbi86pGUmDtd/p9L+fS/rTovOai6Q/q/2NHZC0Q9LLi84pi6SP1fJ8rIy/14UMjJyvShR64NfAOyPiUuAyYJ2ky4tNqS0fAx4vOok2pTSc7u+AeyLi9Uzt/Crl7zgiDtZ+p5cBbwZeBHYWm1U2SQPAnwBDEXEx0ANcW2xWzUm6GPgwUydpXgpcJenCYrOa5RYWNjCybZUo9DHll7W7vbV/pV5llnQe8HvAl4vOpUok/RbwNuArABHxm4g4WmhS7XkX8JOI6PSM8LycBvRJOg04AxgrOJ8sbwAeiIgXI+I48J/AewvOqU6eAyMrUejhZBvkIabGMdwXEQ8WnFIrfwv8OXCi4Dza0fZwuhJ4HTAO/FOtLfbl2pnZZXctsKPoJOYSEaPA3wDPAs8D/xsR9xabVaYDwNskvVrSGUyd37O84Jza0e7AyHmpTKGPiMnaW+DzgNW1t26lJOkq4HBEjBSdS5vaHk5XAqcBbwL+ISJWAf/HIr397RZJpwNXA/9SdC5zqfWLrwEuAJYBZ0r6g2Kzai4iHgf+GrgPuAd4GDheaFIFqkyhn1Z7m/4fzO59lcka4GpJTwO3A++U9LViU8o2czgdUz3k1cVmNKdDwKEZ7+juYKrwl9kVwA8i4qdFJ9LC7wL/FRHjETEB3AX8TsE5ZYqIr0TEmyLibUy1SH5cdE5t+GltUCRzDYycr0oUeklLJfXXbvcx9R/yiUKTmkNE3BgR50XECqbesu+NiFIeGUk6U9JZ07eZGk53YO5nFSci/ht4TtJgLfQu4IcFptSOjZS8bVPzLHC5pDMkianfbSkXugEknVP7eD6wgTR+x9MDIyFjYGQnqnJx8NcAX5XUw9SL19cjotRbFhNyLrBz6u+a04DbEhhO91Hg1lpL5CngDwvOJ1Otf/xu4I+KzqWViHhQ0h3AD5hqg+yn3OMF7pT0amAC+EhEvFB0QjPVBka+HThb0iHgU0wNiPx6bXjks8D7F+V7eQSCmVm1VaJ1Y2Zm2VzozcwqzoXezKziXOjNzCrOhd7MrOJc6M3MKs6F3sys4v4fWkYyxOfqFb8AAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Scatter plot\n",
    "\n",
    "plt.scatter(data['OverallQual'],y=target)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Result\n",
    "Above graph depicts very strong positive relationship between OverallQual and SalePrice. SalePrice is increasing with increase in rates for OverallQual."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Fourth assumption\n",
    "I expected houses with higher lot area will have higher sale price. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x2b10cf8e160>"
      ]
     },
     "execution_count": 625,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Scatter plot\n",
    "\n",
    "plt.scatter(data['LotArea'],y=data['SalePrice'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Result\n",
    "Above graph shows that LotArea & SalePrice are not significantly correlated. It seems like sale price is concentrated around 10000 lot area."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Fifth assumption\n",
    "I expected houses built later on will have better interiors & layout and, hence, will have higher sale price. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x2b10cff3700>"
      ]
     },
     "execution_count": 626,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Scatter plot\n",
    "\n",
    "plt.scatter(data['YearBuilt'],y=target)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Result\n",
    "We can see from the above graph that there is strong positive correlation between sales price & the year the house was built.\n",
    "Newer the house, higher will be sale price. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Sixth assumption\n",
    "I assume Garage built in recent years will have better layout and, hence, will have higher sale price."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x2b1098ef400>"
      ]
     },
     "execution_count": 402,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Scatter plot\n",
    "\n",
    "plt.scatter(data['GarageYrBlt'],y=target)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Result\n",
    "Above graph shows there is strong positive correlation between sales price & the year the garage was built.\n",
    "Newer the garage, higher will be sale price."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Back to top](#Index)\n",
    "\n",
    "### 2.3 Data Preparation\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After data exploration stage, I proceed with data cleaning which involves finding nulls and replacing them.\n",
    "For GarageYrBlt I replaced null values with corresponding values in col YearBuilt. For remaining numerical data, I used interpolate & dropna function to take care of the null values.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>PoolQC</th>\n",
       "      <td>100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alley</th>\n",
       "      <td>94</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MiscFeature</th>\n",
       "      <td>91</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Fence</th>\n",
       "      <td>77</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FireplaceQu</th>\n",
       "      <td>54</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LotFrontage</th>\n",
       "      <td>14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GarageType</th>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GarageYrBlt</th>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GarageFinish</th>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GarageQual</th>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GarageCond</th>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtFinType1</th>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtQual</th>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtCond</th>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtExposure</th>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtFinType2</th>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>KitchenAbvGr</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Functional</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BedroomAbvGr</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HalfBath</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                0\n",
       "PoolQC        100\n",
       "Alley          94\n",
       "MiscFeature    91\n",
       "Fence          77\n",
       "FireplaceQu    54\n",
       "LotFrontage    14\n",
       "GarageType      6\n",
       "GarageYrBlt     6\n",
       "GarageFinish    6\n",
       "GarageQual      6\n",
       "GarageCond      6\n",
       "BsmtFinType1    3\n",
       "BsmtQual        3\n",
       "BsmtCond        3\n",
       "BsmtExposure    3\n",
       "BsmtFinType2    3\n",
       "KitchenAbvGr    0\n",
       "Functional      0\n",
       "BedroomAbvGr    0\n",
       "HalfBath        0"
      ]
     },
     "execution_count": 627,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Checking Nulls in data\n",
    "nulls=pd.DataFrame(data.isnull().sum().sort_values(ascending=False))[0:20]\n",
    "nulls"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above table shows that 16 columns has null values in the dataset. Next, we can check nulls in numerical columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>Id</th>\n",
       "      <th>MSSubClass</th>\n",
       "      <th>LotFrontage</th>\n",
       "      <th>LotArea</th>\n",
       "      <th>OverallQual</th>\n",
       "      <th>OverallCond</th>\n",
       "      <th>YearBuilt</th>\n",
       "      <th>YearRemodAdd</th>\n",
       "      <th>MasVnrArea</th>\n",
       "      <th>...</th>\n",
       "      <th>OpenPorchSF</th>\n",
       "      <th>EnclosedPorch</th>\n",
       "      <th>3SsnPorch</th>\n",
       "      <th>ScreenPorch</th>\n",
       "      <th>PoolArea</th>\n",
       "      <th>PoolQC</th>\n",
       "      <th>MiscVal</th>\n",
       "      <th>MoSold</th>\n",
       "      <th>YrSold</th>\n",
       "      <th>SalePrice</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
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       "      <td>8450</td>\n",
       "      <td>7</td>\n",
       "      <td>5</td>\n",
       "      <td>2003</td>\n",
       "      <td>2003</td>\n",
       "      <td>196</td>\n",
       "      <td>...</td>\n",
       "      <td>61</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>2008</td>\n",
       "      <td>208500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>20</td>\n",
       "      <td>80.0</td>\n",
       "      <td>9600</td>\n",
       "      <td>6</td>\n",
       "      <td>8</td>\n",
       "      <td>1976</td>\n",
       "      <td>1976</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>2007</td>\n",
       "      <td>181500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>60</td>\n",
       "      <td>68.0</td>\n",
       "      <td>11250</td>\n",
       "      <td>7</td>\n",
       "      <td>5</td>\n",
       "      <td>2001</td>\n",
       "      <td>2002</td>\n",
       "      <td>162</td>\n",
       "      <td>...</td>\n",
       "      <td>42</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0</td>\n",
       "      <td>9</td>\n",
       "      <td>2008</td>\n",
       "      <td>223500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>70</td>\n",
       "      <td>60.0</td>\n",
       "      <td>9550</td>\n",
       "      <td>7</td>\n",
       "      <td>5</td>\n",
       "      <td>1915</td>\n",
       "      <td>1970</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>35</td>\n",
       "      <td>272</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>2006</td>\n",
       "      <td>140000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>60</td>\n",
       "      <td>84.0</td>\n",
       "      <td>14260</td>\n",
       "      <td>8</td>\n",
       "      <td>5</td>\n",
       "      <td>2000</td>\n",
       "      <td>2000</td>\n",
       "      <td>350</td>\n",
       "      <td>...</td>\n",
       "      <td>84</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0</td>\n",
       "      <td>12</td>\n",
       "      <td>2008</td>\n",
       "      <td>250000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>95</td>\n",
       "      <td>96</td>\n",
       "      <td>60</td>\n",
       "      <td>NaN</td>\n",
       "      <td>9765</td>\n",
       "      <td>6</td>\n",
       "      <td>8</td>\n",
       "      <td>1993</td>\n",
       "      <td>1993</td>\n",
       "      <td>68</td>\n",
       "      <td>...</td>\n",
       "      <td>63</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>480</td>\n",
       "      <td>4</td>\n",
       "      <td>2009</td>\n",
       "      <td>185000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>96</td>\n",
       "      <td>97</td>\n",
       "      <td>20</td>\n",
       "      <td>78.0</td>\n",
       "      <td>10264</td>\n",
       "      <td>7</td>\n",
       "      <td>5</td>\n",
       "      <td>1999</td>\n",
       "      <td>1999</td>\n",
       "      <td>183</td>\n",
       "      <td>...</td>\n",
       "      <td>29</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0</td>\n",
       "      <td>8</td>\n",
       "      <td>2006</td>\n",
       "      <td>214000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>97</td>\n",
       "      <td>98</td>\n",
       "      <td>20</td>\n",
       "      <td>73.0</td>\n",
       "      <td>10921</td>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>1965</td>\n",
       "      <td>1965</td>\n",
       "      <td>48</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>2007</td>\n",
       "      <td>94750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>98</td>\n",
       "      <td>99</td>\n",
       "      <td>30</td>\n",
       "      <td>85.0</td>\n",
       "      <td>10625</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>1920</td>\n",
       "      <td>1950</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>77</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>400</td>\n",
       "      <td>5</td>\n",
       "      <td>2010</td>\n",
       "      <td>83000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>99</td>\n",
       "      <td>100</td>\n",
       "      <td>20</td>\n",
       "      <td>77.0</td>\n",
       "      <td>9320</td>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>1959</td>\n",
       "      <td>1959</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>400</td>\n",
       "      <td>1</td>\n",
       "      <td>2010</td>\n",
       "      <td>128950</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 40 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    Unnamed: 0   Id  MSSubClass  LotFrontage  LotArea  OverallQual  \\\n",
       "0            0    1          60         65.0     8450            7   \n",
       "1            1    2          20         80.0     9600            6   \n",
       "2            2    3          60         68.0    11250            7   \n",
       "3            3    4          70         60.0     9550            7   \n",
       "4            4    5          60         84.0    14260            8   \n",
       "..         ...  ...         ...          ...      ...          ...   \n",
       "95          95   96          60          NaN     9765            6   \n",
       "96          96   97          20         78.0    10264            7   \n",
       "97          97   98          20         73.0    10921            4   \n",
       "98          98   99          30         85.0    10625            5   \n",
       "99          99  100          20         77.0     9320            4   \n",
       "\n",
       "    OverallCond  YearBuilt  YearRemodAdd  MasVnrArea  ...  OpenPorchSF  \\\n",
       "0             5       2003          2003         196  ...           61   \n",
       "1             8       1976          1976           0  ...            0   \n",
       "2             5       2001          2002         162  ...           42   \n",
       "3             5       1915          1970           0  ...           35   \n",
       "4             5       2000          2000         350  ...           84   \n",
       "..          ...        ...           ...         ...  ...          ...   \n",
       "95            8       1993          1993          68  ...           63   \n",
       "96            5       1999          1999         183  ...           29   \n",
       "97            5       1965          1965          48  ...            0   \n",
       "98            5       1920          1950           0  ...            0   \n",
       "99            5       1959          1959           0  ...            0   \n",
       "\n",
       "    EnclosedPorch  3SsnPorch  ScreenPorch  PoolArea  PoolQC  MiscVal  MoSold  \\\n",
       "0               0          0            0         0     NaN        0       2   \n",
       "1               0          0            0         0     NaN        0       5   \n",
       "2               0          0            0         0     NaN        0       9   \n",
       "3             272          0            0         0     NaN        0       2   \n",
       "4               0          0            0         0     NaN        0      12   \n",
       "..            ...        ...          ...       ...     ...      ...     ...   \n",
       "95              0          0            0         0     NaN      480       4   \n",
       "96              0          0            0         0     NaN        0       8   \n",
       "97              0          0            0         0     NaN        0       5   \n",
       "98             77          0            0         0     NaN      400       5   \n",
       "99              0          0            0         0     NaN      400       1   \n",
       "\n",
       "    YrSold  SalePrice  \n",
       "0     2008     208500  \n",
       "1     2007     181500  \n",
       "2     2008     223500  \n",
       "3     2006     140000  \n",
       "4     2008     250000  \n",
       "..     ...        ...  \n",
       "95    2009     185000  \n",
       "96    2006     214000  \n",
       "97    2007      94750  \n",
       "98    2010      83000  \n",
       "99    2010     128950  \n",
       "\n",
       "[100 rows x 40 columns]"
      ]
     },
     "execution_count": 628,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Select numeric Columns\n",
    "numeric=pd.DataFrame(data.select_dtypes(include=[np.number]))\n",
    "numeric "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have 100 rows & 40 columns with numeric data.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
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       "      <td>14</td>\n",
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       "      <td>6</td>\n",
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       "      <th>OpenPorchSF</th>\n",
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       "      <th>KitchenAbvGr</th>\n",
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       "    <tr>\n",
       "      <th>TotRmsAbvGrd</th>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>Fireplaces</th>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>GarageCars</th>\n",
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       "    <tr>\n",
       "      <th>GarageArea</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>WoodDeckSF</th>\n",
       "      <td>0</td>\n",
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       "      <th>EnclosedPorch</th>\n",
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       "    <tr>\n",
       "      <th>HalfBath</th>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>3SsnPorch</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ScreenPorch</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PoolArea</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MiscVal</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MoSold</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>YrSold</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BedroomAbvGr</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FullBath</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Id</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtFinSF1</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MSSubClass</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LotArea</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>OverallQual</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>OverallCond</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>YearBuilt</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>YearRemodAdd</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MasVnrArea</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtFinSF2</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtHalfBath</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtUnfSF</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TotalBsmtSF</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1stFlrSF</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2ndFlrSF</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LowQualFinSF</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GrLivArea</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtFullBath</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SalePrice</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 0\n",
       "PoolQC         100\n",
       "LotFrontage     14\n",
       "GarageYrBlt      6\n",
       "Unnamed: 0       0\n",
       "OpenPorchSF      0\n",
       "KitchenAbvGr     0\n",
       "TotRmsAbvGrd     0\n",
       "Fireplaces       0\n",
       "GarageCars       0\n",
       "GarageArea       0\n",
       "WoodDeckSF       0\n",
       "EnclosedPorch    0\n",
       "HalfBath         0\n",
       "3SsnPorch        0\n",
       "ScreenPorch      0\n",
       "PoolArea         0\n",
       "MiscVal          0\n",
       "MoSold           0\n",
       "YrSold           0\n",
       "BedroomAbvGr     0\n",
       "FullBath         0\n",
       "Id               0\n",
       "BsmtFinSF1       0\n",
       "MSSubClass       0\n",
       "LotArea          0\n",
       "OverallQual      0\n",
       "OverallCond      0\n",
       "YearBuilt        0\n",
       "YearRemodAdd     0\n",
       "MasVnrArea       0\n",
       "BsmtFinSF2       0\n",
       "BsmtHalfBath     0\n",
       "BsmtUnfSF        0\n",
       "TotalBsmtSF      0\n",
       "1stFlrSF         0\n",
       "2ndFlrSF         0\n",
       "LowQualFinSF     0\n",
       "GrLivArea        0\n",
       "BsmtFullBath     0\n",
       "SalePrice        0"
      ]
     },
     "execution_count": 629,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Checking nulls in Numerical columns\n",
    "nulls=pd.DataFrame(data.select_dtypes(include=[np.number]).isnull().sum().sort_values(ascending=False))\n",
    "nulls"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above table displays there are nulls in three numerical columns. \n",
    "\n",
    "There appears to be 6 null values in Column 'GarageYrBlt' which is one of my variable of interest for predicting house prices.  Instead of using interpolate to replace value in GarageYrBlt, I will replace the missing values with the corresponding value from Col YearBuilt. My assumption is garage was built in the same year when the house was built.\n",
    "\n",
    "For remaining numeric columns having null values, I will clean the data using interpolate & dropna function.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 82)"
      ]
     },
     "execution_count": 630,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Replacing Null Values in GarageYrBlt with corresponding values in col YearBuilt\n",
    "pd.DataFrame(data['GarageYrBlt'].fillna(value=data['YearBuilt'],inplace=True))\n",
    "data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>KitchenAbvGr</th>\n",
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       "      <th>WoodDeckSF</th>\n",
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       "      <th>EnclosedPorch</th>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>HalfBath</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3SsnPorch</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ScreenPorch</th>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>PoolArea</th>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>MiscVal</th>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>MoSold</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>YrSold</th>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>BedroomAbvGr</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FullBath</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Id</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtFinSF1</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MSSubClass</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LotArea</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>OverallQual</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>OverallCond</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>YearBuilt</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>YearRemodAdd</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MasVnrArea</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtFinSF2</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtHalfBath</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtUnfSF</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TotalBsmtSF</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1stFlrSF</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2ndFlrSF</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LowQualFinSF</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GrLivArea</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtFullBath</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SalePrice</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 0\n",
       "PoolQC         100\n",
       "LotFrontage     14\n",
       "Unnamed: 0       0\n",
       "OpenPorchSF      0\n",
       "KitchenAbvGr     0\n",
       "TotRmsAbvGrd     0\n",
       "Fireplaces       0\n",
       "GarageYrBlt      0\n",
       "GarageCars       0\n",
       "GarageArea       0\n",
       "WoodDeckSF       0\n",
       "EnclosedPorch    0\n",
       "HalfBath         0\n",
       "3SsnPorch        0\n",
       "ScreenPorch      0\n",
       "PoolArea         0\n",
       "MiscVal          0\n",
       "MoSold           0\n",
       "YrSold           0\n",
       "BedroomAbvGr     0\n",
       "FullBath         0\n",
       "Id               0\n",
       "BsmtFinSF1       0\n",
       "MSSubClass       0\n",
       "LotArea          0\n",
       "OverallQual      0\n",
       "OverallCond      0\n",
       "YearBuilt        0\n",
       "YearRemodAdd     0\n",
       "MasVnrArea       0\n",
       "BsmtFinSF2       0\n",
       "BsmtHalfBath     0\n",
       "BsmtUnfSF        0\n",
       "TotalBsmtSF      0\n",
       "1stFlrSF         0\n",
       "2ndFlrSF         0\n",
       "LowQualFinSF     0\n",
       "GrLivArea        0\n",
       "BsmtFullBath     0\n",
       "SalePrice        0"
      ]
     },
     "execution_count": 631,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Checking nulls in Numerical columns to make sure GarageYrBlt has no nulls\n",
    "nulls=pd.DataFrame(data.select_dtypes(include=[np.number]).isnull().sum().sort_values(ascending=False))\n",
    "nulls"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 39)"
      ]
     },
     "execution_count": 632,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Clean nulls for remaining numeric columns using interpolate & dropna\n",
    "data=pd.DataFrame(data.select_dtypes(include=[np.number])).interpolate().dropna(axis=1)\n",
    "data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>FullBath</th>\n",
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       "      <th>EnclosedPorch</th>\n",
       "      <td>0</td>\n",
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       "      <th>3SsnPorch</th>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>ScreenPorch</th>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>PoolArea</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MiscVal</th>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>MoSold</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>YrSold</th>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>HalfBath</th>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>BsmtHalfBath</th>\n",
       "      <td>0</td>\n",
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       "      <th>Id</th>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>MasVnrArea</th>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>MSSubClass</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LotFrontage</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LotArea</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>OverallQual</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>OverallCond</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>YearBuilt</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>YearRemodAdd</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtFinSF1</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtFullBath</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtFinSF2</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtUnfSF</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TotalBsmtSF</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1stFlrSF</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2ndFlrSF</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LowQualFinSF</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GrLivArea</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SalePrice</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               0\n",
       "Unnamed: 0     0\n",
       "WoodDeckSF     0\n",
       "BedroomAbvGr   0\n",
       "KitchenAbvGr   0\n",
       "TotRmsAbvGrd   0\n",
       "Fireplaces     0\n",
       "GarageYrBlt    0\n",
       "GarageCars     0\n",
       "GarageArea     0\n",
       "OpenPorchSF    0\n",
       "FullBath       0\n",
       "EnclosedPorch  0\n",
       "3SsnPorch      0\n",
       "ScreenPorch    0\n",
       "PoolArea       0\n",
       "MiscVal        0\n",
       "MoSold         0\n",
       "YrSold         0\n",
       "HalfBath       0\n",
       "BsmtHalfBath   0\n",
       "Id             0\n",
       "MasVnrArea     0\n",
       "MSSubClass     0\n",
       "LotFrontage    0\n",
       "LotArea        0\n",
       "OverallQual    0\n",
       "OverallCond    0\n",
       "YearBuilt      0\n",
       "YearRemodAdd   0\n",
       "BsmtFinSF1     0\n",
       "BsmtFullBath   0\n",
       "BsmtFinSF2     0\n",
       "BsmtUnfSF      0\n",
       "TotalBsmtSF    0\n",
       "1stFlrSF       0\n",
       "2ndFlrSF       0\n",
       "LowQualFinSF   0\n",
       "GrLivArea      0\n",
       "SalePrice      0"
      ]
     },
     "execution_count": 633,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Checking nulls in Numerical columns to make sure there are no more nulls now\n",
    "nulls=pd.DataFrame(data.select_dtypes(include=[np.number]).isnull().sum().sort_values(ascending=False))\n",
    "nulls"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now have 100 rows & 39 numeric columns. Lets run correlation now."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Back to top](#Index)\n",
    "\n",
    "### 2.4 Correlation\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    }\n",
       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SalePrice</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>SalePrice</th>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>OverallQual</th>\n",
       "      <td>0.855061</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GrLivArea</th>\n",
       "      <td>0.735129</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GarageArea</th>\n",
       "      <td>0.688249</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GarageCars</th>\n",
       "      <td>0.663441</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>YearBuilt</th>\n",
       "      <td>0.658636</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TotalBsmtSF</th>\n",
       "      <td>0.616297</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GarageYrBlt</th>\n",
       "      <td>0.612514</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FullBath</th>\n",
       "      <td>0.579505</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MasVnrArea</th>\n",
       "      <td>0.571836</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TotRmsAbvGrd</th>\n",
       "      <td>0.553603</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1stFlrSF</th>\n",
       "      <td>0.550912</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>YearRemodAdd</th>\n",
       "      <td>0.548330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LotArea</th>\n",
       "      <td>0.497124</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Fireplaces</th>\n",
       "      <td>0.487907</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>WoodDeckSF</th>\n",
       "      <td>0.451241</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2ndFlrSF</th>\n",
       "      <td>0.381076</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtUnfSF</th>\n",
       "      <td>0.327020</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HalfBath</th>\n",
       "      <td>0.319304</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LotFrontage</th>\n",
       "      <td>0.302526</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>OpenPorchSF</th>\n",
       "      <td>0.301960</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtFinSF1</th>\n",
       "      <td>0.266713</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MoSold</th>\n",
       "      <td>0.256863</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BedroomAbvGr</th>\n",
       "      <td>0.233426</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtFullBath</th>\n",
       "      <td>0.155689</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ScreenPorch</th>\n",
       "      <td>0.035930</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3SsnPorch</th>\n",
       "      <td>-0.019391</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtHalfBath</th>\n",
       "      <td>-0.055100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MSSubClass</th>\n",
       "      <td>-0.066819</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MiscVal</th>\n",
       "      <td>-0.134707</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtFinSF2</th>\n",
       "      <td>-0.138126</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LowQualFinSF</th>\n",
       "      <td>-0.150027</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Id</th>\n",
       "      <td>-0.162735</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <td>-0.162735</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>OverallCond</th>\n",
       "      <td>-0.170443</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>EnclosedPorch</th>\n",
       "      <td>-0.233483</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>KitchenAbvGr</th>\n",
       "      <td>-0.235659</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>YrSold</th>\n",
       "      <td>-0.262683</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PoolArea</th>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PoolQC</th>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               SalePrice\n",
       "SalePrice       1.000000\n",
       "OverallQual     0.855061\n",
       "GrLivArea       0.735129\n",
       "GarageArea      0.688249\n",
       "GarageCars      0.663441\n",
       "YearBuilt       0.658636\n",
       "TotalBsmtSF     0.616297\n",
       "GarageYrBlt     0.612514\n",
       "FullBath        0.579505\n",
       "MasVnrArea      0.571836\n",
       "TotRmsAbvGrd    0.553603\n",
       "1stFlrSF        0.550912\n",
       "YearRemodAdd    0.548330\n",
       "LotArea         0.497124\n",
       "Fireplaces      0.487907\n",
       "WoodDeckSF      0.451241\n",
       "2ndFlrSF        0.381076\n",
       "BsmtUnfSF       0.327020\n",
       "HalfBath        0.319304\n",
       "LotFrontage     0.302526\n",
       "OpenPorchSF     0.301960\n",
       "BsmtFinSF1      0.266713\n",
       "MoSold          0.256863\n",
       "BedroomAbvGr    0.233426\n",
       "BsmtFullBath    0.155689\n",
       "ScreenPorch     0.035930\n",
       "3SsnPorch      -0.019391\n",
       "BsmtHalfBath   -0.055100\n",
       "MSSubClass     -0.066819\n",
       "MiscVal        -0.134707\n",
       "BsmtFinSF2     -0.138126\n",
       "LowQualFinSF   -0.150027\n",
       "Id             -0.162735\n",
       "Unnamed: 0     -0.162735\n",
       "OverallCond    -0.170443\n",
       "EnclosedPorch  -0.233483\n",
       "KitchenAbvGr   -0.235659\n",
       "YrSold         -0.262683\n",
       "PoolArea             NaN\n",
       "PoolQC               NaN"
      ]
     },
     "execution_count": 634,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Calculate Correlation with respect to SalePrice\n",
    "corr=numeric.corr()\n",
    "cols=pd.DataFrame(corr['SalePrice'].sort_values(ascending=False))\n",
    "cols"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In above table I assumed that OverallQual(0.86) is very strongly correlated, variables with correlation factor between 0.73-0.61 have strong positive correlation, variables with correlation factor between 0.57-0.49 has moderate correlation with SalePrice.\n",
    "\n",
    "I found that variables which I assumed during exploration stage are present in the above list.\n",
    "OverallQual is 86%, GrLivArea is 74%, YearBuilt is 66%, TotalBsmtSF is 62%, GarageYrBlt is 60% & LotArea is 50% correlated with SalePrice. Also, I found other variables such as GarageArea,GarageCars having strong correlation with SalePrice which wasn't included in my assumption initially.\n",
    "\n",
    "Considering above correlation list, I chose to create linear models for three different set of variables & checked the models effectiveness.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### First Set of Variables\n",
    "I have chosen top 4 variables for first set which has correlation of ~69% & above. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
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       "    }\n",
       "\n",
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       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SalePrice</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>SalePrice</th>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>OverallQual</th>\n",
       "      <td>0.855061</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GrLivArea</th>\n",
       "      <td>0.735129</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GarageArea</th>\n",
       "      <td>0.688249</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             SalePrice\n",
       "SalePrice     1.000000\n",
       "OverallQual   0.855061\n",
       "GrLivArea     0.735129\n",
       "GarageArea    0.688249"
      ]
     },
     "execution_count": 635,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Correlation of top 4 numeric variables\n",
    "corr=numeric.corr()\n",
    "cols=pd.DataFrame(corr['SalePrice'].sort_values(ascending=False)[0:4])\n",
    "cols"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['SalePrice', 'OverallQual', 'GrLivArea', 'GarageArea'], dtype='object')"
      ]
     },
     "execution_count": 636,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Creating an array of index\n",
    "corr=numeric.corr()\n",
    "cols=pd.DataFrame(corr['SalePrice'].sort_values(ascending=False)[0:4]).index\n",
    "cols"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, I will pick X and Y variables and create regression model & check its effectiveness"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SalePrice</th>\n",
       "      <th>OverallQual</th>\n",
       "      <th>GrLivArea</th>\n",
       "      <th>GarageArea</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>208500</td>\n",
       "      <td>7</td>\n",
       "      <td>1710</td>\n",
       "      <td>548</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>181500</td>\n",
       "      <td>6</td>\n",
       "      <td>1262</td>\n",
       "      <td>460</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>223500</td>\n",
       "      <td>7</td>\n",
       "      <td>1786</td>\n",
       "      <td>608</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>140000</td>\n",
       "      <td>7</td>\n",
       "      <td>1717</td>\n",
       "      <td>642</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>250000</td>\n",
       "      <td>8</td>\n",
       "      <td>2198</td>\n",
       "      <td>836</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>185000</td>\n",
       "      <td>6</td>\n",
       "      <td>1470</td>\n",
       "      <td>420</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>214000</td>\n",
       "      <td>7</td>\n",
       "      <td>1588</td>\n",
       "      <td>472</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>94750</td>\n",
       "      <td>4</td>\n",
       "      <td>960</td>\n",
       "      <td>432</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>83000</td>\n",
       "      <td>5</td>\n",
       "      <td>835</td>\n",
       "      <td>366</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>128950</td>\n",
       "      <td>4</td>\n",
       "      <td>1225</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    SalePrice  OverallQual  GrLivArea  GarageArea\n",
       "0      208500            7       1710         548\n",
       "1      181500            6       1262         460\n",
       "2      223500            7       1786         608\n",
       "3      140000            7       1717         642\n",
       "4      250000            8       2198         836\n",
       "..        ...          ...        ...         ...\n",
       "95     185000            6       1470         420\n",
       "96     214000            7       1588         472\n",
       "97      94750            4        960         432\n",
       "98      83000            5        835         366\n",
       "99     128950            4       1225           0\n",
       "\n",
       "[100 rows x 4 columns]"
      ]
     },
     "execution_count": 637,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Checking X cols\n",
    "X=pd.DataFrame(data[cols])\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>OverallQual</th>\n",
       "      <th>GrLivArea</th>\n",
       "      <th>GarageArea</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>7</td>\n",
       "      <td>1710</td>\n",
       "      <td>548</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>6</td>\n",
       "      <td>1262</td>\n",
       "      <td>460</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>7</td>\n",
       "      <td>1786</td>\n",
       "      <td>608</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>7</td>\n",
       "      <td>1717</td>\n",
       "      <td>642</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>8</td>\n",
       "      <td>2198</td>\n",
       "      <td>836</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>6</td>\n",
       "      <td>1470</td>\n",
       "      <td>420</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>7</td>\n",
       "      <td>1588</td>\n",
       "      <td>472</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>4</td>\n",
       "      <td>960</td>\n",
       "      <td>432</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>5</td>\n",
       "      <td>835</td>\n",
       "      <td>366</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>4</td>\n",
       "      <td>1225</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    OverallQual  GrLivArea  GarageArea\n",
       "0             7       1710         548\n",
       "1             6       1262         460\n",
       "2             7       1786         608\n",
       "3             7       1717         642\n",
       "4             8       2198         836\n",
       "..          ...        ...         ...\n",
       "95            6       1470         420\n",
       "96            7       1588         472\n",
       "97            4        960         432\n",
       "98            5        835         366\n",
       "99            4       1225           0\n",
       "\n",
       "[100 rows x 3 columns]"
      ]
     },
     "execution_count": 638,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Pick out X cols, Y = SalePrice and drop SalePrice from X\n",
    "X=data[cols]\n",
    "Y=data['SalePrice']\n",
    "X= X.drop(['SalePrice'],axis=1)\n",
    "X"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After picking X and Y variables, its time to build Linear Regression Model and check its effectiveness using R². R² tells how well the data fit the regression model. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R² is :0.789158151143107\n"
     ]
    }
   ],
   "source": [
    "# Build Linear Regression Model & check how good is the model using R²\n",
    "from sklearn import linear_model\n",
    "\n",
    "lr=linear_model.LinearRegression()\n",
    "model=lr.fit(X,Y)\n",
    "predictions=model.predict(X)\n",
    "print(f\"R² is :{model.score(X,Y)}\") "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "R² of ~79% tells that ~79% of the variability in the target variable(i.e. Y) is explained by above independent variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 5.,  3.,  5., 13., 29., 24.,  8.,  8.,  3.,  2.]),\n",
       " array([-84932.65934685, -67293.91268757, -49655.16602829, -32016.41936902,\n",
       "        -14377.67270974,   3261.07394954,  20899.82060882,  38538.56726809,\n",
       "         56177.31392737,  73816.06058665,  91454.80724593]),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "execution_count": 640,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Histogram of predictions\n",
    "plt.hist(Y-predictions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above histogram of residuals tells that the residuals (i.e. error) are normally distributed around zero, verifying the underlying normality assumption for residual plots to be true.Next, lets looks at scatter plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x2b10d0da9a0>"
      ]
     },
     "execution_count": 641,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Scatter plot of predictions\n",
    "\n",
    "plt.scatter(predictions,Y,color='g')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above graph depicts a straight line with some outliers. But our model is good considering we used just three independent variables."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Second Set of Variables\n",
    "I have chosen top 8 variables for my second set of analysis with correlation factor of 60% and above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['SalePrice', 'OverallQual', 'GrLivArea', 'GarageArea', 'GarageCars',\n",
       "       'YearBuilt', 'TotalBsmtSF', 'GarageYrBlt'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 642,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Creating an array of index for top 8 numeric variables\n",
    "corr=numeric.corr()\n",
    "cols=pd.DataFrame(corr['SalePrice'].sort_values(ascending=False)[0:8]).index\n",
    "cols"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>OverallQual</th>\n",
       "      <th>GrLivArea</th>\n",
       "      <th>GarageArea</th>\n",
       "      <th>GarageCars</th>\n",
       "      <th>YearBuilt</th>\n",
       "      <th>TotalBsmtSF</th>\n",
       "      <th>GarageYrBlt</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>7</td>\n",
       "      <td>1710</td>\n",
       "      <td>548</td>\n",
       "      <td>2</td>\n",
       "      <td>2003</td>\n",
       "      <td>856</td>\n",
       "      <td>2003.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>6</td>\n",
       "      <td>1262</td>\n",
       "      <td>460</td>\n",
       "      <td>2</td>\n",
       "      <td>1976</td>\n",
       "      <td>1262</td>\n",
       "      <td>1976.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>7</td>\n",
       "      <td>1786</td>\n",
       "      <td>608</td>\n",
       "      <td>2</td>\n",
       "      <td>2001</td>\n",
       "      <td>920</td>\n",
       "      <td>2001.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>7</td>\n",
       "      <td>1717</td>\n",
       "      <td>642</td>\n",
       "      <td>3</td>\n",
       "      <td>1915</td>\n",
       "      <td>756</td>\n",
       "      <td>1998.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>8</td>\n",
       "      <td>2198</td>\n",
       "      <td>836</td>\n",
       "      <td>3</td>\n",
       "      <td>2000</td>\n",
       "      <td>1145</td>\n",
       "      <td>2000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>6</td>\n",
       "      <td>1470</td>\n",
       "      <td>420</td>\n",
       "      <td>2</td>\n",
       "      <td>1993</td>\n",
       "      <td>680</td>\n",
       "      <td>1993.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>7</td>\n",
       "      <td>1588</td>\n",
       "      <td>472</td>\n",
       "      <td>2</td>\n",
       "      <td>1999</td>\n",
       "      <td>1588</td>\n",
       "      <td>1999.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>4</td>\n",
       "      <td>960</td>\n",
       "      <td>432</td>\n",
       "      <td>1</td>\n",
       "      <td>1965</td>\n",
       "      <td>960</td>\n",
       "      <td>1965.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>5</td>\n",
       "      <td>835</td>\n",
       "      <td>366</td>\n",
       "      <td>1</td>\n",
       "      <td>1920</td>\n",
       "      <td>458</td>\n",
       "      <td>1920.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>4</td>\n",
       "      <td>1225</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1959</td>\n",
       "      <td>950</td>\n",
       "      <td>1959.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 7 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    OverallQual  GrLivArea  GarageArea  GarageCars  YearBuilt  TotalBsmtSF  \\\n",
       "0             7       1710         548           2       2003          856   \n",
       "1             6       1262         460           2       1976         1262   \n",
       "2             7       1786         608           2       2001          920   \n",
       "3             7       1717         642           3       1915          756   \n",
       "4             8       2198         836           3       2000         1145   \n",
       "..          ...        ...         ...         ...        ...          ...   \n",
       "95            6       1470         420           2       1993          680   \n",
       "96            7       1588         472           2       1999         1588   \n",
       "97            4        960         432           1       1965          960   \n",
       "98            5        835         366           1       1920          458   \n",
       "99            4       1225           0           0       1959          950   \n",
       "\n",
       "    GarageYrBlt  \n",
       "0        2003.0  \n",
       "1        1976.0  \n",
       "2        2001.0  \n",
       "3        1998.0  \n",
       "4        2000.0  \n",
       "..          ...  \n",
       "95       1993.0  \n",
       "96       1999.0  \n",
       "97       1965.0  \n",
       "98       1920.0  \n",
       "99       1959.0  \n",
       "\n",
       "[100 rows x 7 columns]"
      ]
     },
     "execution_count": 643,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Pick out X cols, Y = SalePrice and drop SalePrice from X\n",
    "X=data[cols]\n",
    "Y=data['SalePrice']\n",
    "X= X.drop(['SalePrice'],axis=1)\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R² is :0.8504244999297702\n"
     ]
    }
   ],
   "source": [
    "# Build Linear Regression Model & check how good is the model using R²\n",
    "from sklearn import linear_model\n",
    "\n",
    "lr=linear_model.LinearRegression()\n",
    "model=lr.fit(X,Y)\n",
    "predictions=model.predict(X)\n",
    "print(f\"R² is :{model.score(X,Y)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "R² of 85% tells that 85% of the variability in the target variable(i.e. Y) is explained by above independent variables.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 2.,  5.,  6., 27., 31., 13., 11.,  3.,  0.,  2.]),\n",
       " array([-74338.57768371, -57471.59283814, -40604.60799256, -23737.62314698,\n",
       "         -6870.6383014 ,   9996.34654417,  26863.33138975,  43730.31623533,\n",
       "         60597.30108091,  77464.28592648,  94331.27077206]),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "execution_count": 645,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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fbV031ufz7A7fV0xw+Q2D7bF/OunlZISanw+cMTT9j90y8n6O3Sn5vrVS86L67wB+ay2PNYsOppjE2LLK7+BEvihLDNLHgN9e1PYbwEPdoNwP/OrQc3PAHgZ7xf+cZ89Ofh6DPwP3M9hLfsHQa97Rte8fXmhWWe9fAw8CDzC4htHwgndjV9fDdHvm10jN+xlsC9zd3Y4uOGt2nE/y813J4CibR4AbJ7z8/iKDP60fGBrfKye1nKyy5gu6n/k3up//jV37S4BdwL7ufsNaqXmov58Cvg+8aNLfyZOo8XYGm5/+l8Ha+LWTGtvVfAe9vIMkNWjaR/tIkqbA8JekBhn+ktQgw1+SGmT4S1KDDH9JapDhL0kN+j/OwB2R77PJJwAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Histogram of predictions\n",
    "plt.hist(Y-predictions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above histogram of residuals tells that the residuals (i.e. error) are normally distributed around zero. Next, lets looks at scatter plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x2b10d1b7d30>"
      ]
     },
     "execution_count": 646,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Scatter plot of predictions\n",
    "\n",
    "plt.scatter(predictions,Y,color='orange')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From above graph, all data points looks close to a regression line which validates the effectiveness of our model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have improve effectiveness of our model from 79% to 85%. Lets now run third set of variables and see if we can further improve the effectiveness of our model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Third Set of Variables\n",
    "I have chosen top 14 variables for my third set of analysis. I consider all variables with correlation of ~50% or more.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SalePrice</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>SalePrice</th>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>OverallQual</th>\n",
       "      <td>0.855061</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GrLivArea</th>\n",
       "      <td>0.735129</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GarageArea</th>\n",
       "      <td>0.688249</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GarageCars</th>\n",
       "      <td>0.663441</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>YearBuilt</th>\n",
       "      <td>0.658636</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TotalBsmtSF</th>\n",
       "      <td>0.616297</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GarageYrBlt</th>\n",
       "      <td>0.612514</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FullBath</th>\n",
       "      <td>0.579505</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MasVnrArea</th>\n",
       "      <td>0.571836</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TotRmsAbvGrd</th>\n",
       "      <td>0.553603</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1stFlrSF</th>\n",
       "      <td>0.550912</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>YearRemodAdd</th>\n",
       "      <td>0.548330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LotArea</th>\n",
       "      <td>0.497124</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              SalePrice\n",
       "SalePrice      1.000000\n",
       "OverallQual    0.855061\n",
       "GrLivArea      0.735129\n",
       "GarageArea     0.688249\n",
       "GarageCars     0.663441\n",
       "YearBuilt      0.658636\n",
       "TotalBsmtSF    0.616297\n",
       "GarageYrBlt    0.612514\n",
       "FullBath       0.579505\n",
       "MasVnrArea     0.571836\n",
       "TotRmsAbvGrd   0.553603\n",
       "1stFlrSF       0.550912\n",
       "YearRemodAdd   0.548330\n",
       "LotArea        0.497124"
      ]
     },
     "execution_count": 647,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Correlation for top 14 variables\n",
    "corr=pd.DataFrame(numeric.corr())\n",
    "cols=pd.DataFrame(corr['SalePrice'].sort_values(ascending=False)[0:14])\n",
    "cols"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['SalePrice', 'OverallQual', 'GrLivArea', 'GarageArea', 'GarageCars',\n",
       "       'YearBuilt', 'TotalBsmtSF', 'GarageYrBlt', 'FullBath', 'MasVnrArea',\n",
       "       'TotRmsAbvGrd', '1stFlrSF', 'YearRemodAdd', 'LotArea'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 648,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Creating an array of index\n",
    "corr=pd.DataFrame(numeric.corr())\n",
    "cols=pd.DataFrame(corr['SalePrice'].sort_values(ascending=False)[0:14]).index\n",
    "cols"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>OverallQual</th>\n",
       "      <th>GrLivArea</th>\n",
       "      <th>GarageArea</th>\n",
       "      <th>GarageCars</th>\n",
       "      <th>YearBuilt</th>\n",
       "      <th>TotalBsmtSF</th>\n",
       "      <th>GarageYrBlt</th>\n",
       "      <th>FullBath</th>\n",
       "      <th>MasVnrArea</th>\n",
       "      <th>TotRmsAbvGrd</th>\n",
       "      <th>1stFlrSF</th>\n",
       "      <th>YearRemodAdd</th>\n",
       "      <th>LotArea</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>7</td>\n",
       "      <td>1710</td>\n",
       "      <td>548</td>\n",
       "      <td>2</td>\n",
       "      <td>2003</td>\n",
       "      <td>856</td>\n",
       "      <td>2003.0</td>\n",
       "      <td>2</td>\n",
       "      <td>196</td>\n",
       "      <td>8</td>\n",
       "      <td>856</td>\n",
       "      <td>2003</td>\n",
       "      <td>8450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>6</td>\n",
       "      <td>1262</td>\n",
       "      <td>460</td>\n",
       "      <td>2</td>\n",
       "      <td>1976</td>\n",
       "      <td>1262</td>\n",
       "      <td>1976.0</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>1262</td>\n",
       "      <td>1976</td>\n",
       "      <td>9600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>7</td>\n",
       "      <td>1786</td>\n",
       "      <td>608</td>\n",
       "      <td>2</td>\n",
       "      <td>2001</td>\n",
       "      <td>920</td>\n",
       "      <td>2001.0</td>\n",
       "      <td>2</td>\n",
       "      <td>162</td>\n",
       "      <td>6</td>\n",
       "      <td>920</td>\n",
       "      <td>2002</td>\n",
       "      <td>11250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>7</td>\n",
       "      <td>1717</td>\n",
       "      <td>642</td>\n",
       "      <td>3</td>\n",
       "      <td>1915</td>\n",
       "      <td>756</td>\n",
       "      <td>1998.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>7</td>\n",
       "      <td>961</td>\n",
       "      <td>1970</td>\n",
       "      <td>9550</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>8</td>\n",
       "      <td>2198</td>\n",
       "      <td>836</td>\n",
       "      <td>3</td>\n",
       "      <td>2000</td>\n",
       "      <td>1145</td>\n",
       "      <td>2000.0</td>\n",
       "      <td>2</td>\n",
       "      <td>350</td>\n",
       "      <td>9</td>\n",
       "      <td>1145</td>\n",
       "      <td>2000</td>\n",
       "      <td>14260</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>6</td>\n",
       "      <td>1470</td>\n",
       "      <td>420</td>\n",
       "      <td>2</td>\n",
       "      <td>1993</td>\n",
       "      <td>680</td>\n",
       "      <td>1993.0</td>\n",
       "      <td>2</td>\n",
       "      <td>68</td>\n",
       "      <td>6</td>\n",
       "      <td>680</td>\n",
       "      <td>1993</td>\n",
       "      <td>9765</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>7</td>\n",
       "      <td>1588</td>\n",
       "      <td>472</td>\n",
       "      <td>2</td>\n",
       "      <td>1999</td>\n",
       "      <td>1588</td>\n",
       "      <td>1999.0</td>\n",
       "      <td>2</td>\n",
       "      <td>183</td>\n",
       "      <td>6</td>\n",
       "      <td>1588</td>\n",
       "      <td>1999</td>\n",
       "      <td>10264</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>4</td>\n",
       "      <td>960</td>\n",
       "      <td>432</td>\n",
       "      <td>1</td>\n",
       "      <td>1965</td>\n",
       "      <td>960</td>\n",
       "      <td>1965.0</td>\n",
       "      <td>1</td>\n",
       "      <td>48</td>\n",
       "      <td>6</td>\n",
       "      <td>960</td>\n",
       "      <td>1965</td>\n",
       "      <td>10921</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>5</td>\n",
       "      <td>835</td>\n",
       "      <td>366</td>\n",
       "      <td>1</td>\n",
       "      <td>1920</td>\n",
       "      <td>458</td>\n",
       "      <td>1920.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>835</td>\n",
       "      <td>1950</td>\n",
       "      <td>10625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>4</td>\n",
       "      <td>1225</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1959</td>\n",
       "      <td>950</td>\n",
       "      <td>1959.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>1225</td>\n",
       "      <td>1959</td>\n",
       "      <td>9320</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 13 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    OverallQual  GrLivArea  GarageArea  GarageCars  YearBuilt  TotalBsmtSF  \\\n",
       "0             7       1710         548           2       2003          856   \n",
       "1             6       1262         460           2       1976         1262   \n",
       "2             7       1786         608           2       2001          920   \n",
       "3             7       1717         642           3       1915          756   \n",
       "4             8       2198         836           3       2000         1145   \n",
       "..          ...        ...         ...         ...        ...          ...   \n",
       "95            6       1470         420           2       1993          680   \n",
       "96            7       1588         472           2       1999         1588   \n",
       "97            4        960         432           1       1965          960   \n",
       "98            5        835         366           1       1920          458   \n",
       "99            4       1225           0           0       1959          950   \n",
       "\n",
       "    GarageYrBlt  FullBath  MasVnrArea  TotRmsAbvGrd  1stFlrSF  YearRemodAdd  \\\n",
       "0        2003.0         2         196             8       856          2003   \n",
       "1        1976.0         2           0             6      1262          1976   \n",
       "2        2001.0         2         162             6       920          2002   \n",
       "3        1998.0         1           0             7       961          1970   \n",
       "4        2000.0         2         350             9      1145          2000   \n",
       "..          ...       ...         ...           ...       ...           ...   \n",
       "95       1993.0         2          68             6       680          1993   \n",
       "96       1999.0         2         183             6      1588          1999   \n",
       "97       1965.0         1          48             6       960          1965   \n",
       "98       1920.0         1           0             5       835          1950   \n",
       "99       1959.0         1           0             6      1225          1959   \n",
       "\n",
       "    LotArea  \n",
       "0      8450  \n",
       "1      9600  \n",
       "2     11250  \n",
       "3      9550  \n",
       "4     14260  \n",
       "..      ...  \n",
       "95     9765  \n",
       "96    10264  \n",
       "97    10921  \n",
       "98    10625  \n",
       "99     9320  \n",
       "\n",
       "[100 rows x 13 columns]"
      ]
     },
     "execution_count": 649,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Pick out X cols, Y = SalePrice and drop SalePrice from X\n",
    "X=data[cols]\n",
    "Y=data['SalePrice']\n",
    "X= X.drop(['SalePrice'],axis=1)\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R² is :0.8776633426562515\n"
     ]
    }
   ],
   "source": [
    "# Build Linear Regression Model & check how good is the model using R²\n",
    "from sklearn import linear_model\n",
    "\n",
    "lr=linear_model.LinearRegression()\n",
    "model=lr.fit(X,Y)\n",
    "predictions=model.predict(X)\n",
    "print(f\"R² is :{model.score(X,Y)}\") "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "R² of ~88% tells that ~88% of the variability in the target variable(i.e. Y) is explained by above independent variables\n",
    "Lets now assess the quality of regression by looking at the error i.e. Y-predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 1.,  0.,  5., 16., 25., 29., 12., 10.,  1.,  1.]),\n",
       " array([-86294.99548079, -69503.04255124, -52711.08962169, -35919.13669214,\n",
       "        -19127.18376258,  -2335.23083303,  14456.72209652,  31248.67502607,\n",
       "         48040.62795562,  64832.58088517,  81624.53381472]),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "execution_count": 651,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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OC+v5OdnXcsNco43/M8DvLhr7LeCBbuXfC/xG33NzwH56Z5T/gme/3PQien9SHaR3hvnsvte8rxs/2P+LX2XevwHuB+6jdy2Z/o3n2i7Xg3Rntack80F6x/X2dbeFDXRq1/MKf75L6H3y42Hg2nXYhn+V3p/Z9/Wt40vWaltZZeazu9/7t7tt4Npu/BXAXcBD3f2macncvefPAT8EXrbW/ybHcfObmJLUqOZOYkqSeixwSWqUBS5JjbLAJalRFrgkNcoCl6RGWeCS1CgLXJIa9f+9tRhdaKTKTgAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Histogram of predictions\n",
    "plt.hist(Y-predictions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above histogram of residuals tells that the residuals (i.e. error) are normally distributed around zero, verifying the underlying normality assumption for residual plots to be true. Next, lets looks at scatter plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x2b10d2a6160>"
      ]
     },
     "execution_count": 652,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Scatter plot of predictions\n",
    "\n",
    "plt.scatter(predictions,Y,color='r')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From above graph, all data points looks close to a regression line which validates the effectiveness of our model.\n",
    "Also, the effectiveness of our model has further been improved from 85% to 88%."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "[Back to top](#Index)\n",
    "\n",
    "## 3. Project Description\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Back to top](#Index)\n",
    "\n",
    "### 3.1 Linear Regression\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable and one or more independent variables. The most common form of regression analysis is linear regression, in which one finds the line that most closely fits the data according to a specific mathematical criterion.\n",
    "\n",
    "Multiple Linear Regression Equation is given by:   \n",
    "Y=X1β1 + X2β2 + X3β3...   \n",
    "where Y is dependent variable i.e. SalePrice   \n",
    "X1,X2,X3 are indepenedent variables which will help in predicting value for Y   \n",
    "β1,β2,β3 are the betas   \n",
    "\n",
    "For the computation of linear regression, I imported module 'linear_model' from python library 'sklearn'. I used below method to predict Y based on X independent variables:   \n",
    "\n",
    "from sklearn import linear_model           \n",
    "lr=linear_model.LinearRegression()                 \n",
    "model=lr.fit(X,Y)                 \n",
    "predictions=model.predict(X)               \n",
    "print(f\"R² is :{model.score(X,Y)}\")                \n",
    "\n",
    "I checked effectiveness of model using R-squared. R²(The coefficient of determination) is a number between 0 and 1 that measures how well a statistical model predicts an outcome.Generally, a higher coefficient indicates a better fit for the model.\n",
    "\n",
    "After that I analysis histogram of residuals(i.e. error between actual value of 'Y' & predicted value 'Y') to assess quality of regression model.The Histogram of the Residuals can be used to check whether the variance is normally distributed or not. If the histogram indicates that random error is not normally distributed, it suggests that the model's underlying assumptions may have been violated.       \n",
    "\n",
    "I also looked at scatter plot for predicted versus actual values of Y. Scatter plots showed straight line in all three models which validates the effectiveness of models.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Back to top](#Index)\n",
    "\n",
    "### 3.2 Analysis \n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As shown above, I decided to create price prediction model on three set of variables. As I added more independent variables, I was able to improve effectiveness of the models. \n",
    "\n",
    "For first set of data, I selected the variables with correlation of ~69% or more with SalePrice(i.e. 3 variables:OverallQual,GrLivArea & GarageArea). For second set, I chose variables with correlation of 60% or more(i.e. 7 variables: OverallQual, GrLivArea, GarageArea,GarageCars, YearBuilt,TotalBsmtSF, GarageYrBlt). For third set,I chose the variables with correlation of ~50% or more (i.e. 13 variables:OverallQual, GrLivArea, GarageArea,GarageCars, YearBuilt,TotalBsmtSF, GarageYrBlt,FullBath,MasVnrArea,TotRmsAbvGrd,1stFlrSF,YearRemodAdd,LotArea)\n",
    "\n",
    "Model improved from 79%(from first set of variables) to 85%(for second set of variables) & then to 88%(for third set of variables). \n",
    "\n",
    "My prediction improved by 4% on first set of variables from the prediction of Dr. Williams (which was 75% on 2 variables: OverallQual & MasVnrArea). On second set my prediction improved by 2% from that of Dr. Williams(which was 83% on 6 variables:OverallQual, GrLivArea, GarageArea,GarageCars, YearBuilt). I was able to further improve my own model by 3% on third set of variables.\n",
    "\n",
    "Findings & analysis from each set of data has been shown in earlier sections."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Back to top](#Index)\n",
    "\n",
    "### 3.3 Results\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First set of variables: R² is 79%, for second set of variables: R² is 85% & for third set of variables: R² is 88%.\n",
    "\n",
    "Third model with 13 independent variables performed the best as 88% of variability in the target variable(i.e. Y) is explained by these independent variables. This shows that adding more independent variables improves effectiveness of the models. \n",
    "\n",
    "The Histogram of the Residuals showed the residuals (i.e. error) are normally distributed around zero for all three models. Scatter plots for predicted versus actual values for Y also showed a straight line for all three models.\n",
    "\n",
    "Please refer earlier sections for code."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Back to top](#Index)\n",
    "\n",
    "### 3.4 Verify Your Model Against Test Data\n",
    "\n",
    "I verified third model against Test Data & found R² for test data is 84% versus 88% for actual data. R² for test data at 84% is still higher which shows our model is effective.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I am going to test my third model(i.e. model with 13 independent variables & highest R² value) against test data. I started with loading the test data and looking at the shape and head of it to get a sense of the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<bound method NDFrame.head of     Unnamed: 0   Id  MSSubClass MSZoning  LotFrontage  LotArea Street Alley  \\\n",
       "0          100  101          20       RL          NaN    10603   Pave   NaN   \n",
       "1          101  102          60       RL         77.0     9206   Pave   NaN   \n",
       "2          102  103          90       RL         64.0     7018   Pave   NaN   \n",
       "3          103  104          20       RL         94.0    10402   Pave   NaN   \n",
       "4          104  105          50       RM          NaN     7758   Pave   NaN   \n",
       "..         ...  ...         ...      ...          ...      ...    ...   ...   \n",
       "95         195  196         160       RL         24.0     2280   Pave   NaN   \n",
       "96         196  197          20       RL         79.0     9416   Pave   NaN   \n",
       "97         197  198          75       RL        174.0    25419   Pave   NaN   \n",
       "98         198  199          75       RM         92.0     5520   Pave   NaN   \n",
       "99         199  200          20       RL         76.0     9591   Pave   NaN   \n",
       "\n",
       "   LotShape LandContour  ... PoolArea PoolQC  Fence MiscFeature MiscVal  \\\n",
       "0       IR1         Lvl  ...        0    NaN    NaN         NaN       0   \n",
       "1       Reg         Lvl  ...        0    NaN    NaN         NaN       0   \n",
       "2       Reg         Bnk  ...        0    NaN    NaN         NaN       0   \n",
       "3       IR1         Lvl  ...        0    NaN    NaN         NaN       0   \n",
       "4       Reg         Lvl  ...        0    NaN    NaN         NaN       0   \n",
       "..      ...         ...  ...      ...    ...    ...         ...     ...   \n",
       "95      Reg         Lvl  ...        0    NaN    NaN         NaN       0   \n",
       "96      Reg         Lvl  ...        0    NaN    NaN         NaN       0   \n",
       "97      Reg         Lvl  ...      512     Ex  GdPrv         NaN       0   \n",
       "98      Reg         Lvl  ...        0    NaN  MnPrv         NaN       0   \n",
       "99      Reg         Lvl  ...        0    NaN    NaN         NaN       0   \n",
       "\n",
       "   MoSold YrSold SaleType  SaleCondition  SalePrice  \n",
       "0       2   2010       WD         Normal     205000  \n",
       "1       6   2010       WD         Normal     178000  \n",
       "2       6   2009       WD         Alloca     118964  \n",
       "3       5   2010       WD         Normal     198900  \n",
       "4       6   2007       WD         Normal     169500  \n",
       "..    ...    ...      ...            ...        ...  \n",
       "95      7   2009       WD         Normal     148500  \n",
       "96      9   2007      New        Partial     311872  \n",
       "97      3   2006       WD        Abnorml     235000  \n",
       "98      7   2009       WD        Abnorml     104000  \n",
       "99      1   2009       WD         Normal     274900  \n",
       "\n",
       "[100 rows x 82 columns]>"
      ]
     },
     "execution_count": 653,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test=pd.read_csv('jtest.csv')\n",
    "test.shape \n",
    "test.head"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Test data too has 100 rows & 82 columns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>MiscFeature</th>\n",
       "      <td>99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PoolQC</th>\n",
       "      <td>99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alley</th>\n",
       "      <td>97</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Fence</th>\n",
       "      <td>76</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FireplaceQu</th>\n",
       "      <td>43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LotFrontage</th>\n",
       "      <td>22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GarageType</th>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GarageYrBlt</th>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GarageFinish</th>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GarageQual</th>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GarageCond</th>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtFinType1</th>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtQual</th>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtCond</th>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtExposure</th>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtFinType2</th>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>KitchenAbvGr</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Functional</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BedroomAbvGr</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HalfBath</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               0\n",
       "MiscFeature   99\n",
       "PoolQC        99\n",
       "Alley         97\n",
       "Fence         76\n",
       "FireplaceQu   43\n",
       "LotFrontage   22\n",
       "GarageType     9\n",
       "GarageYrBlt    9\n",
       "GarageFinish   9\n",
       "GarageQual     9\n",
       "GarageCond     9\n",
       "BsmtFinType1   3\n",
       "BsmtQual       3\n",
       "BsmtCond       3\n",
       "BsmtExposure   3\n",
       "BsmtFinType2   3\n",
       "KitchenAbvGr   0\n",
       "Functional     0\n",
       "BedroomAbvGr   0\n",
       "HalfBath       0"
      ]
     },
     "execution_count": 654,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Checking Nulls in test data\n",
    "nulls=pd.DataFrame(test.isnull().sum().sort_values(ascending=False))[0:20]\n",
    "nulls"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above table shows that 16 columns has null values in the test data. Next, we can check nulls in numerical columns of test data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>Id</th>\n",
       "      <th>MSSubClass</th>\n",
       "      <th>LotFrontage</th>\n",
       "      <th>LotArea</th>\n",
       "      <th>OverallQual</th>\n",
       "      <th>OverallCond</th>\n",
       "      <th>YearBuilt</th>\n",
       "      <th>YearRemodAdd</th>\n",
       "      <th>MasVnrArea</th>\n",
       "      <th>...</th>\n",
       "      <th>WoodDeckSF</th>\n",
       "      <th>OpenPorchSF</th>\n",
       "      <th>EnclosedPorch</th>\n",
       "      <th>3SsnPorch</th>\n",
       "      <th>ScreenPorch</th>\n",
       "      <th>PoolArea</th>\n",
       "      <th>MiscVal</th>\n",
       "      <th>MoSold</th>\n",
       "      <th>YrSold</th>\n",
       "      <th>SalePrice</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>100</td>\n",
       "      <td>101</td>\n",
       "      <td>20</td>\n",
       "      <td>NaN</td>\n",
       "      <td>10603</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>1977</td>\n",
       "      <td>2001</td>\n",
       "      <td>28.0</td>\n",
       "      <td>...</td>\n",
       "      <td>168</td>\n",
       "      <td>68</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "      <td>2010</td>\n",
       "      <td>205000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>101</td>\n",
       "      <td>102</td>\n",
       "      <td>60</td>\n",
       "      <td>77.0</td>\n",
       "      <td>9206</td>\n",
       "      <td>6</td>\n",
       "      <td>5</td>\n",
       "      <td>1985</td>\n",
       "      <td>1985</td>\n",
       "      <td>336.0</td>\n",
       "      <td>...</td>\n",
       "      <td>192</td>\n",
       "      <td>46</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>2010</td>\n",
       "      <td>178000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>102</td>\n",
       "      <td>103</td>\n",
       "      <td>90</td>\n",
       "      <td>64.0</td>\n",
       "      <td>7018</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>1979</td>\n",
       "      <td>1979</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>2009</td>\n",
       "      <td>118964</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>103</td>\n",
       "      <td>104</td>\n",
       "      <td>20</td>\n",
       "      <td>94.0</td>\n",
       "      <td>10402</td>\n",
       "      <td>7</td>\n",
       "      <td>5</td>\n",
       "      <td>2009</td>\n",
       "      <td>2009</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>36</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>2010</td>\n",
       "      <td>198900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>104</td>\n",
       "      <td>105</td>\n",
       "      <td>50</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7758</td>\n",
       "      <td>7</td>\n",
       "      <td>4</td>\n",
       "      <td>1931</td>\n",
       "      <td>1950</td>\n",
       "      <td>600.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>184</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>2007</td>\n",
       "      <td>169500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>195</td>\n",
       "      <td>196</td>\n",
       "      <td>160</td>\n",
       "      <td>24.0</td>\n",
       "      <td>2280</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>1976</td>\n",
       "      <td>1976</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>87</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>7</td>\n",
       "      <td>2009</td>\n",
       "      <td>148500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>196</td>\n",
       "      <td>197</td>\n",
       "      <td>20</td>\n",
       "      <td>79.0</td>\n",
       "      <td>9416</td>\n",
       "      <td>7</td>\n",
       "      <td>5</td>\n",
       "      <td>2007</td>\n",
       "      <td>2007</td>\n",
       "      <td>205.0</td>\n",
       "      <td>...</td>\n",
       "      <td>171</td>\n",
       "      <td>138</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>266</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>9</td>\n",
       "      <td>2007</td>\n",
       "      <td>311872</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>197</td>\n",
       "      <td>198</td>\n",
       "      <td>75</td>\n",
       "      <td>174.0</td>\n",
       "      <td>25419</td>\n",
       "      <td>8</td>\n",
       "      <td>4</td>\n",
       "      <td>1918</td>\n",
       "      <td>1990</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>16</td>\n",
       "      <td>552</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>512</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>2006</td>\n",
       "      <td>235000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>198</td>\n",
       "      <td>199</td>\n",
       "      <td>75</td>\n",
       "      <td>92.0</td>\n",
       "      <td>5520</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>1912</td>\n",
       "      <td>1950</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>198</td>\n",
       "      <td>30</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>7</td>\n",
       "      <td>2009</td>\n",
       "      <td>104000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>199</td>\n",
       "      <td>200</td>\n",
       "      <td>20</td>\n",
       "      <td>76.0</td>\n",
       "      <td>9591</td>\n",
       "      <td>8</td>\n",
       "      <td>5</td>\n",
       "      <td>2004</td>\n",
       "      <td>2005</td>\n",
       "      <td>262.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>26</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>170</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>2009</td>\n",
       "      <td>274900</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 39 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    Unnamed: 0   Id  MSSubClass  LotFrontage  LotArea  OverallQual  \\\n",
       "0          100  101          20          NaN    10603            6   \n",
       "1          101  102          60         77.0     9206            6   \n",
       "2          102  103          90         64.0     7018            5   \n",
       "3          103  104          20         94.0    10402            7   \n",
       "4          104  105          50          NaN     7758            7   \n",
       "..         ...  ...         ...          ...      ...          ...   \n",
       "95         195  196         160         24.0     2280            6   \n",
       "96         196  197          20         79.0     9416            7   \n",
       "97         197  198          75        174.0    25419            8   \n",
       "98         198  199          75         92.0     5520            6   \n",
       "99         199  200          20         76.0     9591            8   \n",
       "\n",
       "    OverallCond  YearBuilt  YearRemodAdd  MasVnrArea  ...  WoodDeckSF  \\\n",
       "0             7       1977          2001        28.0  ...         168   \n",
       "1             5       1985          1985       336.0  ...         192   \n",
       "2             5       1979          1979         0.0  ...           0   \n",
       "3             5       2009          2009         0.0  ...           0   \n",
       "4             4       1931          1950       600.0  ...           0   \n",
       "..          ...        ...           ...         ...  ...         ...   \n",
       "95            6       1976          1976         0.0  ...          87   \n",
       "96            5       2007          2007       205.0  ...         171   \n",
       "97            4       1918          1990         0.0  ...           0   \n",
       "98            6       1912          1950         0.0  ...           0   \n",
       "99            5       2004          2005       262.0  ...           0   \n",
       "\n",
       "    OpenPorchSF  EnclosedPorch  3SsnPorch  ScreenPorch  PoolArea  MiscVal  \\\n",
       "0            68              0          0            0         0        0   \n",
       "1            46              0          0            0         0        0   \n",
       "2             0              0          0            0         0        0   \n",
       "3            36              0          0            0         0        0   \n",
       "4             0              0          0          184         0        0   \n",
       "..          ...            ...        ...          ...       ...      ...   \n",
       "95            0              0          0            0         0        0   \n",
       "96          138              0          0          266         0        0   \n",
       "97           16            552          0            0       512        0   \n",
       "98          198             30          0            0         0        0   \n",
       "99           26              0          0          170         0        0   \n",
       "\n",
       "    MoSold  YrSold  SalePrice  \n",
       "0        2    2010     205000  \n",
       "1        6    2010     178000  \n",
       "2        6    2009     118964  \n",
       "3        5    2010     198900  \n",
       "4        6    2007     169500  \n",
       "..     ...     ...        ...  \n",
       "95       7    2009     148500  \n",
       "96       9    2007     311872  \n",
       "97       3    2006     235000  \n",
       "98       7    2009     104000  \n",
       "99       1    2009     274900  \n",
       "\n",
       "[100 rows x 39 columns]"
      ]
     },
     "execution_count": 655,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Select numeric Columns\n",
    "numeric=pd.DataFrame(test.select_dtypes(include=[np.number]))\n",
    "numeric "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>LotFrontage</th>\n",
       "      <td>22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GarageYrBlt</th>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>WoodDeckSF</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BedroomAbvGr</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>KitchenAbvGr</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TotRmsAbvGrd</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Fireplaces</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GarageCars</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GarageArea</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>OpenPorchSF</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FullBath</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>EnclosedPorch</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3SsnPorch</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ScreenPorch</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PoolArea</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MiscVal</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MoSold</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>YrSold</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HalfBath</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtHalfBath</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Id</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtFullBath</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MSSubClass</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LotArea</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>OverallQual</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>OverallCond</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>YearBuilt</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>YearRemodAdd</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MasVnrArea</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtFinSF1</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtFinSF2</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtUnfSF</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TotalBsmtSF</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1stFlrSF</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2ndFlrSF</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LowQualFinSF</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GrLivArea</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SalePrice</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                0\n",
       "LotFrontage    22\n",
       "GarageYrBlt     9\n",
       "Unnamed: 0      0\n",
       "WoodDeckSF      0\n",
       "BedroomAbvGr    0\n",
       "KitchenAbvGr    0\n",
       "TotRmsAbvGrd    0\n",
       "Fireplaces      0\n",
       "GarageCars      0\n",
       "GarageArea      0\n",
       "OpenPorchSF     0\n",
       "FullBath        0\n",
       "EnclosedPorch   0\n",
       "3SsnPorch       0\n",
       "ScreenPorch     0\n",
       "PoolArea        0\n",
       "MiscVal         0\n",
       "MoSold          0\n",
       "YrSold          0\n",
       "HalfBath        0\n",
       "BsmtHalfBath    0\n",
       "Id              0\n",
       "BsmtFullBath    0\n",
       "MSSubClass      0\n",
       "LotArea         0\n",
       "OverallQual     0\n",
       "OverallCond     0\n",
       "YearBuilt       0\n",
       "YearRemodAdd    0\n",
       "MasVnrArea      0\n",
       "BsmtFinSF1      0\n",
       "BsmtFinSF2      0\n",
       "BsmtUnfSF       0\n",
       "TotalBsmtSF     0\n",
       "1stFlrSF        0\n",
       "2ndFlrSF        0\n",
       "LowQualFinSF    0\n",
       "GrLivArea       0\n",
       "SalePrice       0"
      ]
     },
     "execution_count": 656,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Checking nulls in Numerical columns\n",
    "nulls=pd.DataFrame(test.select_dtypes(include=[np.number]).isnull().sum().sort_values(ascending=False))\n",
    "nulls"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above table displays there are nulls in two numerical columns. \n",
    "\n",
    "There appears to be 9 null values in Column 'GarageYrBlt' which is one of my variable of interest for predicting house prices.  Instead of using interpolate to replace value in GarageYrBlt, I will replace the missing values with the corresponding value from Col YearBuilt. My assumption is garage was built in the same year when the house was built.\n",
    "\n",
    "For remaining numeric columns having null values, I will clean the data using interpolate & dropna function.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 82)"
      ]
     },
     "execution_count": 657,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Replacing Null Values in GarageYrBlt with corresponding values in col YearBuilt\n",
    "pd.DataFrame(test['GarageYrBlt'].fillna(value=test['YearBuilt'],inplace=True))\n",
    "test.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    <tr>\n",
       "      <th>BedroomAbvGr</th>\n",
       "      <td>0</td>\n",
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       "      <th>KitchenAbvGr</th>\n",
       "      <td>0</td>\n",
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       "      <th>TotRmsAbvGrd</th>\n",
       "      <td>0</td>\n",
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       "      <th>Fireplaces</th>\n",
       "      <td>0</td>\n",
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       "      <th>GarageYrBlt</th>\n",
       "      <td>0</td>\n",
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       "      <th>GarageCars</th>\n",
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       "      <th>GarageArea</th>\n",
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       "    <tr>\n",
       "      <th>OpenPorchSF</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FullBath</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>EnclosedPorch</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3SsnPorch</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ScreenPorch</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PoolArea</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MiscVal</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MoSold</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>YrSold</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HalfBath</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtHalfBath</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Id</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtFullBath</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MSSubClass</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LotArea</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>OverallQual</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>OverallCond</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>YearBuilt</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>YearRemodAdd</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MasVnrArea</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtFinSF1</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtFinSF2</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtUnfSF</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TotalBsmtSF</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1stFlrSF</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2ndFlrSF</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LowQualFinSF</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GrLivArea</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SalePrice</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                0\n",
       "LotFrontage    22\n",
       "Unnamed: 0      0\n",
       "WoodDeckSF      0\n",
       "BedroomAbvGr    0\n",
       "KitchenAbvGr    0\n",
       "TotRmsAbvGrd    0\n",
       "Fireplaces      0\n",
       "GarageYrBlt     0\n",
       "GarageCars      0\n",
       "GarageArea      0\n",
       "OpenPorchSF     0\n",
       "FullBath        0\n",
       "EnclosedPorch   0\n",
       "3SsnPorch       0\n",
       "ScreenPorch     0\n",
       "PoolArea        0\n",
       "MiscVal         0\n",
       "MoSold          0\n",
       "YrSold          0\n",
       "HalfBath        0\n",
       "BsmtHalfBath    0\n",
       "Id              0\n",
       "BsmtFullBath    0\n",
       "MSSubClass      0\n",
       "LotArea         0\n",
       "OverallQual     0\n",
       "OverallCond     0\n",
       "YearBuilt       0\n",
       "YearRemodAdd    0\n",
       "MasVnrArea      0\n",
       "BsmtFinSF1      0\n",
       "BsmtFinSF2      0\n",
       "BsmtUnfSF       0\n",
       "TotalBsmtSF     0\n",
       "1stFlrSF        0\n",
       "2ndFlrSF        0\n",
       "LowQualFinSF    0\n",
       "GrLivArea       0\n",
       "SalePrice       0"
      ]
     },
     "execution_count": 658,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Checking nulls in Numerical columns to make sure GarageYrBlt has no nulls\n",
    "nulls=pd.DataFrame(test.select_dtypes(include=[np.number]).isnull().sum().sort_values(ascending=False))\n",
    "nulls"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Changed data type of GarageYrBlt from float to integer because year should be an integer value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 38)"
      ]
     },
     "execution_count": 659,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Clean nulls for remaining numeric columns using interpolate & dropna\n",
    "test=pd.DataFrame(test.select_dtypes(include=[np.number])).interpolate().dropna(axis=1)\n",
    "test.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, I chose the same independents variables(X) for predicting Sale Price (i.e. dependent variable Y) which I use on third set of data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>OverallQual</th>\n",
       "      <th>GrLivArea</th>\n",
       "      <th>GarageArea</th>\n",
       "      <th>GarageCars</th>\n",
       "      <th>YearBuilt</th>\n",
       "      <th>TotalBsmtSF</th>\n",
       "      <th>GarageYrBlt</th>\n",
       "      <th>FullBath</th>\n",
       "      <th>MasVnrArea</th>\n",
       "      <th>TotRmsAbvGrd</th>\n",
       "      <th>1stFlrSF</th>\n",
       "      <th>YearRemodAdd</th>\n",
       "      <th>LotArea</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>6</td>\n",
       "      <td>1610</td>\n",
       "      <td>480</td>\n",
       "      <td>2</td>\n",
       "      <td>1977</td>\n",
       "      <td>1610</td>\n",
       "      <td>1977.0</td>\n",
       "      <td>2</td>\n",
       "      <td>28.0</td>\n",
       "      <td>6</td>\n",
       "      <td>1610</td>\n",
       "      <td>2001</td>\n",
       "      <td>10603</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>6</td>\n",
       "      <td>1732</td>\n",
       "      <td>476</td>\n",
       "      <td>2</td>\n",
       "      <td>1985</td>\n",
       "      <td>741</td>\n",
       "      <td>1985.0</td>\n",
       "      <td>2</td>\n",
       "      <td>336.0</td>\n",
       "      <td>7</td>\n",
       "      <td>977</td>\n",
       "      <td>1985</td>\n",
       "      <td>9206</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5</td>\n",
       "      <td>1535</td>\n",
       "      <td>410</td>\n",
       "      <td>2</td>\n",
       "      <td>1979</td>\n",
       "      <td>0</td>\n",
       "      <td>1979.0</td>\n",
       "      <td>2</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8</td>\n",
       "      <td>1535</td>\n",
       "      <td>1979</td>\n",
       "      <td>7018</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>7</td>\n",
       "      <td>1226</td>\n",
       "      <td>740</td>\n",
       "      <td>3</td>\n",
       "      <td>2009</td>\n",
       "      <td>1226</td>\n",
       "      <td>2009.0</td>\n",
       "      <td>2</td>\n",
       "      <td>0.0</td>\n",
       "      <td>6</td>\n",
       "      <td>1226</td>\n",
       "      <td>2009</td>\n",
       "      <td>10402</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>7</td>\n",
       "      <td>1818</td>\n",
       "      <td>240</td>\n",
       "      <td>1</td>\n",
       "      <td>1931</td>\n",
       "      <td>1040</td>\n",
       "      <td>1951.0</td>\n",
       "      <td>1</td>\n",
       "      <td>600.0</td>\n",
       "      <td>7</td>\n",
       "      <td>1226</td>\n",
       "      <td>1950</td>\n",
       "      <td>7758</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>6</td>\n",
       "      <td>1456</td>\n",
       "      <td>440</td>\n",
       "      <td>2</td>\n",
       "      <td>1976</td>\n",
       "      <td>855</td>\n",
       "      <td>1976.0</td>\n",
       "      <td>2</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7</td>\n",
       "      <td>855</td>\n",
       "      <td>1976</td>\n",
       "      <td>2280</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>7</td>\n",
       "      <td>1726</td>\n",
       "      <td>786</td>\n",
       "      <td>3</td>\n",
       "      <td>2007</td>\n",
       "      <td>1726</td>\n",
       "      <td>2007.0</td>\n",
       "      <td>2</td>\n",
       "      <td>205.0</td>\n",
       "      <td>8</td>\n",
       "      <td>1726</td>\n",
       "      <td>2007</td>\n",
       "      <td>9416</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>8</td>\n",
       "      <td>3112</td>\n",
       "      <td>795</td>\n",
       "      <td>2</td>\n",
       "      <td>1918</td>\n",
       "      <td>1360</td>\n",
       "      <td>1918.0</td>\n",
       "      <td>2</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8</td>\n",
       "      <td>1360</td>\n",
       "      <td>1990</td>\n",
       "      <td>25419</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>6</td>\n",
       "      <td>2229</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1912</td>\n",
       "      <td>755</td>\n",
       "      <td>1912.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8</td>\n",
       "      <td>929</td>\n",
       "      <td>1950</td>\n",
       "      <td>5520</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>8</td>\n",
       "      <td>1713</td>\n",
       "      <td>856</td>\n",
       "      <td>3</td>\n",
       "      <td>2004</td>\n",
       "      <td>1713</td>\n",
       "      <td>2004.0</td>\n",
       "      <td>2</td>\n",
       "      <td>262.0</td>\n",
       "      <td>7</td>\n",
       "      <td>1713</td>\n",
       "      <td>2005</td>\n",
       "      <td>9591</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 13 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    OverallQual  GrLivArea  GarageArea  GarageCars  YearBuilt  TotalBsmtSF  \\\n",
       "0             6       1610         480           2       1977         1610   \n",
       "1             6       1732         476           2       1985          741   \n",
       "2             5       1535         410           2       1979            0   \n",
       "3             7       1226         740           3       2009         1226   \n",
       "4             7       1818         240           1       1931         1040   \n",
       "..          ...        ...         ...         ...        ...          ...   \n",
       "95            6       1456         440           2       1976          855   \n",
       "96            7       1726         786           3       2007         1726   \n",
       "97            8       3112         795           2       1918         1360   \n",
       "98            6       2229           0           0       1912          755   \n",
       "99            8       1713         856           3       2004         1713   \n",
       "\n",
       "    GarageYrBlt  FullBath  MasVnrArea  TotRmsAbvGrd  1stFlrSF  YearRemodAdd  \\\n",
       "0        1977.0         2        28.0             6      1610          2001   \n",
       "1        1985.0         2       336.0             7       977          1985   \n",
       "2        1979.0         2         0.0             8      1535          1979   \n",
       "3        2009.0         2         0.0             6      1226          2009   \n",
       "4        1951.0         1       600.0             7      1226          1950   \n",
       "..          ...       ...         ...           ...       ...           ...   \n",
       "95       1976.0         2         0.0             7       855          1976   \n",
       "96       2007.0         2       205.0             8      1726          2007   \n",
       "97       1918.0         2         0.0             8      1360          1990   \n",
       "98       1912.0         1         0.0             8       929          1950   \n",
       "99       2004.0         2       262.0             7      1713          2005   \n",
       "\n",
       "    LotArea  \n",
       "0     10603  \n",
       "1      9206  \n",
       "2      7018  \n",
       "3     10402  \n",
       "4      7758  \n",
       "..      ...  \n",
       "95     2280  \n",
       "96     9416  \n",
       "97    25419  \n",
       "98     5520  \n",
       "99     9591  \n",
       "\n",
       "[100 rows x 13 columns]"
      ]
     },
     "execution_count": 660,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X=test[cols]\n",
    "Y=X['SalePrice']\n",
    "X=X.drop(['SalePrice'],axis=1)\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R² is :0.8385090301054547\n"
     ]
    }
   ],
   "source": [
    "# Build Linear Regression Model & check how good is the model using R²\n",
    "model=linear_model.LinearRegression().fit(X,Y)\n",
    "predictions=model.predict(X)\n",
    "print(f\"R² is :{model.score(X,Y)}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "R² of ~84% tells that ~84% of the variability in the target variable(i.e. Y) is explained by above independent variables\n",
    "This shows that our model is still good at 84% on the data we haven't seen versus ~88% on the data we have seen.\n",
    "Lets now assess the quality of regression by looking at the error i.e. Y-predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 1.,  1.,  4., 11., 26., 30., 14.,  9.,  3.,  1.]),\n",
       " array([-110411.52704321,  -89570.0743482 ,  -68728.62165319,\n",
       "         -47887.16895817,  -27045.71626316,   -6204.26356815,\n",
       "          14637.18912686,   35478.64182187,   56320.09451688,\n",
       "          77161.5472119 ,   98002.99990691]),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "execution_count": 662,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Histogram of predictions\n",
    "plt.hist(Y-predictions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As per above histogram,the residuals (i.e. error) are normally distributed around zero. Lets looks at scatter plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x2b10d38e5e0>"
      ]
     },
     "execution_count": 664,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Scatter plot of predictions\n",
    "\n",
    "plt.scatter(predictions,Y,color='g')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above graph looks like a straight line which validates the effectiveness of our model. Though it has some outliers."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Back to top](#Index)\n",
    "\n",
    "## Conclusion\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using Linear Regression model, we are able to predict 88% of the variance in the target variable by independent variables. This shows model is not perfect and can further be improved. Current model doesn't take into account categorical data such as Neighbourhood, Lot Shape etc. which can impact the results.\n",
    "\n",
    "From the result we can see that R² value improves when more independent variables with higher correlation were added in the analysis.\n",
    "\n",
    "When we are trying to predict dependent variable based on multiple independent variables, linear regression comes handy.\n",
    "This model can be used to assess the impact of differnt independent variables on the outcome.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "[Back to top](#Index\n",
    ")\n",
    "## References\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Websites:\n",
    "    \n",
    "- “Regression analysis” Wikipedia. 8/27/2022 https://en.wikipedia.org/wiki/Regression_analysis.\n",
    "- “Residual Plot Analysis” OriginLab. 8/27/2022 https://www.originlab.com/doc/Origin-Help/Residual-Plot-Analysis\n"
   ]
  }
 ],
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