{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# House Prices: Advanced Regression Techniques\n", "\n", "This goal of this project was to predict sales prices and practice feature engineering, RFs, and gradient boosting. The dataset was part of the [House Prices Kaggle Competition](https://www.kaggle.com/c/house-prices-advanced-regression-techniques). \n", "\n", "
\n", "\n", "### Model Accuracy: (RMSE = 0.12220)\n", " Top submissions on the public leaderboard range between 0.10-0.12\n", "\n", "### Competition Description\n", "> Ask a home buyer to describe their dream house, and they probably won't begin with the height of the basement ceiling or the proximity to an east-west railroad. But this playground competition's dataset proves that much more influences price negotiations than the number of bedrooms or a white-picket fence.\n", "\n", ">With 79 explanatory variables describing (almost) every aspect of residential homes in Ames, Iowa, this competition challenges you to predict the final price of each home.\n", "\n", "### Competition Evaluation\n", "As part of a Kaggle competition dataset, the accuracy of the sales prices was evaluated on [Root-Mean-Squared-Error (RMSE)](https://en.wikipedia.org/wiki/Root-mean-square_deviation) between the logarithm of the predicted value and the logarithm of the observed sales price." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 1 Summary\n", "\n", "I started this competition by focusing on getting a thorough understanding of the dataset. Particular attention was paid to impute the missing values within the dataset. The EDA process is detailed as well as visualized.\n", "\n", "In this project, I created a predictive model that has been trained on data collected from homes in Ames, Iowa. Three algorithms were used, and their validation set RMSE and test set RMSE are listed below:\n", "\n", "\n", "| Regression Model | Validation RMSE | Test RMSE |\n", "|------------------|-----------------|-----------|\n", "| Ridge | 0.1130 | 0.12528 |\n", "| Lasso | 0.1125 | 0.12679 |\n", "| XGBoost | 0.1238 | 0.12799 |\n", "| |\n", "| Ensemble | | 0.12220 |\n", "\n", "The Ridge regression model performed the best as a single model, likely due to the high multicollinearity. However, combining it with the Lasso and XGBoost regression models resulting in a higher prediction accuracy and a lower RMSE (0.12220 vs 0.12528). " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 2 Introduction\n", "\n", "The dataset used for this project is the [Ames Housing dataset](https://amstat.tandfonline.com/doi/abs/10.1080/10691898.2011.11889627) that was compiled by Dean De Cock for use in data science education. It is an alternative to the popular but older [Boston Housing dataset](http://lib.stat.cmu.edu/datasets/boston). \n", "\n", "The Ames Housing dataset is also used in the [Advanced Regression Techniques challenge](https://www.kaggle.com/c/house-prices-advanced-regression-techniques) on the Kaggle Website. These competitions is a great way to improve my skills and measure my progress as a data scientist. \n", "\n", "Kaggle describes the competition as follows:\n", "\n", "> Ask a home buyer to describe their dream house, and they probably won't begin with the height of the basement ceiling or the proximity to an east-west railroad. But this playground competition's dataset proves that much more influences price negotiations than the number of bedrooms or a white-picket fence.\n", "\n", ">With 79 explanatory variables describing (almost) every aspect of residential homes in Ames, Iowa, this competition challenges you to predict the final price of each home.\n", "\n", "\n", "![House Image](sold.jpg)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 3 Loading & Exploring the Data Structure" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3.1 Loading Required Libraries and Reading the Data into Python" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Loading Python packages used in the project" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import pandas as pd\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "import missingno as msno\n", "from time import time\n", "\n", "from math import sqrt\n", "import statsmodels.api as sm\n", "from statsmodels.formula.api import ols\n", "import scipy.stats as st\n", "from scipy.special import boxcox1p\n", "\n", "from sklearn.cluster import KMeans\n", "from sklearn import svm\n", "from sklearn.metrics import mean_absolute_error, mean_squared_error\n", "from sklearn.model_selection import train_test_split, KFold, cross_val_score, GridSearchCV\n", "from sklearn.preprocessing import RobustScaler, LabelEncoder, StandardScaler\n", "from sklearn.linear_model import Lasso, Ridge\n", "from sklearn.pipeline import make_pipeline\n", "from xgboost.sklearn import XGBRegressor\n", "\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, we read in the csv's as datarames into Python." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "train = pd.read_csv('train.csv')\n", "test = pd.read_csv('test.csv')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3.2 Data Structure\n", "\n", "In total, there are 81 columns/variables in the train dataset, including the response variable (SalePrice). I am only displaying a subset of the variables, as all of them will be discussed in more detail throughout the notebook.\n", "\n", "The train dataset consists of character and integer variables. Many of these variables are ordinal factors, despite being represented as character or integer variables. These will require cleaning and/or feature engineering later." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Dimensions of Train Dataset:(1460, 81)\n", "Dimensions of Test Dataset:(1459, 80)\n" ] } ], "source": [ "print(\"Dimensions of Train Dataset:\" + str(train.shape))\n", "print(\"Dimensions of Test Dataset:\" + str(test.shape))" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "RangeIndex: 1460 entries, 0 to 1459\n", "Data columns (total 10 columns):\n", "Id 1460 non-null int64\n", "MSSubClass 1460 non-null int64\n", "MSZoning 1460 non-null object\n", "LotFrontage 1201 non-null float64\n", "LotArea 1460 non-null int64\n", "Street 1460 non-null object\n", "Alley 91 non-null object\n", "LotShape 1460 non-null object\n", "LandContour 1460 non-null object\n", "Utilities 1460 non-null object\n", "dtypes: float64(1), int64(3), object(6)\n", "memory usage: 114.1+ KB\n" ] } ], "source": [ "train.iloc[:,0:10].info()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we are going to define a few variables that will be used in later analyses as well as being required for the submission file." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "y_train = train['SalePrice']\n", "test_id = test['Id']\n", "\n", "ntrain = train.shape[0]\n", "ntest = test.shape[0]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Lastly, we are going to merge the train and test datasets to explore the data as well as impute any missing values." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "all_data = pd.concat((train, test), sort=True).reset_index(drop=True)\n", "all_data['Dataset'] = np.repeat(['Train', 'Test'], [ntrain, ntest], axis=0)\n", "all_data.drop('Id', axis=1,inplace=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 4 Exploring the Variables" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4.1 Exploring the Response Variable: SalePrice" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The probability distribution plot show that the sale prices are right skewed. This is to be expected as few people can afford very expensive houses. " ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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r/N2cOZ4tth0WBME6FruzLO2PnJiYSHx8PFKplJiYGIYOHUpeXh7PP/88ZWVl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\nAABJRU5ErkJggg==\n", 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sns.set_style('whitegrid')\n", "sns.distplot(all_data['SalePrice'][~all_data['SalePrice'].isnull()], axlabel=\"Normal Distribution\", fit=st.norm, fit_kws={\"color\":\"red\"})\n", "plt.title('Distribution of Sales Price in Dollars')\n", "(mu, sigma) = st.norm.fit(train['SalePrice'])\n", "plt.legend(['Normal Distribution \\n ($\\mu=$ {:.2f} and $\\sigma=$ {:.2f} )'.format(mu, sigma)],\n", " loc='best', fancybox=True)\n", "plt.show()\n", "\n", "st.probplot(all_data['SalePrice'][~all_data['SalePrice'].isnull()], plot=plt)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Linear models tend to work better with normally distributed data. As such, we need to transform the response variable to make it more normally distributed." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4.2 Log-Transformation of the Response Variable" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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tgwcP5siRI+WOXaJ///7Mnz+fXbt24eTkhEwmM3w43mvixInMnj2bp59+mhYt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\nr9dJzoYNGwJw/PhxYmJiePHFF032N5f+rC6nufSntbU1V69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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "all_data['SalePrice'] = np.log1p(all_data['SalePrice'])\n", "\n", "sns.distplot(all_data['SalePrice'][~all_data['SalePrice'].isnull()], axlabel=\"Normal Distribution\", fit=st.norm, fit_kws={\"color\":\"red\"})\n", "\n", "plt.title('Distribution of Transformed Sales Price in Dollars')\n", "(mu, sigma) = st.norm.fit(train['SalePrice'])\n", "plt.legend(['Normal Distribution \\n ($\\mu=$ {:.2f} and $\\sigma=$ {:.2f} )'.format(mu, sigma)],\n", " loc='best', fancybox=True)\n", "plt.show()\n", "\n", "st.probplot(all_data['SalePrice'][~all_data['SalePrice'].isnull()], plot=plt)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The skew is highly corrected and the distribution of the log-transformed sale prices appears more normally distributed." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 5 Data Imputation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 5.1 Completeness of the Data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We first need to find which variables contain missing values." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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Number of Missing Values
PoolQC2909
MiscFeature2814
Alley2721
Fence2348
SalePrice1459
FireplaceQu1420
LotFrontage486
GarageFinish159
GarageQual159
GarageYrBlt159
GarageCond159
GarageType157
BsmtCond82
BsmtExposure82
BsmtQual81
BsmtFinType280
BsmtFinType179
MasVnrType24
MasVnrArea23
MSZoning4
Utilities2
BsmtFullBath2
BsmtHalfBath2
Functional2
Electrical1
KitchenQual1
Exterior2nd1
Exterior1st1
GarageCars1
GarageArea1
TotalBsmtSF1
BsmtUnfSF1
BsmtFinSF21
BsmtFinSF11
SaleType1
\n", "
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Number of Missing Values
SalePrice1459
LotFrontage486
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" ], "text/plain": [ " Number of Missing Values\n", "SalePrice 1459\n", "LotFrontage 486" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cols_with_missing_values = all_data.isnull().sum().sort_values(ascending=False)\n", "display(pd.DataFrame(cols_with_missing_values[cols_with_missing_values[cols_with_missing_values > 0].index], columns=[\"Number of Missing Values\"]))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Due to its numeric nature and the large number of missing values, the LotFrontage variable will be imputed separately using an SVM algorithm (See Section [7 LotFrontage Imputation](#7-Lot-Frontage-Imputation)). \n", "\n", "
\n", "The remaining variables are all complete! Now to move on to feature engineering." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 6 Feature Engineering" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 6.1 Mixed Conditions\n", "\n", "In order to simplify and boost the accuracy of the preditive models, we will merge the two conditions into one variable: MixedConditions\n", "\n", "The data descriptions states:\n", "* Condition1 represents proximity to various conditions.\n", "* Condition2 represents proximity to various conditions (if more than one is present).\n", "\n", "If a property does not have one or multiple conditions, then it is classified as normal. However, designation of \"normal\" are condition 1 or condition 2 is strictly alphabetical.\n", "\n", "For example, if a property is in proximity to a feeder street (\"Feedr\") and no other condition, then the data would appear as follows:\n", "\n", "Condition1 | Condition2\n", "-----------|-------------\n", " Feedr | Norm\n", "\n", "
\n", " \n", "However, if a property is within 200' of East-West Railroad (RRNe) and no other condition, then the data would appear as follows:\n", "\n", "Condition1 | Condition2\n", "-----------|-------------\n", " Norm | RRNe\n", "\n", "\n", "

\n", "\n", "Once we merge Conditions 1 & 2 into the MixedConditions variable, we will remove them from the analysis." ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": true, "scrolled": true }, "outputs": [], "source": [ "all_data['MixedConditions'] = all_data['Condition1'] + ' - ' + all_data['Condition2']\n", "all_data.drop(labels=['Condition1', 'Condition2'], axis=1, inplace=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 6.2 Mixed Exterior\n", "The Exterior1st and Exterior2nd features are similar to the Conditions feature we merged and remove above. Properties with multiple types of exterior covering the house are assigned to Exterior1st or Exterior2nd alphabetically.\n", "\n", "As such, we will conduct the same process to merge the two columns into a single MixedExterior variable and remove them from the analysis." ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": true }, "outputs": [], "source": [ "all_data['MixedExterior'] = all_data['Exterior1st'] + ' - ' + all_data['Exterior2nd']\n", "all_data.drop(labels=['Exterior1st', 'Exterior2nd'], axis=1, inplace=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 6.3 Total Square Feet\n", "One of the important factors that people consider when buying a house is the total living space in square feet. Since the total square feet is not explicitly listed, we will add a new variable by adding up the square footage of the basement, first floor, and the second floor." ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
TotalBsmtSF1stFlrSF2ndFlrSF
SalePrice Correlation0.6121340.5969810.3193
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BsmtFullBathBsmtHalfBathFullBathHalfBath
SalePrice Correlation0.236224-0.0051490.5947710.313982
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countmeanstdmin25%50%75%max
LotFrontage2433.069.30579523.34490521.059.068.080.0313.0
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" ], "text/plain": [ " count mean std min 25% 50% 75% max\n", "LotFrontage 2433.0 69.305795 23.344905 21.0 59.0 68.0 80.0 313.0" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "train_LotFrontage = all_data[~all_data.LotFrontage.isnull()]\n", "test_LotFrontage = all_data[all_data.LotFrontage.isnull()]\n", "\n", "print(\"\\n\")\n", "print(\"Dimensions of Train LotFrontage Dataset:\" + str(train_LotFrontage.shape))\n", "print(\"Dimensions of Test LotFrontage Dataset:\" + str(test_LotFrontage.shape))\n", "display(pd.DataFrame(all_data['LotFrontage'].describe()).transpose())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's examine the distribution of LotFrontages values in the Train LotFrontage dataset through a boxplot and distribution plot. Through these graphs, we can see several interesting observations appear:\n", "* There is a cluster of low LotFrontage value properties, shown as a peak on the far left of the distribution plot. The boxplot indicates these values may be outliers, shown as outlier points on the left of the whisker of the boxplot.\n", "* There is a long tail of high LotFrontage value properties. These values extend beyond the Median + 1.5IQR range.\n", "\n", "In other words, there are outliers on both ends of the LotFrontage value distributions." ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "image/png": 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4fM5TpP5nFQBtvr/uMRjYf/3NbLnvt5CaUGX71KQYwHvgjhJJEQlFSiRFREQk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\np055OlwRqUNUSIqIiEi1GGNI2XuSX7dqiFVWBsO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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1,2, figsize=(16,4))\n", "sns.boxplot(train_LotFrontage['LotFrontage'], ax=ax[0])\n", "\n", "sns.distplot(train_LotFrontage['LotFrontage'], ax=ax[1], fit=st.norm, fit_kws={\"color\":\"red\"})\n", "(mu, sigma) = st.norm.fit(train_LotFrontage['LotFrontage'])\n", "plt.legend(['Normal Distribution \\n ($\\mu=$ {:.2f} and $\\sigma=$ {:.2f} )'.format(mu, sigma)],\n", " loc='best', fancybox=True)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 7.2 Outlier Detection & Removal\n", "Before we examine the correlations between LotFrontage and other variables, we should remove the outliers seen above. \n", "\n", "To do so, we will use the Interquartile Range (IQR) method, where values outside the Median ± 1.5IQR are considered to be outliers. These outliers are then removed from the LotFrontage datasets." ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def outlier_detection(data):\n", " Q1, Q3 = np.percentile(data, [25,75])\n", " IQR = Q3-Q1\n", " lower_cutoff = Q1 - (IQR * 1.5)\n", " upper_cutoff = Q3 + (IQR * 1.5)\n", " outliers = (data > Q3+1.5*IQR) | (data < Q1-1.5*IQR)\n", " return outliers" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "data": { "image/png": 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c975SLVbqV/WhVuVKvLomljSLFV9PNyolniZ0wxpCNq0jcO8uzH+NNtaqBXXr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\nVZxMI5IiIiIizrJ0KbRvDzYb2Zs2Ex1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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "train_LotFrontage_no_outliers = train_LotFrontage[~outlier_detection(train_LotFrontage.LotFrontage)]\n", "fig, ax = plt.subplots(1,2, figsize=(16,4))\n", "sns.boxplot(train_LotFrontage_no_outliers['LotFrontage'], ax=ax[0])\n", "\n", "sns.distplot(train_LotFrontage_no_outliers['LotFrontage'], ax=ax[1], fit=st.norm, fit_kws={\"color\":\"red\"})\n", "(mu, sigma) = st.norm.fit(train_LotFrontage_no_outliers['LotFrontage'])\n", "plt.legend(['Normal Distribution \\n ($\\mu=$ {:.2f} and $\\sigma=$ {:.2f} )'.format(mu, sigma)],\n", " loc='best', fancybox=True)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Two new values previously not deemed outliers by the first iteration of the IQR range method are now shown as potential outliers in the boxplot. This is caused by having a new smaller IQR value after removing the first batch of outliers. As such, we will keep these values." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 7.3 Determining Relevant Variables of LotFrontage\n", "Now we can explore the relationship between the LotFrontage target variable and other features. In order to confirm a relationship between these key features and we will conduct an ANOVA (Analysis of Variance) test to determine statistical significance (in this case, p < 0.01).\n", "\n", "\n", "
\n", "Using the type III ANOVA, we are confident the variables listed in the table below are correlated with LotFrontage.\n", "\n", "* Note: Variables that begin with a number (1stFlrSF, 2ndFlrSF, and 3SsnPorch) cause a syntax error within the ols formula input. I briefly converted them to an appropriate name in the temp_train dataset for the purpose of the ANOVA." ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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sum_sqdfFPR(>F)
Alley1363.9139112.07.5033675.674399e-04
BldgType20479.6671104.056.3329015.337216e-45
GarageCond1600.6669245.03.5223313.573473e-03
GarageFinish1607.1446653.05.8943095.300349e-04
GarageQual1851.1557705.04.0735421.108720e-03
GarageType4398.0863276.08.0651361.269477e-08
HouseStyle3641.2029497.05.7232941.433756e-06
LotConfig43527.3671854.0119.7296242.398118e-91
LotShape2826.7228883.010.3671939.089207e-07
Neighborhood14742.82446223.07.0526467.333663e-22
RoofMatl2519.6091525.05.5445004.462709e-05
MixedConditions4309.31737218.02.6341182.091806e-04
MixedExterior12661.27170579.01.7633945.468941e-05
GarageCars999.6661841.010.9990269.284905e-04
GarageYrBlt1008.3610791.011.0946938.820554e-04
LotArea5292.7996661.058.2350793.629421e-14
MSSubClass997.0201091.010.9699129.431071e-04
TotalSF636.3620781.07.0017008.209306e-03
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\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
08568540None31Fam43706.00...0110532TrainNorm - NormVinylSd - VinylSd2566.03.50
1126200None31Fam41978.00...29883261TrainFeedr - NormMetalSd - MetalSd2524.02.50
29208660None31Fam42486.00...0108522TrainNorm - NormVinylSd - VinylSd2706.03.50
39617560None31Fam13216.00...025200TrainNorm - NormWd Sdng - Wd Shng2473.02.00
4114510530None41Fam40655.00...192107502TrainNorm - NormVinylSd - VinylSd3343.03.52
\n", "

5 rows × 81 columns

\n", "
" ], "text/plain": [ " 1stFlrSF 2ndFlrSF 3SsnPorch Alley BedroomAbvGr BldgType BsmtCond \\\n", "0 856 854 0 None 3 1Fam 4 \n", "1 1262 0 0 None 3 1Fam 4 \n", "2 920 866 0 None 3 1Fam 4 \n", "3 961 756 0 None 3 1Fam 1 \n", "4 1145 1053 0 None 4 1Fam 4 \n", "\n", " BsmtExposure BsmtFinSF1 BsmtFinSF2 ... WoodDeckSF \\\n", "0 3 706.0 0 ... 0 \n", "1 1 978.0 0 ... 298 \n", "2 2 486.0 0 ... 0 \n", "3 3 216.0 0 ... 0 \n", "4 0 655.0 0 ... 192 \n", "\n", " YearBuilt YearRemodAdd YrSold Dataset MixedConditions \\\n", "0 110 53 2 Train Norm - Norm \n", "1 83 26 1 Train Feedr - Norm \n", "2 108 52 2 Train Norm - Norm \n", "3 25 20 0 Train Norm - Norm \n", "4 107 50 2 Train Norm - Norm \n", "\n", " MixedExterior TotalSF TotalBath Neighborhood_Class \n", "0 VinylSd - VinylSd 2566.0 3.5 0 \n", "1 MetalSd - MetalSd 2524.0 2.5 0 \n", "2 VinylSd - VinylSd 2706.0 3.5 0 \n", "3 Wd Sdng - Wd Shng 2473.0 2.0 0 \n", "4 VinylSd - VinylSd 3343.0 3.5 2 \n", "\n", "[5 rows x 81 columns]" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cat_cols = ['OverallQual', 'OverallCond', 'ExterQual', 'ExterCond', 'BsmtQual', 'BsmtCond', 'BsmtExposure', 'BsmtFinType1', \n", " 'BsmtFinType2', 'BsmtFinSF2', 'HeatingQC', 'BsmtFullBath', 'BsmtHalfBath', 'FullBath', 'HalfBath', 'BedroomAbvGr', \n", " 'KitchenAbvGr', 'KitchenQual', 'TotRmsAbvGrd', 'Fireplaces', 'FireplaceQu', 'GarageFinish', 'GarageCars',\n", " 'GarageQual', 'GarageCond', 'PoolQC', 'Fence', 'YearBuilt', 'YearRemodAdd', 'GarageYrBlt', 'MoSold', 'YrSold']\n", "\n", "for col in cat_cols:\n", " label = LabelEncoder()\n", " label.fit(list(all_data[col].values))\n", " all_data[col] = label.transform(list(all_data[col].values))\n", "\n", "print('Shape all_data: {}'.format(all_data.shape))\n", "all_data.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 8.4 Skewness & Normalization of Numeric Variables\n", "\n", "Skewness is a measure of asymmetry of a distribution, and can be used to define the extent to which the distribution differs from a normal distribution. Therefore, a normal distribution will have a skewness of 0. As a rule of thumb, if skewness is less than -1 or greater than 1, the distribution is highly skewed. \n", "\n", "In order to account for skewness, we will transform the (highly) skewed data into normality using a Log Transformation. We define highly skewed data as variables with a skewness greater than 0.85. This method is similar to the approach used to normalize the [SalePrice Response Variable](#4.2-Log-Transformation-of-the-Response-Variable), except we will use log+1 to avoid division by zero issues." ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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Skew Before TransformationSkew After Transformation
MiscVal21.9396725.255296
PoolArea17.68866415.655054
LotArea13.109495-0.532117
LowQualFinSF12.0845398.605557
3SsnPorch11.3720808.853408
EnclosedPorch4.0023441.983518
ScreenPorch3.9451012.954087
OpenPorchSF2.5293580.019004
WoodDeckSF1.8447920.179665
1stFlrSF1.2572860.031286
GrLivArea1.068750-0.021271
LotFrontage1.067631-0.889232
TotalSF1.009157-0.428615
\n", "
" ], "text/plain": [ " Skew Before Transformation Skew After Transformation\n", "MiscVal 21.939672 5.255296\n", "PoolArea 17.688664 15.655054\n", "LotArea 13.109495 -0.532117\n", "LowQualFinSF 12.084539 8.605557\n", "3SsnPorch 11.372080 8.853408\n", "EnclosedPorch 4.002344 1.983518\n", "ScreenPorch 3.945101 2.954087\n", "OpenPorchSF 2.529358 0.019004\n", "WoodDeckSF 1.844792 0.179665\n", "1stFlrSF 1.257286 0.031286\n", "GrLivArea 1.068750 -0.021271\n", "LotFrontage 1.067631 -0.889232\n", "TotalSF 1.009157 -0.428615" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "numeric_feats = ['LotFrontage', 'LotArea', 'BsmtFinSF1', 'BsmtUnfSF', 'TotalBsmtSF', '1stFlrSF', '2ndFlrSF', \n", " 'LowQualFinSF', 'GrLivArea', 'GarageArea', 'WoodDeckSF', 'OpenPorchSF', 'EnclosedPorch',\n", " '3SsnPorch', 'ScreenPorch', 'PoolArea', 'MiscVal', 'TotalSF']\n", "\n", "skewed_feats = all_data[numeric_feats].apply(lambda x: st.skew(x.dropna())).sort_values(ascending=False)\n", "skewness = pd.DataFrame({'Skew Before Transformation' :skewed_feats})\n", "\n", "skewness = skewness[abs(skewness) > 1].dropna(axis=0)\n", "skewed_features = skewness.index\n", "for feat in skewed_features:\n", " all_data[feat] = np.log1p(all_data[feat]+1)\n", "\n", "skewed_feats = all_data[skewed_features].apply(lambda x: st.skew(x.dropna())).sort_values(ascending=False)\n", "skewness['Skew After Transformation'] = skewed_feats\n", "skewness" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 8.5 One Hot Encoding the Categorical Variables\n", "The last step needed to prepare the data is to make sure that all categorical predictor variables are converted into a form that is usable by machine learning algorithms. This process is known as 'one-hot encoding' the categorical variables.\n", "\n", "The process involved all non-ordinal factors receiving their own separate column with 1's and 0's, and is required by most ML algorithms." ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(2917, 317)\n" ] }, { "data": { "text/html": [ "
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1stFlrSF2ndFlrSF3SsnPorchBedroomAbvGrBsmtCondBsmtExposureBsmtFinSF1BsmtFinSF2BsmtFinType1BsmtFinType2...MixedExterior_Wd Sdng - StoneMixedExterior_Wd Sdng - StuccoMixedExterior_Wd Sdng - VinylSdMixedExterior_Wd Sdng - Wd SdngMixedExterior_Wd Sdng - Wd ShngMixedExterior_WdShing - HdBoardMixedExterior_WdShing - PlywoodMixedExterior_WdShing - StuccoMixedExterior_WdShing - Wd SdngMixedExterior_WdShing - Wd Shng
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26.8265458660.693147342486.0026...0000000000
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3 rows × 317 columns

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1.00.50.250.10.050.0250.010.0050.00250.0010.00050.000250.0001
RMSE0.3988410.3988410.3398970.2399780.1892810.1549910.1358980.1302710.1226060.1149530.112940.1124210.114048
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