631 Portfolio Regression Analysis on Ames Housing
Dileep Kalisetti
2024-08-05
Portfolio
I’m Dileep Kalisetti, currently pursuing a Master’s in Data Science and Analytics. After completing my bachelor’s degree in Computer Science and Engineering, I gained experience working with data analysis. This hands-on experience sparked my interest in deepening my understanding of statistical modeling and predictive analytics.
As part of my master’s program, I have been focusing on advanced analytical techniques, including regression methods. To apply these techniques, I have chosen the Ames Housing dataset for my project. My goal is to develop a robust Generalized Linear Model (GLM) to predict house prices. I aim to analyze the factors affecting house prices, visualize the results, and effectively communicate the insights gained from the model. This project will help me refine my skills in data analysis and predictive modeling, and provide valuable insights into real estate pricing dynamics.
Project Objective
The primary objective of this project is to develop a robust predictive model for estimating house prices using the Ames Housing dataset. By applying advanced regression techniques, the goal is to uncover the key factors influencing property values and to build a Generalized Linear Model (GLM) that accurately predicts house prices based on these features. This analysis aims to enhance understanding of the dynamics of real estate pricing, offering valuable insights for stakeholders in the housing market. The project will also evaluate the model’s performance using various metrics to ensure its reliability and accuracy.
Project Overview
This project focuses on performing a comprehensive regression analysis on the Ames Housing dataset, which contains detailed information about residential properties in Ames, Iowa. The dataset includes various attributes of the houses such as size, age, and quality, which are essential for predicting their sale prices. The analysis begins with data preparation and exploratory data analysis (EDA) to understand the dataset’s characteristics and distribution. Following this, the project involves building a predictive model using regression techniques to estimate house prices and evaluating its effectiveness. The ultimate aim is to provide a detailed analysis that not only predicts house prices but also offers insights into the factors that most significantly impact them.
Method of Approach
The approach for this project is structured into several key phases. First, data preparation involves loading and cleaning the Ames Housing dataset, followed by exploratory data analysis (EDA) to identify patterns and relationships between variables. The next phase involves constructing a regression model, specifically a Generalized Linear Model (GLM), to predict house prices based on selected features such as ground living area, year built, and overall quality. The model’s performance is then assessed using various evaluation metrics, including Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE). Additionally, visualizations are created to compare predicted versus actual prices and to present the correlation matrix of relevant features. This methodical approach ensures a thorough analysis of the data and the development of a reliable predictive model.
Introduction
In this project, we will perform a regression analysis on the Ames Housing dataset to predict house prices. The dataset contains various features of houses in Ames, Iowa. We aim to build a model that can accurately predict the sale price based on these features.
Data Preparation
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## The following object is masked from 'package:purrr':
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## lift# Load the Ames Housing dataset
ames_data <- read.csv("AmesHousing.csv")
# Inspect the data
head(ames_data)## Order PID MS.SubClass MS.Zoning Lot.Frontage Lot.Area Street Alley
## 1 1 526301100 20 RL 141 31770 Pave <NA>
## 2 2 526350040 20 RH 80 11622 Pave <NA>
## 3 3 526351010 20 RL 81 14267 Pave <NA>
## 4 4 526353030 20 RL 93 11160 Pave <NA>
## 5 5 527105010 60 RL 74 13830 Pave <NA>
## 6 6 527105030 60 RL 78 9978 Pave <NA>
## Lot.Shape Land.Contour Utilities Lot.Config Land.Slope Neighborhood
## 1 IR1 Lvl AllPub Corner Gtl NAmes
## 2 Reg Lvl AllPub Inside Gtl NAmes
## 3 IR1 Lvl AllPub Corner Gtl NAmes
## 4 Reg Lvl AllPub Corner Gtl NAmes
## 5 IR1 Lvl AllPub Inside Gtl Gilbert
## 6 IR1 Lvl AllPub Inside Gtl Gilbert
## Condition.1 Condition.2 Bldg.Type House.Style Overall.Qual Overall.Cond
## 1 Norm Norm 1Fam 1Story 6 5
## 2 Feedr Norm 1Fam 1Story 5 6
## 3 Norm Norm 1Fam 1Story 6 6
## 4 Norm Norm 1Fam 1Story 7 5
## 5 Norm Norm 1Fam 2Story 5 5
## 6 Norm Norm 1Fam 2Story 6 6
## Year.Built Year.Remod.Add Roof.Style Roof.Matl Exterior.1st Exterior.2nd
## 1 1960 1960 Hip CompShg BrkFace Plywood
## 2 1961 1961 Gable CompShg VinylSd VinylSd
## 3 1958 1958 Hip CompShg Wd Sdng Wd Sdng
## 4 1968 1968 Hip CompShg BrkFace BrkFace
## 5 1997 1998 Gable CompShg VinylSd VinylSd
## 6 1998 1998 Gable CompShg VinylSd VinylSd
## Mas.Vnr.Type Mas.Vnr.Area Exter.Qual Exter.Cond Foundation Bsmt.Qual
## 1 Stone 112 TA TA CBlock TA
## 2 None 0 TA TA CBlock TA
## 3 BrkFace 108 TA TA CBlock TA
## 4 None 0 Gd TA CBlock TA
## 5 None 0 TA TA PConc Gd
## 6 BrkFace 20 TA TA PConc TA
## Bsmt.Cond Bsmt.Exposure BsmtFin.Type.1 BsmtFin.SF.1 BsmtFin.Type.2
## 1 Gd Gd BLQ 639 Unf
## 2 TA No Rec 468 LwQ
## 3 TA No ALQ 923 Unf
## 4 TA No ALQ 1065 Unf
## 5 TA No GLQ 791 Unf
## 6 TA No GLQ 602 Unf
## BsmtFin.SF.2 Bsmt.Unf.SF Total.Bsmt.SF Heating Heating.QC Central.Air
## 1 0 441 1080 GasA Fa Y
## 2 144 270 882 GasA TA Y
## 3 0 406 1329 GasA TA Y
## 4 0 1045 2110 GasA Ex Y
## 5 0 137 928 GasA Gd Y
## 6 0 324 926 GasA Ex Y
## Electrical X1st.Flr.SF X2nd.Flr.SF Low.Qual.Fin.SF Gr.Liv.Area Bsmt.Full.Bath
## 1 SBrkr 1656 0 0 1656 1
## 2 SBrkr 896 0 0 896 0
## 3 SBrkr 1329 0 0 1329 0
## 4 SBrkr 2110 0 0 2110 1
## 5 SBrkr 928 701 0 1629 0
## 6 SBrkr 926 678 0 1604 0
## Bsmt.Half.Bath Full.Bath Half.Bath Bedroom.AbvGr Kitchen.AbvGr Kitchen.Qual
## 1 0 1 0 3 1 TA
## 2 0 1 0 2 1 TA
## 3 0 1 1 3 1 Gd
## 4 0 2 1 3 1 Ex
## 5 0 2 1 3 1 TA
## 6 0 2 1 3 1 Gd
## TotRms.AbvGrd Functional Fireplaces Fireplace.Qu Garage.Type Garage.Yr.Blt
## 1 7 Typ 2 Gd Attchd 1960
## 2 5 Typ 0 <NA> Attchd 1961
## 3 6 Typ 0 <NA> Attchd 1958
## 4 8 Typ 2 TA Attchd 1968
## 5 6 Typ 1 TA Attchd 1997
## 6 7 Typ 1 Gd Attchd 1998
## Garage.Finish Garage.Cars Garage.Area Garage.Qual Garage.Cond Paved.Drive
## 1 Fin 2 528 TA TA P
## 2 Unf 1 730 TA TA Y
## 3 Unf 1 312 TA TA Y
## 4 Fin 2 522 TA TA Y
## 5 Fin 2 482 TA TA Y
## 6 Fin 2 470 TA TA Y
## Wood.Deck.SF Open.Porch.SF Enclosed.Porch X3Ssn.Porch Screen.Porch Pool.Area
## 1 210 62 0 0 0 0
## 2 140 0 0 0 120 0
## 3 393 36 0 0 0 0
## 4 0 0 0 0 0 0
## 5 212 34 0 0 0 0
## 6 360 36 0 0 0 0
## Pool.QC Fence Misc.Feature Misc.Val Mo.Sold Yr.Sold Sale.Type Sale.Condition
## 1 <NA> <NA> <NA> 0 5 2010 WD Normal
## 2 <NA> MnPrv <NA> 0 6 2010 WD Normal
## 3 <NA> <NA> Gar2 12500 6 2010 WD Normal
## 4 <NA> <NA> <NA> 0 4 2010 WD Normal
## 5 <NA> MnPrv <NA> 0 3 2010 WD Normal
## 6 <NA> <NA> <NA> 0 6 2010 WD Normal
## SalePrice
## 1 215000
## 2 105000
## 3 172000
## 4 244000
## 5 189900
## 6 195500## Order PID MS.SubClass MS.Zoning
## Min. : 1.0 Min. :5.263e+08 Min. : 20.00 Length:2930
## 1st Qu.: 733.2 1st Qu.:5.285e+08 1st Qu.: 20.00 Class :character
## Median :1465.5 Median :5.355e+08 Median : 50.00 Mode :character
## Mean :1465.5 Mean :7.145e+08 Mean : 57.39
## 3rd Qu.:2197.8 3rd Qu.:9.072e+08 3rd Qu.: 70.00
## Max. :2930.0 Max. :1.007e+09 Max. :190.00
##
## Lot.Frontage Lot.Area Street Alley
## Min. : 21.00 Min. : 1300 Length:2930 Length:2930
## 1st Qu.: 58.00 1st Qu.: 7440 Class :character Class :character
## Median : 68.00 Median : 9436 Mode :character Mode :character
## Mean : 69.22 Mean : 10148
## 3rd Qu.: 80.00 3rd Qu.: 11555
## Max. :313.00 Max. :215245
## NA's :490
## Lot.Shape Land.Contour Utilities Lot.Config
## Length:2930 Length:2930 Length:2930 Length:2930
## Class :character Class :character Class :character Class :character
## Mode :character Mode :character Mode :character Mode :character
##
##
##
##
## Land.Slope Neighborhood Condition.1 Condition.2
## Length:2930 Length:2930 Length:2930 Length:2930
## Class :character Class :character Class :character Class :character
## Mode :character Mode :character Mode :character Mode :character
##
##
##
##
## Bldg.Type House.Style Overall.Qual Overall.Cond
## Length:2930 Length:2930 Min. : 1.000 Min. :1.000
## Class :character Class :character 1st Qu.: 5.000 1st Qu.:5.000
## Mode :character Mode :character Median : 6.000 Median :5.000
## Mean : 6.095 Mean :5.563
## 3rd Qu.: 7.000 3rd Qu.:6.000
## Max. :10.000 Max. :9.000
##
## Year.Built Year.Remod.Add Roof.Style Roof.Matl
## Min. :1872 Min. :1950 Length:2930 Length:2930
## 1st Qu.:1954 1st Qu.:1965 Class :character Class :character
## Median :1973 Median :1993 Mode :character Mode :character
## Mean :1971 Mean :1984
## 3rd Qu.:2001 3rd Qu.:2004
## Max. :2010 Max. :2010
##
## Exterior.1st Exterior.2nd Mas.Vnr.Type Mas.Vnr.Area
## Length:2930 Length:2930 Length:2930 Min. : 0.0
## Class :character Class :character Class :character 1st Qu.: 0.0
## Mode :character Mode :character Mode :character Median : 0.0
## Mean : 101.9
## 3rd Qu.: 164.0
## Max. :1600.0
## NA's :23
## Exter.Qual Exter.Cond Foundation Bsmt.Qual
## Length:2930 Length:2930 Length:2930 Length:2930
## Class :character Class :character Class :character Class :character
## Mode :character Mode :character Mode :character Mode :character
##
##
##
##
## Bsmt.Cond Bsmt.Exposure BsmtFin.Type.1 BsmtFin.SF.1
## Length:2930 Length:2930 Length:2930 Min. : 0.0
## Class :character Class :character Class :character 1st Qu.: 0.0
## Mode :character Mode :character Mode :character Median : 370.0
## Mean : 442.6
## 3rd Qu.: 734.0
## Max. :5644.0
## NA's :1
## BsmtFin.Type.2 BsmtFin.SF.2 Bsmt.Unf.SF Total.Bsmt.SF
## Length:2930 Min. : 0.00 Min. : 0.0 Min. : 0
## Class :character 1st Qu.: 0.00 1st Qu.: 219.0 1st Qu.: 793
## Mode :character Median : 0.00 Median : 466.0 Median : 990
## Mean : 49.72 Mean : 559.3 Mean :1052
## 3rd Qu.: 0.00 3rd Qu.: 802.0 3rd Qu.:1302
## Max. :1526.00 Max. :2336.0 Max. :6110
## NA's :1 NA's :1 NA's :1
## Heating Heating.QC Central.Air Electrical
## Length:2930 Length:2930 Length:2930 Length:2930
## Class :character Class :character Class :character Class :character
## Mode :character Mode :character Mode :character Mode :character
##
##
##
##
## X1st.Flr.SF X2nd.Flr.SF Low.Qual.Fin.SF Gr.Liv.Area
## Min. : 334.0 Min. : 0.0 Min. : 0.000 Min. : 334
## 1st Qu.: 876.2 1st Qu.: 0.0 1st Qu.: 0.000 1st Qu.:1126
## Median :1084.0 Median : 0.0 Median : 0.000 Median :1442
## Mean :1159.6 Mean : 335.5 Mean : 4.677 Mean :1500
## 3rd Qu.:1384.0 3rd Qu.: 703.8 3rd Qu.: 0.000 3rd Qu.:1743
## Max. :5095.0 Max. :2065.0 Max. :1064.000 Max. :5642
##
## Bsmt.Full.Bath Bsmt.Half.Bath Full.Bath Half.Bath
## Min. :0.0000 Min. :0.00000 Min. :0.000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.00000 1st Qu.:1.000 1st Qu.:0.0000
## Median :0.0000 Median :0.00000 Median :2.000 Median :0.0000
## Mean :0.4314 Mean :0.06113 Mean :1.567 Mean :0.3795
## 3rd Qu.:1.0000 3rd Qu.:0.00000 3rd Qu.:2.000 3rd Qu.:1.0000
## Max. :3.0000 Max. :2.00000 Max. :4.000 Max. :2.0000
## NA's :2 NA's :2
## Bedroom.AbvGr Kitchen.AbvGr Kitchen.Qual TotRms.AbvGrd
## Min. :0.000 Min. :0.000 Length:2930 Min. : 2.000
## 1st Qu.:2.000 1st Qu.:1.000 Class :character 1st Qu.: 5.000
## Median :3.000 Median :1.000 Mode :character Median : 6.000
## Mean :2.854 Mean :1.044 Mean : 6.443
## 3rd Qu.:3.000 3rd Qu.:1.000 3rd Qu.: 7.000
## Max. :8.000 Max. :3.000 Max. :15.000
##
## Functional Fireplaces Fireplace.Qu Garage.Type
## Length:2930 Min. :0.0000 Length:2930 Length:2930
## Class :character 1st Qu.:0.0000 Class :character Class :character
## Mode :character Median :1.0000 Mode :character Mode :character
## Mean :0.5993
## 3rd Qu.:1.0000
## Max. :4.0000
##
## Garage.Yr.Blt Garage.Finish Garage.Cars Garage.Area
## Min. :1895 Length:2930 Min. :0.000 Min. : 0.0
## 1st Qu.:1960 Class :character 1st Qu.:1.000 1st Qu.: 320.0
## Median :1979 Mode :character Median :2.000 Median : 480.0
## Mean :1978 Mean :1.767 Mean : 472.8
## 3rd Qu.:2002 3rd Qu.:2.000 3rd Qu.: 576.0
## Max. :2207 Max. :5.000 Max. :1488.0
## NA's :159 NA's :1 NA's :1
## Garage.Qual Garage.Cond Paved.Drive Wood.Deck.SF
## Length:2930 Length:2930 Length:2930 Min. : 0.00
## Class :character Class :character Class :character 1st Qu.: 0.00
## Mode :character Mode :character Mode :character Median : 0.00
## Mean : 93.75
## 3rd Qu.: 168.00
## Max. :1424.00
##
## Open.Porch.SF Enclosed.Porch X3Ssn.Porch Screen.Porch
## Min. : 0.00 Min. : 0.00 Min. : 0.000 Min. : 0
## 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 0.000 1st Qu.: 0
## Median : 27.00 Median : 0.00 Median : 0.000 Median : 0
## Mean : 47.53 Mean : 23.01 Mean : 2.592 Mean : 16
## 3rd Qu.: 70.00 3rd Qu.: 0.00 3rd Qu.: 0.000 3rd Qu.: 0
## Max. :742.00 Max. :1012.00 Max. :508.000 Max. :576
##
## Pool.Area Pool.QC Fence Misc.Feature
## Min. : 0.000 Length:2930 Length:2930 Length:2930
## 1st Qu.: 0.000 Class :character Class :character Class :character
## Median : 0.000 Mode :character Mode :character Mode :character
## Mean : 2.243
## 3rd Qu.: 0.000
## Max. :800.000
##
## Misc.Val Mo.Sold Yr.Sold Sale.Type
## Min. : 0.00 Min. : 1.000 Min. :2006 Length:2930
## 1st Qu.: 0.00 1st Qu.: 4.000 1st Qu.:2007 Class :character
## Median : 0.00 Median : 6.000 Median :2008 Mode :character
## Mean : 50.63 Mean : 6.216 Mean :2008
## 3rd Qu.: 0.00 3rd Qu.: 8.000 3rd Qu.:2009
## Max. :17000.00 Max. :12.000 Max. :2010
##
## Sale.Condition SalePrice
## Length:2930 Min. : 12789
## Class :character 1st Qu.:129500
## Mode :character Median :160000
## Mean :180796
## 3rd Qu.:213500
## Max. :755000
## Exploratory Data Analysis
##
## Attaching package: 'gridExtra'## The following object is masked from 'package:dplyr':
##
## combine# Create the first plot: Distribution of Sale Price
plot1 <- ggplot(ames_data, aes(x = SalePrice)) +
geom_histogram(bins = 30, fill = "steelblue", color = "white") +
labs(title = "Distribution of Sale Price", x = "Sale Price", y = "Count")
# Create the second plot: Scatter plot of GrLivArea vs. SalePrice
plot2 <- ggplot(ames_data, aes(x = Gr.Liv.Area, y = SalePrice)) +
geom_point(alpha = 0.5) +
geom_smooth(method = "lm", se = FALSE, color = "red") +
labs(title = "Living Area vs. Sale Price", x = "Ground Living Area", y = "Sale Price")
# Arrange the plots on a single page
grid.arrange(plot1, plot2, ncol = 1)## `geom_smooth()` using formula = 'y ~ x'
Correlation matrix
## corrplot 0.92 loadedcorrelation_matrix <- ames_data %>%
select(SalePrice, Gr.Liv.Area, Year.Built, Overall.Qual) %>%
cor()
corrplot(correlation_matrix, method = "circle",
type = "upper", # Display only the upper triangle
tl.col = "black", tl.srt = 45, # Text label color and rotation
addCoef.col = "black", # Add correlation coefficients
number.cex = 0.8, # Size of correlation coefficients
col = colorRampPalette(c("blue", "white", "red"))(200), # Color palette
title = "Correlation Matrix",
mar = c(0, 0, 2, 0)) # Margins
## SalePrice Gr.Liv.Area Year.Built Overall.Qual
## SalePrice 1.0000000 0.7067799 0.5584261 0.7992618
## Gr.Liv.Area 0.7067799 1.0000000 0.2417258 0.5705559
## Year.Built 0.5584261 0.2417258 1.0000000 0.5970272
## Overall.Qual 0.7992618 0.5705559 0.5970272 1.0000000Regression Model
# Build a linear regression model
set.seed(123)
train_index <- createDataPartition(ames_data$SalePrice, p = 0.8, list = FALSE)
train_data <- ames_data[train_index, ]
test_data <- ames_data[-train_index, ]
model <- lm(SalePrice ~ Gr.Liv.Area + Year.Built + Overall.Qual, data = train_data)
summary(model)##
## Call:
## lm(formula = SalePrice ~ Gr.Liv.Area + Year.Built + Overall.Qual,
## data = train_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -396787 -23094 -2289 18563 287167
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.058e+06 6.616e+04 -15.99 <2e-16 ***
## Gr.Liv.Area 6.181e+01 1.974e+00 31.30 <2e-16 ***
## Year.Built 4.998e+02 3.484e+01 14.34 <2e-16 ***
## Overall.Qual 2.623e+04 8.784e+02 29.86 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 39980 on 2342 degrees of freedom
## Multiple R-squared: 0.7511, Adjusted R-squared: 0.7508
## F-statistic: 2356 on 3 and 2342 DF, p-value: < 2.2e-16Model Evaluation
# Predictions on test data
predictions <- predict(model, test_data)
# Calculate RMSE
rmse <- sqrt(mean((predictions - test_data$SalePrice)^2))
rmse## [1] 38230.1# Calculate MAPE
mape <- mean(abs((predictions - test_data$SalePrice) / test_data$SalePrice)) * 100
mape## [1] 15.6333# Plot predicted vs. actual
ggplot(data = test_data, aes(x = SalePrice, y = predictions)) +
geom_point(alpha = 0.5) +
geom_abline(slope = 1, intercept = 0, color = "red") +
labs(title = "Predicted vs. Actual Sale Price", x = "Actual Sale Price", y = "Predicted Sale Price")
Conclusion
The regression analysis conducted on the Ames Housing dataset has provided valuable insights into the factors influencing house prices. By developing and evaluating a Generalized Linear Model (GLM), we have been able to quantify the impact of key features such as living area, year built, and overall quality on sale prices. The analysis revealed that:
Living Area: A significant predictor of house prices, with larger living
areas generally associated with higher prices.
Year Built:
Houses built more recently tend to have higher prices, reflecting the
importance of modern features and potentially updated amenities.
Overall Quality: This feature strongly influences house prices, with
higher quality ratings corresponding to higher sale prices.
The
model’s performance was assessed using metrics like RMSE and MAPE, which
provided a measure of its predictive accuracy. Despite some limitations,
such as the potential for omitted variables and data quality issues, the
model offers a robust starting point for understanding housing price
dynamics in Ames.
Reflection
Working on this project has been a valuable learning experience in applying advanced analytical techniques to real-world data. Through this process, I have gained a deeper understanding of:
Data Preparation and Exploration: Handling and cleaning data, performing
exploratory analysis, and visualizing relationships between
variables.
Model Building and Evaluation: Developing regression
models, evaluating their performance, and interpreting the results to
make data-driven decisions.
Communication of Insights:
Presenting complex analyses in a clear and accessible manner, which is
crucial for effective communication with stakeholders.
This project has also highlighted areas for further improvement, such as incorporating additional features or experimenting with different modeling approaches to enhance predictive accuracy. Overall, the experience has solidified my skills in data analysis and statistical modeling, and it has reinforced the importance of rigorous evaluation and validation in any analytical project.