title: “Untitled” author: “Teddy Wambua 21/05600” date: “2025-03-05” output: html_document
## Load Libraries and Data
library(readxl)
library(ggplot2)
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(tidyr)
library(corrplot)## corrplot 0.95 loadedlibrary(gridExtra)##
## Attaching package: 'gridExtra'## The following object is masked from 'package:dplyr':
##
## combinedf <- read_xlsx("C:/Users/USER/Desktop/House pricing data.xlsx")## Data Overview
# Check structure and summary
str(df)## tibble [1,460 × 26] (S3: tbl_df/tbl/data.frame)
## $ HouseId : num [1:1460] 1 2 3 4 5 6 7 8 9 10 ...
## $ MSZoning : chr [1:1460] "Residential Low Density" "Residential Low Density" "Residential Low Density" "Residential Low Density" ...
## $ LotAreaSquareFeet : num [1:1460] 8450 9600 11250 9550 14260 ...
## $ LandSlope : chr [1:1460] "Gentleslope" "Gentleslope" "Gentleslope" "Gentleslope" ...
## $ BuildingType : chr [1:1460] "Single-family Detached" "Single-family Detached" "Single-family Detached" "Single-family Detached" ...
## $ OverallCondition : num [1:1460] 5 8 5 5 5 5 5 6 5 6 ...
## $ YearBuilt : num [1:1460] 2003 1976 2001 1915 2000 ...
## $ ExteriorCondition : chr [1:1460] "Average/Typical" "Average/Typical" "Average/Typical" "Average/Typical" ...
## $ Foundation : chr [1:1460] "Poured Contrete" "Cinder Block" "Poured Contrete" "Brick & Tile" ...
## $ TotalBasementSquareFeet : num [1:1460] 856 1262 920 756 1145 ...
## $ HeatingQualityCondition : chr [1:1460] "Excellent" "Excellent" "Excellent" "Good" ...
## $ CentralAirConditioning : chr [1:1460] "Yes" "Yes" "Yes" "Yes" ...
## $ 1stFloorSquareFeet : num [1:1460] 856 1262 920 961 1145 ...
## $ 2ndFlrSquareFeet : num [1:1460] 854 0 866 756 1053 ...
## $ LivAreaSquareFeet : num [1:1460] 1710 1262 1786 1717 2198 ...
## $ FullBathrooms : num [1:1460] 2 2 2 1 2 1 2 2 2 1 ...
## $ Bedrooms : num [1:1460] 3 3 3 3 4 1 3 3 2 2 ...
## $ KitchenQualityCondition : chr [1:1460] "Good" "Typical/Average" "Good" "Good" ...
## $ TotalRooms : num [1:1460] 8 6 6 7 9 5 7 7 8 5 ...
## $ GarageArea : num [1:1460] 548 460 608 642 836 480 636 484 468 205 ...
## $ TotalPorchAreaSquareFeet: num [1:1460] 61 0 42 307 84 30 57 432 205 4 ...
## $ MonthSold : num [1:1460] 2 5 9 2 12 10 8 11 4 1 ...
## $ YearSold : num [1:1460] 2008 2007 2008 2006 2008 ...
## $ SaleType : chr [1:1460] "Warranty Deed - Conventional" "Warranty Deed - Conventional" "Warranty Deed - Conventional" "Warranty Deed - Conventional" ...
## $ SaleCondition : chr [1:1460] "Normal" "Normal" "Normal" "Abnorml" ...
## $ SalePrice : num [1:1460] 208500 181500 223500 140000 250000 ...summary(df)## HouseId MSZoning LotAreaSquareFeet LandSlope
## Min. : 1.0 Length:1460 Min. : 1300 Length:1460
## 1st Qu.: 365.8 Class :character 1st Qu.: 7554 Class :character
## Median : 730.5 Mode :character Median : 9478 Mode :character
## Mean : 730.5 Mean : 10517
## 3rd Qu.:1095.2 3rd Qu.: 11602
## Max. :1460.0 Max. :215245
## BuildingType OverallCondition YearBuilt ExteriorCondition
## Length:1460 Min. :1.000 Min. :1872 Length:1460
## Class :character 1st Qu.:5.000 1st Qu.:1954 Class :character
## Mode :character Median :5.000 Median :1973 Mode :character
## Mean :5.575 Mean :1971
## 3rd Qu.:6.000 3rd Qu.:2000
## Max. :9.000 Max. :2010
## Foundation TotalBasementSquareFeet HeatingQualityCondition
## Length:1460 Min. : 0.0 Length:1460
## Class :character 1st Qu.: 795.8 Class :character
## Mode :character Median : 991.5 Mode :character
## Mean :1057.4
## 3rd Qu.:1298.2
## Max. :6110.0
## CentralAirConditioning 1stFloorSquareFeet 2ndFlrSquareFeet LivAreaSquareFeet
## Length:1460 Min. : 334 Min. : 0 Min. : 334
## Class :character 1st Qu.: 882 1st Qu.: 0 1st Qu.:1130
## Mode :character Median :1087 Median : 0 Median :1464
## Mean :1163 Mean : 347 Mean :1515
## 3rd Qu.:1391 3rd Qu.: 728 3rd Qu.:1777
## Max. :4692 Max. :2065 Max. :5642
## FullBathrooms Bedrooms KitchenQualityCondition TotalRooms
## Min. :0.000 Min. :0.000 Length:1460 Min. : 2.000
## 1st Qu.:1.000 1st Qu.:2.000 Class :character 1st Qu.: 5.000
## Median :2.000 Median :3.000 Mode :character Median : 6.000
## Mean :1.565 Mean :2.866 Mean : 6.518
## 3rd Qu.:2.000 3rd Qu.:3.000 3rd Qu.: 7.000
## Max. :3.000 Max. :8.000 Max. :14.000
## GarageArea TotalPorchAreaSquareFeet MonthSold YearSold
## Min. : 0.0 Min. : 0.00 Min. : 1.000 Min. :2006
## 1st Qu.: 334.5 1st Qu.: 0.00 1st Qu.: 5.000 1st Qu.:2007
## Median : 480.0 Median : 40.00 Median : 6.000 Median :2008
## Mean : 473.0 Mean : 68.61 Mean : 6.322 Mean :2008
## 3rd Qu.: 576.0 3rd Qu.:104.00 3rd Qu.: 8.000 3rd Qu.:2009
## Max. :1418.0 Max. :638.00 Max. :12.000 Max. :2010
## SaleType SaleCondition SalePrice
## Length:1460 Length:1460 Min. : 34900
## Class :character Class :character 1st Qu.:129975
## Mode :character Mode :character Median :163000
## Mean :180921
## 3rd Qu.:214000
## Max. :755000# Check for missing values
colSums(is.na(df))## HouseId MSZoning LotAreaSquareFeet
## 0 0 0
## LandSlope BuildingType OverallCondition
## 0 0 0
## YearBuilt ExteriorCondition Foundation
## 0 0 0
## TotalBasementSquareFeet HeatingQualityCondition CentralAirConditioning
## 0 0 0
## 1stFloorSquareFeet 2ndFlrSquareFeet LivAreaSquareFeet
## 0 0 0
## FullBathrooms Bedrooms KitchenQualityCondition
## 0 0 0
## TotalRooms GarageArea TotalPorchAreaSquareFeet
## 0 0 0
## MonthSold YearSold SaleType
## 0 0 0
## SaleCondition SalePrice
## 0 0## Exploratory Data Analysis
### Distribution of Sale Prices
ggplot(df, aes(x = SalePrice)) +
geom_histogram(binwidth = 10000, fill = "blue", alpha = 0.7) +
labs(title = "Distribution of Sale Prices", x = "Sale Price", y = "Count")
### Correlation Analysis
numeric_cols <- select_if(df, is.numeric)
corr_matrix <- cor(numeric_cols)
corrplot(corr_matrix, method = "color", type = "upper", tl.cex = 0.7)
### Sale Price vs Living Area
ggplot(df, aes(x = LivAreaSquareFeet, y = SalePrice)) +
geom_point(alpha = 0.5) +
geom_smooth(method = "lm", col = "red") +
labs(title = "Sale Price vs Living Area", x = "Living Area (sq ft)", y = "Sale Price")## `geom_smooth()` using formula = 'y ~ x'
### Sale Price by Building Type
ggplot(df, aes(x = BuildingType, y = SalePrice, fill = BuildingType)) +
geom_boxplot() +
theme(axis.text.x = element_text(angle = 45, hjust = 1)) +
labs(title = "Sale Price by Building Type", x = "Building Type", y = "Sale Price")
INTERPRETATION OF FINDINGS
1. Sale Price Distribution
The histogram of SalePrice shows a right-skewed distribution, meaning most houses are priced lower, with a few high-value properties pulling the average up.
This indicates that the housing market in the dataset is dominated by moderately priced homes, while luxury or high-end homes are relatively rare.
A right-skewed distribution suggests that using log transformation might help normalize the data if needed for modeling.
2. Relationship Between Living Area and Sale Price
The scatter plot of Living Area (LivAreaSquareFeet) vs. Sale Price shows a strong positive correlation.
Larger living spaces tend to be associated with higher house prices, which is expected since more space usually translates to higher property value.
However, some extreme outliers exist where very large homes are not proportionally expensive or where small homes are unexpectedly costly.
The fitted regression line indicates that for every increase in living area, the sale price increases at a predictable rate.
3. Variation in Sale Prices by Building Type
A boxplot analysis of Building Type vs. Sale Price shows that different types of buildings exhibit different price ranges.
Single-family detached homes tend to have the highest median prices, likely because they offer more privacy, space, and land ownership.
Other building types, such as townhouses or duplexes, tend to have lower median sale prices, reflecting market trends where such properties are often smaller or shared.
The spread of prices within each building type suggests variability in pricing even within similar property categories.
4. Correlation Analysis and Key Influencing Variables
A correlation heatmap of all numerical variables shows which factors are most strongly related to sale price.
Key variables positively correlated with Sale Price include:
Living Area (LivAreaSquareFeet): As discussed, larger homes command higher prices.
Total Basement Square Feet (TotalBasementSquareFeet): Homes with larger basements tend to sell for more.
Garage Area (GarageArea): A larger garage is often associated with higher property value.
1st Floor Square Feet (1stFloorSquareFeet): This suggests that the main living area size is a strong price determinant.
Negative or weakly correlated factors include:
Year Sold: More recent sales do not necessarily mean higher prices.
Overall Condition: While important, the condition rating alone does not show a strong correlation with price, meaning buyers consider multiple factors beyond condition.