This project explores how various factors influence home prices using the “HomesForSale” dataset. The analysis focuses on homes in California to examine the effects of size, number of bedrooms, and number of bathrooms on pricing individually and collectively. Additionally, the project investigates price variations across four states—California, New York, New Jersey, and Pennsylvania. Using regression and ANOVA methods, this study aims to uncover significant predictors of home prices and regional differences. The insights gained provide valuable information for real estate market analysis and decision-making. We are going to explore these questions in this project:
Q1. Use the data only for California. How much does the size of a home influence its price?
Q2. Use the data only for California. How does the number of bedrooms of a home influence its price?
Q3. Use the data only for California. How does the number of bathrooms of a home influence its price?
Q4. Use the data only for California. How do the size, the number of bedrooms, and the number of bathrooms of a home jointly influence its price?
Q5. Are there significant differences in home prices among the four states (CA, NY, NJ, PA)? This will help you determine if the state in which a home is located has a significant impact on its price. All data should be used.
The dataset used in this project, “HomesForSale,” was sourced from the Lock5Stat website. It includes information on home prices and their attributes across several states in the United States. Key variables in the dataset include:
Price: The sale price of the home (in dollars). Size: The total area of the home (in square feet). Bedrooms: The number of bedrooms in the home. Bathrooms: The number of bathrooms in the home. State: The location of the home (CA, NY, NJ, PA). The dataset allows for a focused analysis of homes in California to understand how specific features impact prices and a broader comparison across states to determine regional pricing differences. Data preprocessing steps include filtering for relevant states, handling missing values, and ensuring variables are correctly formatted for regression and ANOVA analysis.
college = read.csv("https://www.lock5stat.com/datasets3e/HomesForSale.csv")In this section we are going to discuss all the questions in detail.
# Load data
home <- read.csv("https://www.lock5stat.com/datasets3e/HomesForSale.csv")
# Filter data for California
home_CA <- subset(home, State == "CA")
# Regression model: Size vs Price
model_size <- lm(Price ~ Size, data = home_CA)
summary(model_size)##
## Call:
## lm(formula = Price ~ Size, data = home_CA)
##
## Residuals:
## Min 1Q Median 3Q Max
## -462.55 -139.69 39.24 147.65 352.21
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -56.81675 154.68102 -0.367 0.716145
## Size 0.33919 0.08558 3.963 0.000463 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 219.3 on 28 degrees of freedom
## Multiple R-squared: 0.3594, Adjusted R-squared: 0.3365
## F-statistic: 15.71 on 1 and 28 DF, p-value: 0.0004634# Regression model: Bedrooms vs Price
model_bedrooms <- lm(Price ~ Beds, data = home_CA)
summary(model_bedrooms)##
## Call:
## lm(formula = Price ~ Beds, data = home_CA)
##
## Residuals:
## Min 1Q Median 3Q Max
## -413.83 -236.62 29.94 197.69 570.94
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 269.76 233.62 1.155 0.258
## Beds 84.77 72.91 1.163 0.255
##
## Residual standard error: 267.6 on 28 degrees of freedom
## Multiple R-squared: 0.04605, Adjusted R-squared: 0.01198
## F-statistic: 1.352 on 1 and 28 DF, p-value: 0.2548# Regression model: Bathrooms vs Price
model_bathrooms <- lm(Price ~ Baths, data = home_CA)
summary(model_bathrooms)##
## Call:
## lm(formula = Price ~ Baths, data = home_CA)
##
## Residuals:
## Min 1Q Median 3Q Max
## -374.93 -181.56 -2.74 152.31 614.81
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 90.71 148.57 0.611 0.54641
## Baths 194.74 62.28 3.127 0.00409 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 235.8 on 28 degrees of freedom
## Multiple R-squared: 0.2588, Adjusted R-squared: 0.2324
## F-statistic: 9.779 on 1 and 28 DF, p-value: 0.004092# Multiple regression model
model_multiple <- lm(Price ~ Size + Beds + Baths, data = home_CA)
summary(model_multiple)##
## Call:
## lm(formula = Price ~ Size + Beds + Baths, data = home_CA)
##
## Residuals:
## Min 1Q Median 3Q Max
## -415.47 -130.32 19.64 154.79 384.94
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -41.5608 210.3809 -0.198 0.8449
## Size 0.2811 0.1189 2.364 0.0259 *
## Beds -33.7036 67.9255 -0.496 0.6239
## Baths 83.9844 76.7530 1.094 0.2839
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 221.8 on 26 degrees of freedom
## Multiple R-squared: 0.3912, Adjusted R-squared: 0.3209
## F-statistic: 5.568 on 3 and 26 DF, p-value: 0.004353# ANOVA: State vs Price
model_anova <- aov(Price ~ State, data = home)
summary(model_anova)## Df Sum Sq Mean Sq F value Pr(>F)
## State 3 1198169 399390 7.355 0.000148 ***
## Residuals 116 6299266 54304
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1This project analyzes the factors influencing home prices using the “HomesForSale” dataset. It examines the relationship between home price and characteristics such as size, number of bedrooms, and bathrooms in California, applying regression techniques for individual and joint effects. Additionally, it investigates whether home prices significantly differ across California, New York, New Jersey, and Pennsylvania using ANOVA. The results provide insights into critical predictors of home value and regional price variations, offering a comprehensive understanding of the real estate market dynamics.