Introduction

We will use the “HomesForSale” data from www.lock5stat.com to answer the following questions:

Analysis

We will use different statistical methods….

Q1: Use the data only for California. How much does the size of a home influence its price?

homes_CA <- subset(homes, State == "CA")

model_size <- lm(Price ~ Size, data = homes_CA)
summary(model_size)
## 
## Call:
## lm(formula = Price ~ Size, data = homes_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

The data shows that the size of a home in California affects its price. Bigger homes usually cost more, and size explains part of the difference in home prices.

Q2: Use the data only for California. How does the number of bedrooms of a home influence its price?

model_bed <- lm(Price ~ Beds, data = homes_CA)
summary(model_bed)
## 
## Call:
## lm(formula = Price ~ Beds, data = homes_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

The data shows that the number of bedrooms in a California home does not have a clear effect on its price.

Q3: Use the data only for California. How does the number of bathrooms of a home influence its price?

model_bath <- lm(Price ~ Baths, data = homes_CA)
summary(model_bath)
## 
## Call:
## lm(formula = Price ~ Baths, data = homes_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

The data shows that the number of bathrooms in a California home significantly affects its price. More bathrooms generally mean higher prices.

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?

model_multi <- lm(Price ~ Size + Beds + Baths, data = homes_CA)
summary(model_multi)
## 
## Call:
## lm(formula = Price ~ Size + Beds + Baths, data = homes_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

The data shows that the home size is the most important factor affecting California home prices, while bedrooms and bathrooms do not have as much of an affect.

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.

model_state <- aov(Price ~ State, data = homes)
summary(model_state)
##              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 ' ' 1

The data shows that home prices vary significantly between different states.

Summary

Exploring Homes in CA, NJ, NY, and PA Home size is the main factor that affects California home prices, with bigger homes costing more. Bathrooms also have some effect, but bedrooms don’t really have an affect. Overall, home prices vary significantly between different states.