1. Introduction

We use the data from ….

I propose the following 10 questions based on my own understanding of the data and ChatGPT.

2. Anaylsis

We will explore the questions in detail.

home = read.csv("https://www.lock5stat.com/datasets3e/HomesForSale.csv")
head(home)                   
##   State Price Size Beds Baths
## 1    CA   533 1589    3   2.5
## 2    CA   610 2008    3   2.0
## 3    CA   899 2380    5   3.0
## 4    CA   929 1868    3   3.0
## 5    CA   210 1360    2   2.0
## 6    CA   268 2131    3   2.0

Q1: How much does the size of a home influence its price?

california_data <- subset(home, State == "CA")

model_size <- lm(Price ~ Size, data = california_data)
summary(model_size)
## 
## Call:
## lm(formula = Price ~ Size, data = california_data)
## 
## 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 size of the home makes the price go up if its high, and down if its low

Q2: How does the number of bedrooms of a home influence its price?

 lm(Price~Beds, data = california_data)
## 
## Call:
## lm(formula = Price ~ Beds, data = california_data)
## 
## Coefficients:
## (Intercept)         Beds  
##      269.76        84.77

Shows that the more bedrooms there are, the higher the price goes up (by $84.77.)

Q3. How does the number of bathrooms of a home influence its price?

model_bathrooms <- lm(Price ~ Baths, data = california_data)
summary(model_bathrooms)
## 
## Call:
## lm(formula = Price ~ Baths, data = california_data)
## 
## 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 cost is varied between periods of ups and downs

Q4. How do the size, the number of bedrooms, and the number of bathrooms of a home jointly influence its price?

model_joint <- lm(Price ~ Size + Beds + Baths, data = california_data)
summary(model_joint)
## 
## Call:
## lm(formula = Price ~ Size + Beds + Baths, data = california_data)
## 
## 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

When they are all large, the price of the home greatly increases

Q5. Are there significant differences in home prices among the four states (CA, NY, NJ, PA)?

selected_states <- subset(home, State %in% c("CA", "NY", "NJ", "PA"))
anova_model <- aov(Price ~ State, data = selected_states)
tukey_results <- TukeyHSD(anova_model)
print(tukey_results)
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Price ~ State, data = selected_states)
## 
## $State
##             diff       lwr        upr     p adj
## NJ-CA -206.83333 -363.6729  -49.99379 0.0044754
## NY-CA -170.03333 -326.8729  -13.19379 0.0280402
## PA-CA -269.80000 -426.6395 -112.96045 0.0001011
## NY-NJ   36.80000 -120.0395  193.63955 0.9282064
## PA-NJ  -62.96667 -219.8062   93.87288 0.7224830
## PA-NY  -99.76667 -256.6062   57.07288 0.3505951
summary(anova_model)
##              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

There are significant differences in home prices between states, snd California has the most expensive homes

3. Summary

The results came in as expected, the answers verify the questions and my assumptions. Price data is varied, dependent on other factors, and may not always align with assumptions.