Discussion 11

Discussion 11

#Loading package
library(readxl)

## Warning: package 'readxl' was built under R version 4.3.3

#Replacing the file path with the correct path to your Excel file
file_path <- "C:/Users/aleja/Desktop/Real estate valuation data set.xlsx"

#Reading the first 5 rows of the Excel file
data <- read_excel(file_path, n_max = 5)

#Viewing the first 5 rows of the data
print(data)

## # A tibble: 5 × 8
##      No `X1 transaction date` `X2 house age` X3 distance to the nearest MRT st…¹
##   <dbl>                 <dbl>          <dbl>                               <dbl>
## 1     1                 2013.           32                                  84.9
## 2     2                 2013.           19.5                               307. 
## 3     3                 2014.           13.3                               562. 
## 4     4                 2014.           13.3                               562. 
## 5     5                 2013.            5                                 391. 
## # ℹ abbreviated name: ¹​`X3 distance to the nearest MRT station`
## # ℹ 4 more variables: `X4 number of convenience stores` <dbl>,
## #   `X5 latitude` <dbl>, `X6 longitude` <dbl>,
## #   `Y house price of unit area` <dbl>

Summary statistics

summary(data)

##        No    X1 transaction date  X2 house age  
##  Min.   :1   Min.   :2013        Min.   : 5.00  
##  1st Qu.:2   1st Qu.:2013        1st Qu.:13.30  
##  Median :3   Median :2013        Median :13.30  
##  Mean   :3   Mean   :2013        Mean   :16.62  
##  3rd Qu.:4   3rd Qu.:2014        3rd Qu.:19.50  
##  Max.   :5   Max.   :2014        Max.   :32.00  
##  X3 distance to the nearest MRT station X4 number of convenience stores
##  Min.   : 84.88                         Min.   : 5.0                   
##  1st Qu.:306.59                         1st Qu.: 5.0                   
##  Median :390.57                         Median : 5.0                   
##  Mean   :381.20                         Mean   : 6.8                   
##  3rd Qu.:561.98                         3rd Qu.: 9.0                   
##  Max.   :561.98                         Max.   :10.0                   
##   X5 latitude     X6 longitude   Y house price of unit area
##  Min.   :24.98   Min.   :121.5   Min.   :37.90             
##  1st Qu.:24.98   1st Qu.:121.5   1st Qu.:42.20             
##  Median :24.98   Median :121.5   Median :43.10             
##  Mean   :24.98   Mean   :121.5   Mean   :45.06             
##  3rd Qu.:24.99   3rd Qu.:121.5   3rd Qu.:47.30             
##  Max.   :24.99   Max.   :121.5   Max.   :54.80

# Check for multicollinearity
cor_matrix <- cor(data)
high_correlation <- which(cor_matrix > 0.7 & cor_matrix < 1, arr.ind = TRUE)
high_correlation

##                                        row col
## X3 distance to the nearest MRT station   4   2
## X5 latitude                              6   2
## X6 longitude                             7   2
## Y house price of unit area               8   2
## X4 number of convenience stores          5   3
## X1 transaction date                      2   4
## X6 longitude                             7   4
## Y house price of unit area               8   4
## X2 house age                             3   5
## X1 transaction date                      2   6
## X6 longitude                             7   6
## X1 transaction date                      2   7
## X3 distance to the nearest MRT station   4   7
## X5 latitude                              6   7
## Y house price of unit area               8   7
## X1 transaction date                      2   8
## X3 distance to the nearest MRT station   4   8
## X6 longitude                             7   8

# Load necessary libraries

library(corrplot)

## Warning: package 'corrplot' was built under R version 4.3.3

## corrplot 0.92 loaded

# Compute the correlation matrix
correlation_matrix <- cor(data)

# Compute the correlation matrix
correlation_matrix <- cor(data)

# Increase the plot size and decrease the text size
par(mar = c(1, 1, 1, 1))  # Adjust margin to leave space for larger plot
corrplot(correlation_matrix, method = "color", type = "upper", order = "hclust", tl.col = "black", tl.srt = 45, tl.cex = 0.7)

Running a regression model

#Running a linear regression model with only X3 distance to the nearest MRT station
model <- lm(`Y house price of unit area` ~ `X3 distance to the nearest MRT station`, data = data)

#Showing the summary of the regression model
summary(model)

## 
## Call:
## lm(formula = `Y house price of unit area` ~ `X3 distance to the nearest MRT station`, 
##     data = data)
## 
## Residuals:
##       1       2       3       4       5 
##  1.2030 -0.7544 -2.8621  4.6379 -2.2243 
## 
## Coefficients:
##                                           Estimate Std. Error t value Pr(>|t|)
## (Intercept)                              34.301523   3.691416   9.292  0.00264
## `X3 distance to the nearest MRT station`  0.028222   0.008772   3.217  0.04869
##                                            
## (Intercept)                              **
## `X3 distance to the nearest MRT station` * 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.496 on 3 degrees of freedom
## Multiple R-squared:  0.7753, Adjusted R-squared:  0.7004 
## F-statistic: 10.35 on 1 and 3 DF,  p-value: 0.04869

#Extracting the residuals from the linear regression model
residuals <- residuals(model)

par(mfrow=c(2,2))
plot(model)

#Shapiro-Wilk test for normality of residuals
shapiro.test(residuals)

## 
##  Shapiro-Wilk normality test
## 
## data:  residuals
## W = 0.92129, p-value = 0.5383

The results suggest that X3 distance to the nearest MRT station is a statistically significant predictor of Y house price of unit area. The model explains a significant portion of the variability in house prices, and the normality assumption for the residuals is not violated.