Housing
mydata <- read.csv2("Apartments.csv")
head(mydata)## ID PriceM2 Size Distance Floor Parking Age
## 1 1 2.64 70 8.4 3 0 3
## 2 2 3.80 51 0.6 1 1 3
## 3 3 2.66 68 8.4 3 0 3
## 4 4 2.85 70 8.1 3 0 3
## 5 5 2.64 68 5.4 3 1 3
## 6 6 2.77 76 3.6 2 0 3Description of the variables:
- ID
- PriceM2: Price per m2 in EUR.
- Size: Size in m2.
- Distance: Distance from city center in km.
- Floor: Floor level.
- Parking: Does the apartment have a parking space? (0: No, 1: Yes)
- Age: (1:New, 2:Up to 10 years old, 3: Older than 10 years)
mydata$ParkingF <- factor(mydata$Parking,
levels = c(0, 1),
labels = c("No", "Yes"))
mydata$AgeF <- factor(mydata$Age,
levels = c(1, 2, 3),
labels = c("New", "≤10 yrs", ">10 yrs"))
summary(mydata[c(-1, -6, -7)])## PriceM2 Size Distance Floor
## Min. :2.400 Min. :40.00 Min. :0.100 Min. :0.000
## 1st Qu.:2.808 1st Qu.:57.00 1st Qu.:1.125 1st Qu.:2.000
## Median :3.250 Median :63.00 Median :3.600 Median :3.000
## Mean :3.434 Mean :63.01 Mean :3.761 Mean :3.634
## 3rd Qu.:3.915 3rd Qu.:70.00 3rd Qu.:5.575 3rd Qu.:5.000
## Max. :4.980 Max. :82.00 Max. :8.700 Max. :9.000
## ParkingF AgeF
## No :29 New :48
## Yes:53 ≤10 yrs:20
## >10 yrs:14
##
##
## library(GGally) # Load tools for scatterplot matrices
ggpairs(
mydata[c("PriceM2", "Size", "Distance", "Floor", "ParkingF", "AgeF")], # Variables to display
upper = list(
continuous = wrap("smooth", method = "lm", se = FALSE, alpha = 0.6) # Scatterplots with OLS line
),
lower = list(continuous = "cor"), # Pearson correlation coefficients
diag = list(continuous = "densityDiag") # Density plots on the diagonal
) +
theme(
axis.text.x = element_text(angle = 45, hjust = 1, size = 7),
axis.text.y = element_text(size = 7)
)
fit <- lm(PriceM2 ~ Size + Distance + Floor + ParkingF + AgeF,
data = mydata)library(car)## Loading required package: carDatavif(fit) #Checking multicolinearity## GVIF Df GVIF^(1/(2*Df))
## Size 1.788840 1 1.337475
## Distance 1.701312 1 1.304344
## Floor 1.200754 1 1.095789
## ParkingF 1.313215 1 1.145956
## AgeF 1.241904 2 1.055655mean(vif(fit)[, "GVIF^(1/(2*Df))"])## [1] 1.187844mydata$StdResid <- rstandard(fit)hist(mydata$StdResid,
xlab = "Standardised residuals",
ylab = "Frequency",
main = "Histogram of standardised residuals")
shapiro.test(mydata$StdResid)##
## Shapiro-Wilk normality test
##
## data: mydata$StdResid
## W = 0.98681, p-value = 0.5686library(dplyr)##
## Attaching package: 'dplyr'## The following object is masked from 'package:car':
##
## recode## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union# Calculate Cook's distance
mydata$CooksD <- cooks.distance(fit)
# Define Cook's distance threshold
cd_threshold <- 4/nrow(mydata)
# Display apartments with Cook's distance above the threshold
influential_units <- mydata %>%
filter(CooksD > cd_threshold) %>%
arrange(desc(CooksD)) %>%
select(ID, PriceM2, Size, Distance, Floor, ParkingF, AgeF, CooksD)
influential_units %>%
mutate(CooksD = round(CooksD, 3))## ID PriceM2 Size Distance Floor ParkingF AgeF CooksD
## 1 81 4.90 66 0.1 4 Yes New 0.075
## 2 75 4.60 68 1.2 4 Yes New 0.051
## 3 10 3.57 59 1.2 8 Yes >10 yrs 0.051
## 4 4 2.85 70 8.1 3 No >10 yrs 0.049mydata$StdFittedValues <- scale(fit$fitted.values)
library(car)
scatterplot(y = mydata$StdResid, x = mydata$StdFittedValues,
ylab = "Standardised residuals",
xlab = "Standardised fitted values",
boxplots = FALSE,
regLine = FALSE,
smooth = FALSE)
library(olsrr)##
## Attaching package: 'olsrr'## The following object is masked from 'package:datasets':
##
## riversols_test_breusch_pagan(fit)##
## Breusch Pagan Test for Heteroskedasticity
## -----------------------------------------
## Ho: the variance is constant
## Ha: the variance is not constant
##
## Data
## -----------------------------------
## Response : PriceM2
## Variables: fitted values of PriceM2
##
## Test Summary
## ----------------------------
## DF = 1
## Chi2 = 2.069615
## Prob > Chi2 = 0.1502595summary(fit) ##
## Call:
## lm(formula = PriceM2 ~ Size + Distance + Floor + ParkingF + AgeF,
## data = mydata)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.73396 -0.22692 -0.02825 0.22486 0.87658
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.16921 0.36885 14.015 < 2e-16 ***
## Size -0.02511 0.00556 -4.517 2.29e-05 ***
## Distance -0.12199 0.01835 -6.648 4.21e-09 ***
## Floor 0.04792 0.02197 2.181 0.032285 *
## ParkingFYes 0.33227 0.08990 3.696 0.000414 ***
## AgeF≤10 yrs -0.14155 0.09720 -1.456 0.149484
## AgeF>10 yrs -0.28479 0.10999 -2.589 0.011551 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3396 on 75 degrees of freedom
## Multiple R-squared: 0.807, Adjusted R-squared: 0.7916
## F-statistic: 52.27 on 6 and 75 DF, p-value: < 2.2e-16sqrt(summary(fit)$r.squared) ## [1] 0.8983382library(lm.beta)
lm.beta(fit)##
## Call:
## lm(formula = PriceM2 ~ Size + Distance + Floor + ParkingF + AgeF,
## data = mydata)
##
## Standardized Coefficients::
## (Intercept) Size Distance Floor ParkingFYes
## NA -0.30645540 -0.43985221 0.12125659 0.21485378
## AgeF≤10 yrs AgeF>10 yrs
## -0.08221483 -0.14492675fitNEW <- lm(
PriceM2 ~ Size + I(Size^2) +
Distance + I(Distance^2) +
Floor + ParkingF + AgeF,
data = mydata
)
mydata$StdResid <- round(rstandard(fitNEW), 3)
mydata$StdFittedValues <- scale(fitNEW$fitted.values)
library(car)
scatterplot(y = mydata$StdResid, x = mydata$StdFittedValues,
ylab = "Standardized residuals",
xlab = "Standardized fitted values",
boxplots = FALSE,
regLine = FALSE,
smooth = FALSE)
summary(fitNEW)##
## Call:
## lm(formula = PriceM2 ~ Size + I(Size^2) + Distance + I(Distance^2) +
## Floor + ParkingF + AgeF, data = mydata)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.8072 -0.1295 0.0215 0.1549 0.6680
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.6265496 1.2696166 4.432 3.23e-05 ***
## Size -0.0354422 0.0403222 -0.879 0.38230
## I(Size^2) 0.0001386 0.0003156 0.439 0.66190
## Distance -0.3914330 0.0504730 -7.755 4.06e-11 ***
## I(Distance^2) 0.0305664 0.0054130 5.647 2.95e-07 ***
## Floor 0.0415768 0.0185466 2.242 0.02802 *
## ParkingFYes 0.3342930 0.0755459 4.425 3.31e-05 ***
## AgeF≤10 yrs -0.0472774 0.0833000 -0.568 0.57208
## AgeF>10 yrs -0.3167237 0.0928486 -3.411 0.00106 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2852 on 73 degrees of freedom
## Multiple R-squared: 0.8675, Adjusted R-squared: 0.853
## F-statistic: 59.77 on 8 and 73 DF, p-value: < 2.2e-16mydata$FittedValues <- fitted.values(fit)
mydata$Residuals <- residuals(fit) mydata[2 , colnames(mydata) %in% c("ID", "PriceM2", "FittedValues", "Residuals")]## ID PriceM2 FittedValues Residuals
## 2 2 3.8 3.910591 -0.1105908