Loading cars data set
summary(cars)
## speed dist
## Min. : 4.0 Min. : 2.00
## 1st Qu.:12.0 1st Qu.: 26.00
## Median :15.0 Median : 36.00
## Mean :15.4 Mean : 42.98
## 3rd Qu.:19.0 3rd Qu.: 56.00
## Max. :25.0 Max. :120.00
cars_data = cars
head(cars_data)
## speed dist
## 1 4 2
## 2 4 10
## 3 7 4
## 4 7 22
## 5 8 16
## 6 9 10
Building a Linear Model for stopping distance as a function of
speed
#the linear model
model <- lm(dist ~ speed, data=cars_data)
#Summarizing the model to get the coefficients and other statistics
summary(model)
##
## Call:
## lm(formula = dist ~ speed, data = cars_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -29.069 -9.525 -2.272 9.215 43.201
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -17.5791 6.7584 -2.601 0.0123 *
## speed 3.9324 0.4155 9.464 1.49e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15.38 on 48 degrees of freedom
## Multiple R-squared: 0.6511, Adjusted R-squared: 0.6438
## F-statistic: 89.57 on 1 and 48 DF, p-value: 1.49e-12
# Plotting the data and the linear model
plot(cars_data$speed, cars_data$dist, main="Stopping Distance as a Function of Speed", xlab="Speed", ylab="Stopping Distance")
abline(model, col="red")
Quality evaluation of the model, and Analyzing Residual
qqnorm(resid(model))
qqline(resid(model))
library(car)
## Loading required package: carData
# Checking for linearity and homoscedasticity visually
plot(model, which=1) # Residuals vs Fitted
plot(model, which=3) # Scale-Location (also for checking homoscedasticity)
# Residual Analysis
par(mfrow=c(2,2))
plot(model)
# Normality of residuals
hist(residuals(model), breaks=10, main="Histogram of Residuals", xlab="Residuals") # Histogram of residuals
shapiro.test(residuals(model)) # Shapiro-Wilk test for normality
##
## Shapiro-Wilk normality test
##
## data: residuals(model)
## W = 0.94509, p-value = 0.02152
# Independence of residuals
durbinWatsonTest(model)
## lag Autocorrelation D-W Statistic p-value
## 1 0.1604322 1.676225 0.216
## Alternative hypothesis: rho != 0
