Using the “cars” dataset in R, build a linear model for stopping distance as a function of speed and replicate the analysis of your textbook chapter 3 (visualization, quality evaluation of the model, and residual analysis.)
Take a look at dataset
head(cars)
## speed dist
## 1 4 2
## 2 4 10
## 3 7 4
## 4 7 22
## 5 8 16
## 6 9 10
Visualize the data
plot(cars, xlab = "Speed (mph)", ylab = "Stopping distance (ft)",
las = 1, xlim = c(0, 25))
The Linear Model Fuction
attach(cars)
liner <- lm(dist ~ speed)
liner
##
## Call:
## lm(formula = dist ~ speed)
##
## Coefficients:
## (Intercept) speed
## -17.579 3.932
Evaluate the quality of the model
summary(liner)
##
## Call:
## lm(formula = dist ~ speed)
##
## 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
Resudual Analysis
plot(fitted(liner), resid(liner))
qqnorm(resid(liner))
qqline(resid(liner))
