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.)
head(cars)
## speed dist
## 1 4 2
## 2 4 10
## 3 7 4
## 4 7 22
## 5 8 16
## 6 9 10
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
plot(cars)
clm = lm(cars$dist~cars$speed, data=cars)
clm
##
## Call:
## lm(formula = cars$dist ~ cars$speed, data = cars)
##
## Coefficients:
## (Intercept) cars$speed
## -17.579 3.932
plot(cars$speed, cars$dist, xlab='Speed (mph)', ylab='Stopping Distance (ft)', main='Stopping Distance vs. Speed')
abline(clm,col=c("red"))
summary(clm)
##
## Call:
## lm(formula = cars$dist ~ cars$speed, data = cars)
##
## Residuals:
## Min 1Q Median 3Q Max
## -29.069 -9.525 -2.272 9.215 43.201
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -17.5791 6.7584 -2.601 0.0123 *
## cars$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
Looks like the distribution is normal.
plot(clm$fitted.values, clm$residuals, xlab='Fitted Values', ylab='Residuals')
abline(0,0,col=c("red"))
qqnorm(clm$residuals)
qqline(clm$residuals)
