• There are no “groups” in simple linear regression; thus, you do not assess “within-” and “among-group” independence here. Independence is assessed among the individuals.
  • The residual plot should be obviously non-linear or heteroscedastic to consider the linearity and homoscedasticity assumptions violated.

Car Horsepower and Gas Mileage II

  1. The cars appear to be independent as no car make was used twice and they were all of different makes and models.
  2. No non-linearity was detected as the residual plot does not exhibit a distinct curvature (Figure 1-Left).
  3. The residual plot does show a very slight heteroscedasticity (Figure 1-Right). This is likely not enough to worry about.
  4. The Anderson-Darling test shows weak but insignificant evidence for non-normality (p=0.0784) and the histogram of residuals is approximately symmetric (Figure 1-Left).
  5. There are no significant outliers according to the outlier test (p=0.4334). There is also no evidence for any outliers on the histogram of residuals (Figure 1-Left).


Figure 1: Histogram of residuals (left) and residual plot (right) for regression of miles per gallon on horsepower in the cars study.

R Appendix.

car <- read.csv("CarMPG.csv")
lm1 <- lm(mpg~hp,data=car)