Page 280 - Applied Statistics with R

280 CHAPTER 13. MODEL DIAGNOSTICS

Normal Q-Q Plot, fit_3

30
20
Sample Quantiles 10 0

-20 -10

-3 -2 -1 0 1 2 3

Theoretical Quantiles

Lastly, for fit_3, we again have a suspect Q-Q plot. We would probably not
believe the errors follow a normal distribution.

13.2.5 Shapiro-Wilk Test

Histograms and Q-Q Plots give a nice visual representation of the residuals
distribution, however if we are interested in formal testing, there are a number
of options available. A commonly used test is the Shapiro–Wilk test, which
is implemented in R.

set.seed(42)
shapiro.test(rnorm(25))

##
## Shapiro-Wilk normality test
##
## data: rnorm(25)
## W = 0.9499, p-value = 0.2495

shapiro.test(rexp(25))

##