Question

Some statistical methods require that the residuals from a regression line have a normal distribution. Consider the following residuals.

0.37	-0.70	0.10	-0.34	0.19	0.61	-0.26	-0.98
1.64	-0.18	-0.23	0.54	-0.54	-1.11	0.93	-0.03

Is their distribution close to normal? Make a normal quantile plot to find out. (Do this on paper. Your instructor may ask you to turn this in.)

Answer 1

Let us use the following R code to make the Normal Quantile plot and judging its linearity by correlation test.

z <- c(0.37,-0.70,0.10,-0.34,0.19,0.61,-0.26,-0.98, 1.64,-0.18,-0.23,0.54,-0.54,-1.11,0.93,-0.03)
with(qqnorm(z), cor(x, y))

We obtain the following graph:

The plot looks linear enough.

Still, we calculate and according to Table 4.2 of Applied Multivariate Statistical Analysis (6th Edition) by Johnson - Wichern, this is more than the required critictical point for sample size 16 to achieve normality.

Hence, the distribution of the residuals can be assumed to be normal.