INTRODUCTION TO STATISTICAL MODELLING IN R

P.M.E.Altham, University of Cambridge 27The potash data, as a boxplot (potash being a factor)7.2 7.4 7.6 7.8 8.036 54 72 108 144Figure 4.2: Boxplot for cotton bundles datasetmay fail: we may be able to remedy this by replacing Y i by log Y i , or some othertransformation of Y , in the original linear model.Further, ˆɛ should be N(0, (I − H)σ 2 ).In order to check whether this is plausible, we find F n (u) say, the sample distributionfunction of the residuals. We would like to see whetherF n (u) ≃ Φ(u/σ)for some σ (where Φ is as usual, the distribution function of N(0, 1)). This is hardto assess visually, so instead we try to see ifΦ −1 F n (u) ≃ u/σ.This is what lies behind the qqplot. We are just doing a quick check of the linearityof the function Φ −1 F n (u).It’s fun to generate a random sample of size 100 from the t-distribution with 5 df,and find its qqnorm, qqline plots, to assess the systematic departure from a normaldistribution. To do this, tryy