Exercise 14.5.4. Let v1 = (2,1,1,0), v2 = (0,1,1,0), v3 = (0,0,0,2), and = 3 i=1

Exercise 14.5.4. Let v1 = (2,1,1,0), v2 = (0,1,−1,0), v3 = (0,0,0,2), and

Σ =

3Σ

i=1 viv

i .

(a) Find the principal components of Σ .

(b) What is the predictive variance of each principal component? What percentage of the maximum prediction error is accounted for by the first two principal components?

(c) Interpret the principal components.

(d) What are the correlations between the principal components and the original variables?