11.3. (Sec. 11.2) Let z = y +x, where rly = rlx = 0, rlyy' =~, rlu' = u 2[, rlyx'

= O. The p components of y can be called systematic parts, and the components of x errors.

(a) Find the linear combination "I' z of unit variance that has minimum error variance (i.e., "I' x has minimum variance).

(b) Suppose 4>ii + u 2 = 1, i = 1, ... ,p. Find the linear function "I I z of unit variance that maximizes the sum of squares of the correlations between Zj and 'Y'z, i = 1, ... ,p.

(c) Relate these results to principal components.