(Sec. 11.2) Let z=y+x, where &y=&x=0, yy' = 0, 8x' = o1, &xx' = 0. The...

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(Sec. 11.2) Let z=y+x, where &y=&x=0, yy' = 0, 8x' = o²1, &xx' = 0. The p components of y can be called systematic parts, and the compo- nents of errors. (a) Find the linear combination y'z of unit variance that has minimum error variance (i.e., y'x has minimum variance). (b) Suppose + o² = 1, i = 1,..., p. Find the linear function y'z of unit variance that maximizes the sum of squares of the correlations between z; and y'z, i = 1,..., p. (c) Relate these results to principal components. (Sec. 11.2) Let z=y+x, where &y=&x=0, yy' = 0, 8x' = o²1, &xx' = 0. The p components of y can be called systematic parts, and the compo- nents of errors. (a) Find the linear combination y'z of unit variance that has minimum error variance (i.e., y'x has minimum variance). (b) Suppose + o² = 1, i = 1,..., p. Find the linear function y'z of unit variance that maximizes the sum of squares of the correlations between z; and y'z, i = 1,..., p. (c) Relate these results to principal components.

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