Use equation 12.23 to express W W as a quadratic function of Y. Likewise, obtain e e, where e = Y − W , as a quadratic function of Y. Show that: (a) neither coefficient matrix is idempotent; (b) the...

Use equation 12.23 to express

<sub>W

W</sub>
as a quadratic function of Y. Likewise, obtain e e, where e = Y −

_W, as a quadratic function of Y. Show that:

(a) neither coefficient matrix is idempotent;

(b) the two coefficient matrices are not orthogonal. What are the implications of these results?