a. Express the ith residual (where ) in the form , a linear function of the Yj

Question:

a. Express the ith residual (where )

in the form , a linear function of the Yj

’s. Then use rules of variance to verify that is given by Expression (13.2).

b. It can be shown that and (the ith predicted value and residual) are independent of one another. Use this fact, the relation , and the expression for from Section 12.4 to again verify Expression (13.2).

c. As xi moves farther away from , what happens to and to ?

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