a. Express the ith residual Yi Y i (where Y i 0 1xi )

a. Express the ith residual Yi Yˆ

i (where Yˆ

i
ˆ

0 ˆ

1xi

) in the form
cj Yj

, a linear function of the Yjs. Then use rules of variance to verify that V(Yi Yˆ

i

) is given by Expression (13.2).

b. It can be shown that Yˆi and Yi Yˆ

i (the ith predicted value and residual) are independent of one another. Use this fact, the relation Yi
Yˆ

i (Yi Yˆ

i

), and the expression for V(Yˆ) from Section 12.4 to again verify Expression (13.2).

c. As xi moves farther away from x

, what happens to V(Yˆi

)

and to V(Yi Yˆ

i

)?