Let ŷ = β̂_{o}, + β̂_{1}x_{1} + β̂_{2}x_{2}, ... β̂_{k}x_{k }be the least squares prediction equation, and let y be some observation to be obtained in the future.

a. Explain why (ŷ - y) is normally distributed.

b. Show that

E(ŷ - y) = 0

and

V(ŷ - y) = [1 + a'(X'X)^{-1}a]σ^{2}