Let y = o , + 1 x 1 + 2 x 2 ,

Let ŷ = β̂_o, + β̂₁x₁ + β̂₂x₂, ... β̂_kx_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)^-1a]σ²