Suppose Y = X + where (i) X is fixed not random, n p of rank

Suppose Y = Xβ +  where

(i) X is fixed not random, n× p of rank p, and

(ii) the i are IID with mean 0 and variance σ2, but

(iii) the i need not be normal.

Let βˆ = (X X)−1X Y . True or false and explain:

(a) E(β)ˆ = β.

(b) cov(β)ˆ = σ2(X X)−1.

(c) If n = 100 and p = 6, it is probably OK to use the t-test.

(d) If n = 100 and p = 96, it is probably OK to use the t-test.