Linear Statistical Inference

Prob 2. Suppose the linear regression model is given by Yij = Mi + Eij, i = 1, ...k; j = 1, ...,n where &'s are i.i.d errors following N (0, o2) . In the matrix form, response vector is expressed as Y = (Yl1, . .. Yin; ...; Ykl, ... Ykn)' and parameter vector is M = (M1, ..., MK) . Consider null hypothesis Ho : M1 = ... = Hk. (1). Rewrite the null (testable) hypothesis as Ho : Hu = 0, where matrix H is a (k - 1) x k matrix and C (H') CC (X') . (2). Derive the distribution of Hu, where u is the least square esti- mator of u