Question

B3. Suppose that we have the matrix form linear model Y = X0 + €, where Y = (Y1, ..., Yn)T, O = (01,02, ..., 0p)T, E = (€1, ..., en)T, X is the n xp design matrix, and e~ N(0,0²I). You may assume throughout that det XTX = 0, so that XTX is invertible. (d) Show that Covcê, ê) = 0pxn, where Opxn denotes a p x n matrix of zeroes. Hence explain why ô2 and 0 are independent, where ô 2 denotes the unbiased estimator of o2. [6]