Consider the special case of model (4.17), y = XT + e, where the ei mutually independent N(0, 2) random variables. Show that the REML

Consider the special case of model (4.17), y = XφT + e, where the ei mutually independent N(0, σ2) random variables.

Show that the REML estimate of σ2 is given by rss/(n − p − 1) and that the maximised profile restricted loglikelihood is equal to

−0.5(n − p − 1){log 2π + log[rss/(n − p − 1)] + 1} − 0.5 log |XT X|.

Derive expressions for the maximised profile restricted loglikelihood for the following special cases of (4.17): (i) yi = µ + ei and (ii) yi = α + βxi.