Consider a p-dimensional response variable ~y, containing p variables, with n observation vectors ~y1, . . . , ~yn. The sample mean vector of these observation vectors is denoted by ~y = (1/n) Pn i=1 ~yi . Consider a linear combination z of the observation vector ~y, defined as z = a1y1 + a2y2 + + apyp = ~a>~y, where ~a> = (a1, a2, . . . , ap). i) Show that the mean of z is z = ~a>~y; [4 marks] 1