se for cagorical

'4' LIME! lllUll U Let K = {1, 2, 3} be a categorical variable with three levels, and consider tting the model E(Y|K) = [30 + 51K2 + {32K3a where K,- = 1 if K = 2'. Assume each group has the same sample size 11.1,, and 3n], = n. a) Show that 56(1|K) = 36(32IK). b) Show that se([0|K) = 38(5'0 +E1|K) = 36(50 + 32m). (You only need to carry out these derivations to the point that you can show the equality, not derive the nal values. Hint: You'll need to start taking a matrix inverse, but you may not need to complete the inverse. There is a closed form solution for a 3X3 matrix inverse.)