from the context, I can conclude E(Y |K=1) = 0, E(Y |K=2) = 0+1 , E(Y |K=3) =0+ 2 , then get a matrix M* = y. But what is the next? what is se(hat beta1|K)?

Plz help with part (a) at least.

Let K = {1, 2, 3} be a categorical variable with three levels, and consider tting the model E(Y|K) = n + 131K2 + 52K3a where K, = 1 if K = 2'. Assume each group has the same sample size 711,, and 3n}, = n. a) Show that 33(31|K) = se(5'2|K). b) Show that 36(30|K) = se(5'0 + 31m) = 3450 + 32m). (You only need to carry out these derivations to the point that you can show the equality, not derive the final 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.)