Let K = {1, 2, 3} be a categorical variable with three levels, and consider fitting the model

E(Y |K) = 0 +1K₂ + 2K₃,where K_i = 1 if K = i. Assume each group has the same sample size n_k, and 3n_k = n.

(a) Show that se(1^|K) = se(2^ |K).

(b) Show that se(0^ |K) = se( 0^+1^ |K) = se(0^+2^ |K)

(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.)

I already know that E(YK=1)=0 ,E(YK=2)=0+1 , E(YK=3)=0+2 . What's next for part(a)?