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Question 3 Let K = {1, 2, 3} be a categorical variable with three levels, and consider tting the model E(Y|K) = o + 1K2 + 52K3, where K, = 1 if K = 2'. Assume each group has the same sample size nk, and 371k = n. a) Show that se(31|K) = se(,2|K). b) Show that 86(3olK) = sew} + 31m = seat + MK). (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.)