1 Suppose That The Full Model Is 94 30 3 3 212 Er 1 For I 1 2 N Where Za And 22 Have Been Coded So That S 1 (22.5 KiB) Viewed 16 times
1 Suppose That The Full Model Is 94 30 3 3 212 Er 1 For I 1 2 N Where Za And 22 Have Been Coded So That S 2 (22 KiB) Viewed 16 times
1 Suppose That The Full Model Is 94 30 3 3 212 Er 1 For I 1 2 N Where Za And 22 Have Been Coded So That S 3 (22 KiB) Viewed 16 times
1. Suppose that the full model is 94 = 30 +3₁ +3₂212+ er (1) for i=1,2,.....n, where za and 22 have been coded so that S₁1=S22=1. We will also consider fitting a subset model, say y = Bo +8₁₁+. a. Let ; be the least-squares estimate of 3, from the full model. Show that Var(8) ²/(1-₂). (2) where rig is the correlation between ₁ and 22. b. Let 3 be the least-squares estimate of 3, from the subset model. Show that Var(₁) = 0². Is 8₁ estimated more precisely from the subset model or from the full model? Explain. c. Show that E(3₁) = 1 +r1282. Under what circumstances is ₁ an unbiased estimator of 3₁? d. Find the mean square error for the subset estimator 3₁. Compare MSE(3₁) with Var(3). Under what circumstances is 3₁ a preferable estimator, with respect to MSE?
1. Suppose that the full model is 9-80 +8₁ +₂12 + (1) for i=1,2,..., n, where za and 2 have been coded so that S₁1=S221. We will also consider fitting a subset model, say yo+Bia +.. a. Let i be the least-squares estimate of 3₁ from the full model. Show that Var (3)-²/(1-₂). (2) where r12 is the correlation between 1 and 2₂. b. Let 3 be the least-squares estimate of 31 from the subset model. Show that Var(3₁). Is 3₁ estimated more precisely from the subset model or from the full model? Explain. e. Show that E(3₁) 31+r1282. Under what circumstances is 31 an unbiased estimator of 3₁? d. Find the mean square error for the subset estimator 3₁. Compare MSE(31) with Var(3;). Under what circumstances is 3₁ a preferable estimator, with respect to MSE?
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