## Question

###### Consider mltiple linear regression mocel Y _ XB + Ã¢â€šÂ¬ with 8 Ã¢â€šÂ¬ Rr+1 AId Ã¢â€šÂ¬ N,(6.o?). Split X and G into X = (X, X2) Ad 6 (8T.61 respectively: So(lat Wc' Write Y X8, XBz Let 0s,1 (XTX)-'XTY. 85 (851.852)" (XX)-IXTY #dl A = (XTX)-'XTXLet tz (F) 217 614 + 2" B12 . 5z (y) = 2,70s2 A =(xi"x)-X"xz Prove the following (Wo iclentities E(Y(F) - z" 8)? 2f var(85.1)21 + (22 - ATz)" var(852)(22 A Tz1) . E(z(S) - 2" 8)2 2] var(85,1z1 + (22 - TA 21)T 8p28F2

Consider mltiple linear regression mocel Y _ XB + Ã¢â€šÂ¬ with 8 Ã¢â€šÂ¬ Rr+1 AId Ã¢â€šÂ¬ N,(6.o?). Split X and G into X = (X, X2) Ad 6 (8T.61 respectively: So(lat Wc' Write Y X8, XBz Let 0s,1 (XTX)-'XTY. 85 (851.852)" (XX)-IXTY #dl A = (XTX)-'XTX Let tz (F) 217 614 + 2" B12 . 5z (y) = 2,70s2 A =(xi"x)-X"xz Prove the following (Wo iclentities E(Y(F) - z" 8)? 2f var(85.1)21 + (22 - ATz)" var(852)(22 A Tz1) . E(z(S) - 2" 8)2 2] var(85,1z1 + (22 - TA 21)T 8p28F2(22 ATz1).

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