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Exercise 1 Suppose X is the initial matrix in a multiple regression problem. We then add an extra predictor z. So the regress

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Exercise -1 Solutions - Given that * let us suppose that at first we had the Follow eng regressfion model. Yi = Bo + BXxi + Bwhere a szir z = 1 11 212- 0ki? 1 712---- 2- 219 --1kn Therefore, w!!!! ! 2012120--. con 121 322 --- 92.n Z XK XK2Rkn tox(K+where AB, C and D are some square matrices. then on TV-f44[T+840-CA1B)ca) -A8{0-c46b) | -(D-CA*B)CA (o-ca-e) | Thus, OnThen , 2* is residual rector of regression Z on X- mney * (I-H)7 and H= x(xx) x Theredere, * * = 2 (I-H)(I-H) z since 2*

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