Ch._5_Exercise_Solutions - Sol - 1 Chapter 5 Solutions 1....

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Sol - 1 Chapter 5 Solutions 1. Suppose the columns of X are orthogonal. Show that the estimate of β j , the coefficient of x j , is not dependent on which are columns of X are included in the model. Suppose we have a model that includes x j and any other columns of X . We can write the model as yU r =+ α . Note that the columns of U are also orthogonal so that UU is diagonal and the diagonal element corresponding to t j is xx . Hence the diagonal element of ( corresponding to j t j ) t 1 j is 1 and since ( / j t j ) t 1 is also diagonal, we have $ j j t j t j xy = independent of all the other explanatory variates 2. Show that c for the full model that includes all p explanatory variates. p p 1 By definition if there are k explanatory variates in the model (plus a constant term), then ck p = estimated residual sum of squares 2 $ () n + + σ 21 . If we fit the full model with p explanatory variates, we get c np pn p p + = (- -) 2 2 1 $ $ + 1 as required. 3. The file ch6Exercise3.txt contains a response variate y and 10 explanatory variates x x 1 ,..., 1 0 for 100 cases. These data were created artificially for practice. The model
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This note was uploaded on 05/03/2011 for the course ECON 202 taught by Professor Na during the Spring '11 term at University of Toronto- Toronto.

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Ch._5_Exercise_Solutions - Sol - 1 Chapter 5 Solutions 1....

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