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# ExtraCredit - STAT 8260 Extra Credit Problems Thursday May...

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STAT 8260 Extra Credit Problems – Thursday, May 1, 2008* SHOW ALL WORK Name: 1. Consider the “seemingly unrelated regressions:” y 1 = X 1 β 1 + e 1 , e 1 N n 1 ( 0 2 1 I n 1 ) y 2 = X 2 β 2 + e 2 , e 2 N n 2 ( 0 2 2 I n 2 ) for data y = ( y T 1 , y T 2 ) T , where cov( e 1 , e 2 ) = 0 , and the design matrices X 1 and X 2 are n 1 × p and n 2 × p , respectively, each of full rank with more rows than columns. a. (4 pts) Write the two seemingly unrelated regressions as a single linear model for y of the form y = X β + e . Deﬁne all quantities and state the assumptions on e . * These questions pertain to the full-rank linear model material and allow a maxi- mum of 26 points that can be applied to your exam # 2 score. 1

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(3 pts) State the hypothesis H 0 : β 1 = β 2 in the form of the general linear hypothesis. c. (2 pts) Is the ordinary least squares estimator in your model from part (a) optimal in any sense (e.g., BLUE, MVUE)? Explain why or why not. 2
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ExtraCredit - STAT 8260 Extra Credit Problems Thursday May...

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