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Unformatted text preview: Answers to exercises in: The GaussMarkov Theorem Stat 640 Answer 1 The linear combination of parameters is defined by c = (1 , 1 , 0) . Because the columns of the design matrix are orthogonal, we have ( X X ) 1 = . 05 . 05 . 05 . Therefore, c ( X X ) 1 c = 0 . 1. With the usual assumptions on the oneway ANOVA model, the linear combination 1 2 is normally distributed with mean 1 2 and variance 0 . 1 2 . Answer 2 We have 60 observations and three parameters, so the error degrees of freedom is 57. The test statistic is T = 1 2 radicalBig . 1 SSE/ 57 = . 5 radicalBig . 1 82 . 8 / 57 = 1 . 31 . We accept H : 1 = 2 . Answer 3 The linear combination of parameters is defined by c = (0 , 1 , 1 , , 0) . Using the given expression for ( X X ) 1 , we get c ( X X ) 1 c = 0 . 4, so that the expected value of c hat = 1 2 , and its variance is 0 .....
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 Spring '08
 MaryMeyer

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