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L05_moretestsans

# L05_moretestsans - Answers to exercises in The Gauss-Markov...

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Unformatted text preview: Answers to exercises in: The Gauss-Markov 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 one-way ANOVA model, the linear combination ˆ β 1 − ˆ β 2 is normally distributed with mean β 1 − β 2 and variance 0 . 1 σ 2 . Answer 2 We have 60 observations and three parameters, so the error degrees of freedom is 57. The test statistic is T = ˆ β 1 − ˆ β 2 radicalBig . 1 SSE/ 57 = − . 5 radicalBig . 1 × 82 . 8 / 57 = 1 . 31 . We accept H : β 1 = β 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 β = β 1 − β 2 , and its variance is 0 .....
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L05_moretestsans - Answers to exercises in The Gauss-Markov...

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