HW5 - STA131C Spring 2007 Prof W Polonik HW 5 due in class...

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Unformatted text preview: STA131C, Spring 2007 Prof. W. Polonik HW # 5 due: May 16, 2007 in class 1. Consider the normal simple linear regression model, i.e. Y i = a + b x i + ǫ i , i = 1 , . . ., n, where ǫ 1 , . . . , ǫ n ∼ iid N (0 , σ 2 ) with σ 2 > , a, b ∈ R all unknown, and assume that not all of the known constants x i are equal. Construct a 95%-confidence interval for b . Proceed as follows: Find a pivot quantity based on hatwide b and hatwide σ 2 (the MLEs of b and σ 2 ). Justify the independence of hatwide b and hatwide σ 2 in the given regression model. Then use this to construct the confidence interval. (HINT: Use similar arguments as used in class for constructing confidence intervals for the regression function a + bx . NOTICE: The degrees of freedom involved here are different as compared to the material presented in class.) 2. Consider the normal simple linear regression model without intercept , i.e....
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