*For the statistic t= B-B SE Vi to have a 1-distribution, the estimators B; and Se...
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*For the statistic t= B₁-B₁ SE √Vi to have a 1-distribution, the estimators B; and Se must be independent. [Here, vij is the jth diag- onal entry of (X'X)¹.] The coefficient B; is the jth element of b, and SE= √ee/(n-k-1) is a function of the residuals e. Because both b and e are normally distributed, it suffices to prove that their covariance is 0. Demonstrate that this is the case. [Hint: Use C(e. b) = E[e(b-3)], and begin by showing that b-3= (XX) 'X'E.] *For the statistic t= B₁-B₁ SE √Vi to have a 1-distribution, the estimators B; and Se must be independent. [Here, vij is the jth diag- onal entry of (X'X)¹.] The coefficient B; is the jth element of b, and SE= √ee/(n-k-1) is a function of the residuals e. Because both b and e are normally distributed, it suffices to prove that their covariance is 0. Demonstrate that this is the case. [Hint: Use C(e. b) = E[e(b-3)], and begin by showing that b-3= (XX) 'X'E.]
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To prove that the statistic has a tdistribution we must show that the estimators Bj an... View the full answer
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
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