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examf06_answersja - Suggested Solutions 1(a The...

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Suggested Solutions 1. (a) The interpretation of the coefficient on the dummy term, β 2 is the reduction in the number of labor hours due to a highly rated management when log( X i ) = 0. It is the effect of good management on the regression intercept. (b) The coefficient of the coefficient β 3 , the “interaction term” is, the effect of good management on the slope coefficient relating asset size to labor hours. (c) The fact that we care about “does not reduce the effect” hints that we’re interested in testing H 0 : β 3 0, with an alternative H 1 : β 3 < 0. The test statistic is given by t * = ˆ β 3 - β 3 se ( ˆ β 3 ) t n - k - 1 under H 0 . Substituting, we get t * = ˆ β 3 - β 3 se ( ˆ β 3 ) = - 0 . 10 0 . 02 = - 5, and we reject if t * < - t 0 . 05 n - k - 1 In this case t 0 . 05 28 - 3 - 1 = - 1 . 71 hence the null is rejected, leading to conclude that good management decreases the examination hours. (d) β 1 [ ˆ β 1 - se ( ˆ β 1 ) t ( . 025) 24 , ˆ β 1 + se ( ˆ β 1 ) t ( . 025) 24 ], or in numbers, [0.35-(2.06)(0.05), 0.35+(2.06)(0.05)]. 2. (a) The critical assumptions to ensure existence is no perfect collinearity. The estimator is given by ˆ β 2 = n i =1 ˆ r 2 i y i n i =1 ˆ r 2 i 2 . (b) To the previously stated above (no perfect collinearity) you add linearity, plus random sampling and E ( u | X ) = 0. These four assumptions allow to prove unbiasedness:

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examf06_answersja - Suggested Solutions 1(a The...

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