econ466mt1a - test score is the average(c Given that...

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Economics 466: Introductory Econometrics State University of New York at Binghamton Department of Economics Fall 2011 Midterm I — Answers 1. (a) n X i =1 b v i = n X i =1 y i b φ b γx i = n X i =1 y i ( y b γ x ) b γx i = n y n y + b γn x b γn x =0 (b) n X i =1 b v i x i = n X i =1 ³ y i b φ b γx i ´ x i = n X i =1 [ y i ( y b γ x ) b γx i ] x i = n X i =1 [( y i y ) b γ ( x i x )] x i = n X i =1 [( y i y ) b γ ( x i x )] ( x i x )= n X i =1 h ( y i y )( x i x ) b γ ( x i x ) 2 i = n X i =1 ( y i y )( x i x ) b γ n X i =1 ( x i x ) 2 = n X i =1 ( y i y )( x i x ) n X i =1 ( y i y )( x i x ) n X i =1 ( x i x ) 2 n X i =1 ( x i x ) 2 = n X i =1 ( y i y )( x i x ) n X i =1 ( y i y )( x i x )=0 2. 1
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3. (a) 52.43538. This can be obtained by taking multiplying the t-Statistic by the standard error c (1) = ( t stat ) × se ( c (1)) = 334 . 8851 × 0 . 156577. The more direct way is to recognize that the coe cient when there is no regressor is the mean of the dependent variable (listed in the table) as 52.43538. (b) The intuition behind this result is that if you don’t have any regressors, your best guess of the
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Unformatted text preview: test score is the average. (c) Given that homework does not come into the model, an additional hour of homework has no impact on the test scores. (d) One way to determine this is to look at the formula for R 2 . We know that R 2 = SSE/SST . For now, all we need to show is the numerator. SSE = P n i =1 ( b y i − y ) 2 . As we noted above, the coe ffi cient on c (1) is simply the mean of y ( y ). Therefore, the f tted value b y i = y for all i . Hence, SSE = 0 and thus R 2 = 0. (e) R 2 is a measure of how well the x explains the y . If there is no x in the model, then it cannot explain y . 2...
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econ466mt1a - test score is the average(c Given that...

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