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Unformatted text preview: Economics 120B Name: _________________________ Professor Yongil Jeon March 18, 2005 Student ID#: _________________________ Answer to Exam 3: Econometrics 1. (5 points) If an additional independent variable, however irrelevant, is added to a multiple regression model, a smaller sum of squared errors will result. Explain why this is so, and discuss the consequences for the interpretation of R 2 . Answer Suppose we estimate two models, where the second model includes more explanatory variables. Then the following holds: SST=SSR 1 +SSE 1 = SSR 2 +SSE 2 . Since the second regression has more explanatory variables SSR 1 SSR 2 , which implies that SSE 1 SSE 2 . As a consequence, R 2 will only provide a meaningful measure of the explanatory power of a regression if the coefficients for the explanatory variables are significantly different from zero. 2. (5 points) A dependent variable is regressed on two independent variables. Is it possible that the hypotheses : 1 = H and : 2 = H cannot be rejected at low significance levels, yet the hypothesis : 2 1 = = H can be rejected at a very low significance level. In what circumstances might this result arise? Answer This occurs when the explanatory variables 1 x and 2 x are highly correlated. 2 EXAM #3, ECON 120B, Winter 2005 2 3. (40 points) Based on 107 students scores on the first examination in a course on managerial cost accounting, the following model was estimated by least squares (Note that the standard errors are in parentheses) y = 2.178 + 0.469 x 1 +3.369 x+3....
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