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# ps7-1 - k is the number of explanatory variables in the...

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Problem set 7 Due on November 11 in class. Problem 1. Using the data on 104 apartments, you run 2 di ff erent re- gressions: a regression of rent on living space and # of bedrooms, and a regression of rent on living space, # of bedrooms, and a dummy for studios interacted with Living Space. The results of the regressions are given below: d Rent = 800 + 3 ( Living Space ) + 100 ( # of bedrooms ) , and d Rent = 600 + 3 ( Living Space ) + 80 ( # of bedrooms ) +4 ( Living Space ) ( Dummy for studios ) The sum of the squared residuals in the fi rst regression is 105 and in the second regression is 100. a) Interpret the coe cient on # of bedrooms in the fi rst regression (that is, describe its economic meaning) b) Interpret coe cient on ( Living Space ) ( Dummy for studios ) in the second regression c) Using the rule of thumb F-test (F-statistic is equal to ( SSR restricted SSR unrestricted ) /q SSR unrestricted / ( n k 1) , where q is the number of contraints in the null hypothesis relative to the al- ternative hypothesis and

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Unformatted text preview: k is the number of explanatory variables in the unrestricted regression), test a hypothesis that there is no systematic di f er-ence in the marginal e f ect of the Living Space on the Rent between studios and other apartments. Problem 2. You are given the following regression data d Expenditure = 300 (100) + 0 . 5 (0 . 4) ∗ Income − 100 (50) ∗ D + 0 . 3 (0 . 3) ∗ Income ∗ D where the standard errors of the OLS estimators are given in the parentheses 1 and D is a dummy variable equal to 1 if individual is African American and 0 otherwise. a) What is the economic interpretation of all the coe ﬃ cients in the above regression? b) Assuming that the OLS estimators of the coe ﬃ cients on Income and on Income ∗ D are independent, provide a 95% con f dence interval for a forecast of the increase in the expenditure of an African American, whose income has just increased by 100. 2...
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