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Unformatted text preview: Department of Economics Spring 2011 University of California Prof. Woroch Economics 140: Problem Set 3 SUGGESTED SOLUTIONS True/False/Uncertain and Explain. 1. A researcher should go ahead and add a new regressor whenever adding it to the regression model increases the adjusted 2 R because that measure of goodness of fit corrects for the fact that the usual 2 R will always increase with inclusion of an additional variable. False. Economic theory should be our guide when specifying which variables enter into the population regression. 2 R measures the linear relationship between dependent variable and independent variables, but does not imply a causal relationship. It is true that usual 2 R will always increase with inclusion of an additional variable, and so looking instead at the value of the adjusted- 2 R will help identify the inclusion of irrelevant explanatory variables, but it not the criterion to include a variable. 2. A researcher is worried about multicollinearity in a multivariate regression model because the correlation coefficient between two regressors, 2 X and 3 X , is equal to -0.89. Her solution is to drop one of the regressors, 3 X , expecting that the t stat value on the other remaining regressor, 2 X , will get much larger. True. Dropping one of the two collinear variables will remove the main symptom of multicollinearity which is large standard errors of the individual regressors. Accordingly, the standard error on the remaining regressor will greatly diminish and so have a much larger t stat. But keep in mind that, while dropping the regressor will have this effect, it is not advisable if economic principles dictate that both variables should be in the regression. 3. If you reject a joint null hypothesis using the F- test in a multivariate linear regression model, then you will reject the null hypotheses that each of the coefficients is equal to zero by performing individual t-tests on them. False. The size of the one at a time t-test is not the same as the size of the F-test at a given significance level. If the t-statistics are correlated, the F-test may reject the null hypothesis when one or more of the t-test does not reject the null hypothesis. Multi-Part Questions. 1. The Excel spreadsheet wages.xls contains data from a survey of 526 U.S. workers in 1976. The dataset includes information on each workers age, hourly wage, years working for their current employer (tenure), years of education, gender, and marital status. a) Estimate the following model using linear regression: i i i u X Y 1 1 (1) where i Y is the wage, i X 1 is the age, and i indexes the i = 1, . . ., 526 workers....
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