# ps4_sol - Department of Economics Columbia University...

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Department of Economics W3412 Columbia University Spring 2010 SOLUTION TO Problem Set 4 Introduction to Econometrics Prof. Marcelo J. Moreira and Seyhan E Arkonac, PhD Spring 2010 1. Use Table 2 to answer the following questions. Table 2 presents the results of four regressions, one in each column. Estimate the indicated regressions and fill in the values (you may either handwrite or type the entries in; if you choose to type up the table, an electronic copy of Table 2 in .doc format is available on the course Web site). For example, to fill in column (2), estimate the regression with colGPA as the dependent variable and hsGPA and skipped as the independent variables, using the “robust” option, and fill in the estimated coefficients a) Fill out the table with necessary numbers, some will be on STATA output some you will need to calculate yourself. b) Common sense predicts that your high school GPA (hsGPA) and the number of classes you skipped (skipped) are determinants of your college GPA (colGPA). Use regression (2) to test the hypothesis (at the 5% significance level) that the coefficients on these two economic variables are all zero, against the alternative that at least one coefficient is nonzero. at least one coef. is nonzero The p-value for the F-statistic =.00<.05, thus we reject at the 5% significance level. We tend to conclude at least one coefficient is nonzero. c) Find the F-statistic for regression (3) and explain what is it testing? The F-statistic for regression (3) is 12.07; it is jointly testing whether all of the coefficients are equal to 0, that is - if all the regressors jointly have no explanatory power. d) Find the F-statistics for regression (4) and explain what is it testing? The F-statistic for regression (4) is 11.14 (this is not from the table); it is jointly testing whether all of the coefficients are equal to 0, that is - if all the regressors jointly have no explanatory power. e) Are bgfriend (whether you have a boy/girlfriend) and campus (whether you live on campus) jointly significant determinants of college GPA? Use regression (2) and (4) to test your hypothesis. (i.e. use homoskedasticity-only F stat formula, eq.7.14 in the book, instead of directly testing with STATA)

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at least one coef. is nonzero where and are obtained from regression (4) and (2) respectively; the number of restrictions is q =2; is the number of regressors in the unrestricted regression; q and are degrees of freedom for the F distriction (here we perform non-robust regressions). F (2, 135, α=0.05) =3.06>2.62, thus we cannot reject at the 5% significance level. We tend to conclude that bgfriend and campus jointly have no explanatory power. Alternatively, we can use the Stata command: di fprob(2, 135, 2.62) to find the associated p-value = .077>.05, again we cannot reject at the 5% significance level. Table 1
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ps4_sol - Department of Economics Columbia University...

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