hw6_metrics_sp18.pdf - Problem Set 6 Econometrics Timothy Roeper Due March 29th 1 Suppose we want to estimate the effects of alcohol consumption(alcohol

hw6_metrics_sp18.pdf - Problem Set 6 Econometrics Timothy...

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Problem Set 6 Econometrics Timothy Roeper Due March 29th 1. Suppose we want to estimate the effects of alcohol consumption ( alcohol ) on college grade point average ( colGPA ). In addition to collecting information on grade point averages and alcohol usage, we also have data on attendance ( skipped , the number of lectures skipped per week). A standardized test score ( ACT ) and high school GPA ( hsGPA ) are also available. (a) Should we include skipped along with alcohol as explanatory variables in a multiple regression model? (Think about how you would interpret β alcohol and what your theory is about how frequency of alcohol consumption could affect GPA). Answer One effect of alcohol consumption is that it might lead students to skip more classes and that may be a reason why it hurts student performance. So if you control for classes skipped, you might be significantly underestimating the causal impact of alcohol consumption on student performance. (b) Should ACT and hsGPA be included as explanatory variables? Explain. Answer Yes. These variables may not be strictly uneccessary to get unbiased estimates (although they can’t hurt), but they will probably help reduce the standard errors by signifcantly reducing the variance of the disturbance term. (c) Load the gpa1 data and test the hypothesis that alcohol consumption affects GPA using the regression that seems most appropriate to you. > library(wooldridge) > data("gpa1") > my_reg <- lm(colGPA ~ alcohol + hsGPA + ACT, data = gpa1) > summary(my_reg) Call: lm(formula = colGPA ~ alcohol + hsGPA + ACT, data = gpa1) 1
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Residuals: Min 1Q Median 3Q Max -0.84870 -0.25571 -0.02872 0.27773 0.83642 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 1.278706 0.342886 3.729 0.00028 *** alcohol 0.006456 0.021435 0.301 0.76372 hsGPA 0.456741 0.096747 4.721 5.73e-06 *** ACT 0.008771 0.011030 0.795 0.42787 --- Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1 Residual standard error: 0.3414 on 137 degrees of freedom Multiple R-squared: 0.177,Adjusted R-squared: 0.1589 F-statistic: 9.819 on 3 and 137 DF, p-value: 6.555e-06 2. Download 401k data provided on NYU classes and load it in to R data_401k <- read.csv("~/Dropbox/Econometrics/data_401k.csv")
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