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Econ 526 Econometrics Problem Set #3 1. Add variable labels to beauty course_eval intro nnenglish and then describe and summarize your data. Below, report the mean of course_eval and the mean of beauty. Interpret these numbers. (10 points) storage variable name type display value format label variable label ----------------------------------------------------------------------------------minority float %9.0g Minority age float %9.0g Professor's age female float %9.0g female = 1 onecredit byte %8.0g Equal 1 if a one-credit course beauty float %9.0g Standardized ranking of Beauty course_eval float %9.0g Teaching Evaluation 1-poor 5-great intro float %9.0g Introductory Course nnenglish float %9.0g Non-Native English Speaker . summarize *; Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------minority | 463 .1382289 .3455134 0 1 age | 463 48.36501 9.802742 29 73 female | 463 .4211663 .4942802 0 1 onecredit | 463 .0583153 .2345922 0 1 beauty | 463 4.75e-08 .7886477 -1.450494 1.970023 -------------+-------------------------------------------------------course_eval | 463 3.998272 .5548656 2.1 5 intro | 463 .3390929 .4739135 0 1 1 nnenglish | 463 .0604752 .2386229 0 1 Mean Beauty = 0. Mean Course evaluation = 3.998 out of a five point scale. Course evaluations are skewed to the right. 2. Create a histogram of beauty and impose the normal distribution on this graph. Do the same for course evaluations. Print and attach these graphs. Interpret these graphs. Do the data violate any regression assumptions? (15 points) 2 Beauty is skewed to the left—which means that there are more people with below average beauty. However Course Evaluations are skewed to the right. Both distributions also have multiple modes. Given that both data series are skewed, the assumption of normally distributed errors is likely violated. 3. Create a scatterplot of Course_eval and beauty. Insert a regression line in this scatterplot. Print off and attach your graph (be sure to have a title). Report the correlation between course_eval and beauty below. (15 points). Beauty and Course_eval have a small positive correlation of .189. You can see that there is a positive slope on the graph. 4. Regress course_eval on beauty. Write the equation for the regression line below. Explain why the intercept is equal to the sample mean of course_eval (hint: see your answer to question 1 above) Is beauty significantly different from zero? (10 points). Course_ eval = 3.998 +.133Beauty Beauty is significantly different from zero. The t-statistic tests the null hypothesis that the coefficient on beauty equals zero, and 4.13 > 1.96, so we reject the null. 3 5. Professor Watson has average beauty while Professor Holmes beauty is one standard deviation above average. Predict Professor Watson’s and Professor Holmes’ course evaluations. (10 points) Watson’s course evaluations: Course_ eval = 3.998 + .133 ´ 0 = 3.998 Holmes’ course evaluations: Course_ eval = 3.998 +.133´.789 = 4.102 6. Now regress Course_eval on beauty, intro, onecredit, female, minority, and nnenglish. Use robust standard errors. How will the standard errors change now that you have relaxed the homoscedasticity assumption? How does the coefficient on beauty change compared to question 3? Is beauty significantly different from zero? (15 points) The standard errors will be larger than in the previous regression because of correcting for heteroskedasticity. The table below shows the coefficients from the regression for Question 4, 6, and 8. The coefficient on beauty actually increases once you control for other characteristics. It is significantly different from zero in this regression as well. VARIABLES Standardized ranking of Beauty (1) (2) Question 4 Question 6 0.133*** [0.032] 0.104* [0.040] 0.244*** [0.048] 3.998*** [0.025] -0.240* [0.094] 0.363 [0.205] -0.148 [0.109] -0.021 [0.094] 3.932*** [0.049] 0.027 [0.094] 0.708*** [0.104] -0.407** [0.127] 0.039 [0.069] 4.049*** [0.042] 463 0.036 463 0.155 195 0.071 268 0.223 Minority Equal 1 if a one-credit course Non-Native English Speaker Introductory Course Observations R-squared Standard errors in brackets *** p<0.001, ** p<0.01, * p<0.05 (4) Male 0.166*** [0.032] -0.173*** [0.049] -0.167* [0.067] 0.635*** [0.108] -0.244** [0.094] 0.011 [0.056] 4.068*** [0.037] female = 1 Constant (3) Female 4 7. Professor Smith is a black man with average beauty and a nonnative English speaker. He teaches a three credit upper-division course. Predict Professor Smith’s course evaluations. (10 points) Course _ eval = 4.068 + .166Beauty -.173Female -.166Minority + .635onecredit -.244Nnenglish + .011int ro Course _ eval = 4.068 -.166 -.224 = 3.658 8. Run the same regression in #6 separately for male and female professors. Compare and contrast the coefficients in each regression. Predict the effect of one standard deviation increase in beauty on course evaluations for a white professor who is a native speaker of English teaching an upper level course for both men and women. Explain your result. (15 points) Examining the table above, you see that the effect of beauty is more than twice as large for men compared to women. Also, women are penalized in teaching evaluation more for being minorities. Men get over twice as much ‘return’ on teaching one credit courses compared to women. However, they are penalized almost three times as much for being non-native English speakers. As shown by the predictions below, women of above average beauty get less of a return on that compared to men. Course _ evalF = 3.932 + .104 Beauty - .240Minority +.363onecredit - .148 Nnenglish - .021int ro Course _ eval M = 4.049 + .244 Beauty - .027Minority +.708onecredit - .407Nnenglish - .039 int ro Course _ evalF = 3.932 + .104 ´ .789 = 4.01 Course _ eval M = 4.049 + .244 ´ .789 = 4.24 5 Do-file commands ******* Question 1 *********; label var beauty "Standardized ranking of Beauty"; label var course_eval "Teaching Evaluation 1-poor 5-great"; label var intro "Introductory Course"; label var nnenglish "Non-Native English Speaker"; describe *; summarize *; ******* Question 2 *********; histogram beauty, normal; histogram course_eval, normal; ******* Question 3 *********; twoway scatter course_eval beauty || lfit course_eval beauty; corr beauty course_eval; ******* Question 4 *********; regress course_eval beauty; outreg2 using problemset3sol.xls, bd(3) td(3) label alpha(.001, .01, .05) bracket ct(1) replace; ******* Question 6 *********; regress course_eval beauty female minority onecredit nnenglish intro, robust; outreg2 using problemset3sol.xls, bd(3) td(3) label alpha(.001, .01, .05) bracket ct(1) append; ******* Question 8 *********; regress course_eval beauty minority onecredit nnenglish intro if female==1, robust; outreg2 using problemset3sol.xls, bd(3) td(3) label alpha(.001, .01, .05) bracket ct(1) append; regress course_eval beauty minority onecredit nnenglish intro if female==0, robust; outreg2 using problemset3sol.xls, bd(3) td(3) label alpha(.001, .01, .05) bracket ct(1) append; 6