STATA Problems 7. (18 points) Use the data in GPA3.DTA for this problem. Keep only the observations from students 2 semester (keep if terme-2). a) (1 point) Estimate following model. cumgpa = 4 + 8.football +Bhssize + Bxhssize? +Byhsperc + # where cumgra is college GPA, hasize is size of high school graduating class, in hundreds; hspere is academic percentile in graduating class; Football is a binary variable which ! for students on the football team. (Hint: You will need to create the square of hssize: "generate hssizeaq-hasize-2" OR "generate hasizesquhssize*hasize") b) (3 points) What is the estimated GPA differential between football players and non- players? Is it statistically significant? (Hint: This involves conducting a 2-sided test on 80.) c) 3 points) Drop hspere from the model in (a) and reestimate the equation Now what is the estimated effect of being a football player? Why does the estimate differ from the one obtained in (c)? d) points) Returning to the original model in (a) (so including hsperc), modify this model to answer the question: does the effect of hspere on cumgra differ for football players? Explain how you know (Hint : Create an interaction term: generate hspetchall-hsperc football. Add this to the model in part (a).) c) (2 points) What is the partial effect of high school size on GPA in the population model in (a)? f) (2 points) Do we have the correct functional form of hssize in our model - should we keep the square of high school size in the regression? In other words, conduct a hypothesis test (about B2) to determine whether hssize is statistically significant. (Use the p-value to conduct the test, again focusing on the estimated regression in part (a).) 3 - reg cumgpa football hssize hssizesq hsperc Source ss df MS 4 Model Residual 35.525495 96.368191 8.88137376 .266947897 Number of obs F(4, 361) Prob > F R-squared Adj R-squared Root MSE 366 33.27 0.0000 0.2693 0.2613 .51667 361 Total 131.893686 365 361352564 cumpa Coef. Std. Err. t P>|t1 (95% Conf. Interval] football hssize hssizes hsperc cons -.1571279 -.0003566 3.55e-07 - .013137 2.907822 0591125 .000478 6.40e-07 .0012401 .0893455 -2.66 -0.75 0.55 - 10.59 32.55 0.008 0.456 0.580 0.000 0.000 ..273376 -.0012966 -9.04-07 -.0155758 2.732119 -.0408798 .0005833 1.61e-06 - .0106983 3.083525 STATA Problems 7. (18 points) Use the data in GPA3.DTA for this problem. Keep only the observations from students 2 semester (keep if terme-2). a) (1 point) Estimate following model. cumgpa = 4 + 8.football +Bhssize + Bxhssize? +Byhsperc + # where cumgra is college GPA, hasize is size of high school graduating class, in hundreds; hspere is academic percentile in graduating class; Football is a binary variable which ! for students on the football team. (Hint: You will need to create the square of hssize: "generate hssizeaq-hasize-2" OR "generate hasizesquhssize*hasize") b) (3 points) What is the estimated GPA differential between football players and non- players? Is it statistically significant? (Hint: This involves conducting a 2-sided test on 80.) c) 3 points) Drop hspere from the model in (a) and reestimate the equation Now what is the estimated effect of being a football player? Why does the estimate differ from the one obtained in (c)? d) points) Returning to the original model in (a) (so including hsperc), modify this model to answer the question: does the effect of hspere on cumgra differ for football players? Explain how you know (Hint : Create an interaction term: generate hspetchall-hsperc football. Add this to the model in part (a).) c) (2 points) What is the partial effect of high school size on GPA in the population model in (a)? f) (2 points) Do we have the correct functional form of hssize in our model - should we keep the square of high school size in the regression? In other words, conduct a hypothesis test (about B2) to determine whether hssize is statistically significant. (Use the p-value to conduct the test, again focusing on the estimated regression in part (a).) 3 - reg cumgpa football hssize hssizesq hsperc Source ss df MS 4 Model Residual 35.525495 96.368191 8.88137376 .266947897 Number of obs F(4, 361) Prob > F R-squared Adj R-squared Root MSE 366 33.27 0.0000 0.2693 0.2613 .51667 361 Total 131.893686 365 361352564 cumpa Coef. Std. Err. t P>|t1 (95% Conf. Interval] football hssize hssizes hsperc cons -.1571279 -.0003566 3.55e-07 - .013137 2.907822 0591125 .000478 6.40e-07 .0012401 .0893455 -2.66 -0.75 0.55 - 10.59 32.55 0.008 0.456 0.580 0.000 0.000 ..273376 -.0012966 -9.04-07 -.0155758 2.732119 -.0408798 .0005833 1.61e-06 - .0106983 3.083525
