Question 1 (parts a-g). (50 points. ~75 minutes)ow This question uses informatio

Question

Question 1 (parts a-g). (50 points. ~75 minutes)ow This question uses information about recent college graduates GPASa they relate to background information about the students and their hig at admission tocollege, and whether or not they were an athlete in college. Stata outputs are reported below. h schools First, we define an interaction variable, and then we present variable descriptions and summary statistics. . gen male_ath (1-female) athlete · Label va r maleath "male*athlete" . des - Contains data from /Users/thomasmroz/Desktop/Econ 4950_2017/final_exam/gpa2.dta 4,137 132,384 storage display value obs: vars: size: 25 May 2002 14:39 variable name typeformat Labe varia %10.0g int float %9.0g byte %8.0g double %10.0g float %9.0g byte %9.0g float %9.0g double %10.0g combined SAT score GPA after fall semester -1 if athlete size grad. class, 100s high school percentile, from top -1 if female hsize 2 sat colgpa athlete hsize hsperc female hsizesq male_ath malexathlete Sorted by: Note: Dataset has changed since last saved.

Explanation / Answer

1 (a) For the resulted table, the estimated GPA differential between athletes and nonathletes is 0.1693. From the table, we see that p-value is less than level of significance 5%. Thus, we reject the null hypothesis and concluded that It is statistically significant.

1 (b) The estimate on athlete is 0.0054 when sat variable is not included. Because, on average athlete tends to have a low SAT score, whereas non Athlete on average has higher SAT score. In fact, the correlation between Athlete and SAT is equal to -0.1851. It also incrase is p-value which is greater than level of significance 5%. So, the coefficient of Athlete in the new model is biased downward.

1 (c) To allow the effect of being an athlete to differ by gender we would include the following dummy variables into the model: femaleathlete, maleathlete, malenonathlete. We choose to make femalenonathlete to be the base group so that we can test the null hypothesis that there is no difference between women athletes and non athletes. These categories need to be constructed in the data. So If you give the data, then we can test the null hypothesis.

1 (d) -0.0076 is interpreted as the difference in the predicted value in Y for each one-unit difference in male_ath, if other variables are remains constant. However, since male_ath is a categorical variable coded as 0 or 1, a one unit difference represents switching from one category to the other.

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