$$
\begin{array}{l}{\text { Use the data in GPA2 for this exercise. }} \\ {\text { (i) Consider the equation }}\end{array}
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$$
\begin{aligned} \text {colgpa}=& \beta_{0}+\beta_{1} h s i z e+\beta_{2} h s i z e^{2}+\beta_{3} h s p e r c+\beta_{4} s a t \\ &+\beta_{5} \text {female}+\beta_{6} \text {athlete}+u \end{aligned}
$$
$$
\begin{array}{l}{\text { where colgpa is cumulative college grade point average; hsize is size of high school graduating }} \\ {\text { class, in hundreds; hsperc is academic percentile in graduating class; sat is combined SAT }} \\ {\text { score; female is a binary gender variable; and athlete is a binary variable, which is one for }}\end{array}
$$ $$
\begin{array}{l}{\text { student-athletes. What are your expectations for the coefficients in this equation? Which ones }} \\ {\text { are you unsure about? }}\end{array}
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\begin{array}{l}{\text { (ii) Estimate the equation in part (i) and report the results in the usual form. What is the estimated }} \\ {\text { GPA differential between athletes and nonathletes? Is it statistically significant? }}\end{array}
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$$
\begin{array}{l}{\text { (iii) Drop sat from the model and reestimate the equation. Now, what is the estimated effect of being }} \\ {\text { an athlete? Discuss why the estimate is different than that obtained in part (ii). }}\end{array}
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\begin{array}{l}{\text { (iv) In the model from part (i), allow the effect of being an athlete to differ by gender and test the }} \\ {\text { null hypothesis that there is no ceteris paribus difference between women athletes and women }} \\ {\text { nonathletes. }} \\ {\text { (v) Does the effect of sat on colgpa differ by gender? Justify your answer. }}\end{array}
$$