Problem 1

This problem uses the GPA.xlsx data posted on Canvas and requires Excel's Data Analysis Toolpak. Note that you must copy the output when asked for, but if it's not asked for then no output is required and you can just write the answer.

While working at a university in the U.S., the administration decides that it wants to use data to identify first year students that might be at risk of struggling to maintain a good GPA. You are assigned to work on this project and have data on the following variables for 4,137 first year students:

College GPA: The GPA of the student at the end of their first academic year

SAT Score: The total SAT score of the student

HS Size: The size of the student's graduating high school class,measured in 100s of students.

Athlete: = 1 if the student plays on one the university's sports teams, = 0 if they do not

Note: Remember that running a regression is phrased as running "Y on X", meaning that you are running your dependent variableon your independent variables.

A. (3 points) Run a regression of log(College GPA) on log(SAT Score), log(HS Size), and Athlete.Copy and paste just the coefficients table (the 3^rd one on the bottom) below. Then, interpretall slope coefficients of the regression and determine if the slope coefficients are statically significant at the 5% level.

B. (2 points) Run a regression of College GPA on SAT Score, HS Size, and HS Size squared.Copy and paste the coefficients table below. Based on your result, determine the turning point of HS Size's impact on College GPAand explain its meaning.

C. (3 points) Run a regression of College GPA on SAT Score, HS Size, and SAT Score*HS Size andcopy and paste the coefficients table below. Test for the statistical significance at the 5% level of HS Size's impact on College GPA if a student has an SATScore of 1200. Explain how you arrived at this conclusion.

D. (2 points) Create alinear probability model that uses College GPA, SAT Score, and HS Size to predict if a student is an Athlete.Copy and paste the coefficients table below. Then, interpretall slope coefficients of the regression and determine if the slope coefficients are statically significant at the 5% level.