Let grad be a dummy variable for whether a student-athlete at a large university gradu- ates in three years. Let hsGPA and SAT be high school grade point average and SAT score, respectively. Let Study be the number of hours spent per week in an organized study hall. Suppose we are interested in the following relation grad = Be + BihsGPA+ B2SAT + B3 Study + u (1) Suppose that, given the sample of 1000 student-athletes, the following Probit model is obtained: (grad=1|hsGPA, SAT, study) = G(-1.1023+.3216 hsGPA+ 0.0008 SAT +0.0922 Study) where G(z) is the Cumulative Distribution Function (CDF) of the the standard normal distribution. 1. Compute the partial effect at the average for the variable hsGPA and Study (The mean of the hsGPA is 3.1769, the mean of the SAT is 1202.9372 and the mean of Study is 6.4739). Show your calculation process. Keep four digits after the decimal point. (3 marks) 2. Suppose we estimate the equation (1) using OLS and obtain , and se(). We want to use the t-test to conduct the following hypothesis testing H: B1 = 0 H: B170 Can we trust the t-test in this context? Explain. (1.5 marks) Let grad be a dummy variable for whether a student-athlete at a large university gradu- ates in three years. Let hsGPA and SAT be high school grade point average and SAT score, respectively. Let Study be the number of hours spent per week in an organized study hall. Suppose we are interested in the following relation grad = Be + BihsGPA+ B2SAT + B3 Study + u (1) Suppose that, given the sample of 1000 student-athletes, the following Probit model is obtained: (grad=1|hsGPA, SAT, study) = G(-1.1023+.3216 hsGPA+ 0.0008 SAT +0.0922 Study) where G(z) is the Cumulative Distribution Function (CDF) of the the standard normal distribution. 1. Compute the partial effect at the average for the variable hsGPA and Study (The mean of the hsGPA is 3.1769, the mean of the SAT is 1202.9372 and the mean of Study is 6.4739). Show your calculation process. Keep four digits after the decimal point. (3 marks) 2. Suppose we estimate the equation (1) using OLS and obtain , and se(). We want to use the t-test to conduct the following hypothesis testing H: B1 = 0 H: B170 Can we trust the t-test in this context? Explain. (1.5 marks)