Question

2. Let grad be an indicator variable for whether a student-athlete graduates from a large uni- versity within 5 years of starting. Using data from 420 student-athletes, the following logit estimates were obtained: Pigrad = 1 hsGPASAT, Study) = G(-1.17+.24hsGPA+.00058S AT+.073Study); 6(x) = (a) Holding hsGPA fixed at 3 and SAT fixed at 1200, compute the estimated difference in the graduation probability for someone who spent 10 hours per week in study hall (Study10) and someone who spent 5 hours per week (Study 5). (b) Compute the marginal effect of an extra hour of study for someone who hsGPA=3, SAT=1200, and Study=10.

Answer 1

a> P[grad=1|hsGPA=3,sat=1200,Study=10]=exp(-1.17+0.24*3+0.00058*1200+0.073*10)/[1+exp(-1.17+0.24*3+0.00058*1200+0.073*10)]=exp(0.976)/[1+exp(0.976)]=0.7263138083

P[grad=1|hsGPA=3,sat=1200,Study=5]=exp(-1.17+0.24*3+0.00058*1200+0.073*5)/[1+exp(-1.17+0.24*3+0.00058*1200+0.073*5)]=exp(0.611)/[1+exp(0.611)]=0.7263138083=0.64816888

The estimated difference in graduation probability is 0.7263138083-0.64816888=0.0781449

b> To get a close estimate, we consider 10.5 and 9.5 study hour.

P[grad=1|hsGPA=3,sat=1200,Study=10.5]=exp(-1.17+0.24*3+0.00058*1200+0.073*10.5)/[1+exp(-1.17+0.24*3+0.00058*1200+0.073*10.5)]=exp(1.0125)/[1+exp(1.0125)]=0.733509118

P[grad=1|hsGPA=3,sat=1200,Study=9.5]=exp(-1.17+0.24*3+0.00058*1200+0.073*9.5)/[1+exp(-1.17+0.24*3+0.00058*1200+0.073*9.5)]=exp(0.9395)/[1+exp(0.9395)]=0.71899864868

The marginal effect of an extra hour would be 0.733509118-0.71899864868=0.0145