2. Suppose that ColLGPA = Bo + B1PC+U, where Col_GPA denotes the student's college GPA and PC is a binary variable with PC = 1 if the student owns a PC and PC = 0 otherwise. Define noPC as a dummy variable for whether the student does not own a PC, with noPC=1 if the student does not own a PC and noPC=0 if the student does own a PC. Suppose that, in the data, there are 34 students who do not own a PC and 53 students who own a PC. The sample average of Col_GPA for those students without a PC is 2.5, and the sample average of Col_GPA for those students with a PC is 3.5. Suppose further that, in the data, the sample standard deviation of Col_GPA for those students without a PC is .62, and the sample variance of Col_GPA for those students with a PC is .47. (a) What are the OLS estimates of Bo and B? Why can you compute them in this fashion? (b) Test Ho : B1 0 versus H1 : B1 > 0 at the 5% significance level. What is the p-value for this hypothesis test? What do you conclude? (c) Suppose that the researcher instead wishes to do an OLS regression of Col GPA on noPC. What would be the resulting OLS estimates for that regression