Show transcribed image text 2. (prediction/forecast intervals): a. Let CollegeGPA be estimated in a linear regression on SAT scores, orn Highschoolrank, on high school size (number of students), and the square of high school size. Obtain (write down the expression for) the prediction and forecast of college GPA for a student with SAT-1200; HSrank 30, and HSsize = 500. b. Obtain and contrast the prediction variance and forecast variance. Explain the difference. C. Define new regressor variables relative to this student's characteristics which will allow you to obtain the "prediction" and its standard error from a simple regression. d. Give the confidence interval for your prediction from the regression in part c. Explain all the assumptions that you have made to justify your expression for the confidence interval. e. Suppose you wish to test the joint hypothesis that High school size and high school rank do not determine college GPA. Describe the test of this hypothesis. What is the asymptotic distribution of this test and what does it mean for inference when you do not know the distribution of the regression errors?
2. (prediction/forecast intervals): a. Let CollegeGPA be estimated in a linear regression on SAT scores, orn Highschoolrank, on high school size (number of students), and the square of high school size. Obtain (write down the expression for) the prediction and forecast of college GPA for a student with SAT-1200; HSrank 30, and HSsize = 500. b. Obtain and contrast the prediction variance and forecast variance. Explain the difference. C. Define new regressor variables relative to this student's characteristics which will allow you to obtain the "prediction" and its standard error from a simple regression. d. Give the confidence interval for your prediction from the regression in part c. Explain all the assumptions that you have made to justify your expression for the confidence interval. e. Suppose you wish to test the joint hypothesis that High school size and high school rank do not determine college GPA. Describe the test of this hypothesis. What is the asymptotic distribution of this test and what does it mean for inference when you do not know the distribution of the regression errors?
