\fGrade Point Average. The director of admissions of a small college selected 120 students at random from the new freshman class in a study to determine whether a student's grade point average (GPA) at the end of the freshman year (Y) can be predicted from the ACT test score (X1). The results of the study are shown in Table 1 below. Assume that normal error regression model is appropriate. a. Select a random sample consisting of 90% of the data provided (refer to Table 1). Attach your random sample as reference. [3 marks] Obtain the least squares estimates of ,60 and 1, and state the estimated regression function. [4 marks] Plot the estimated regression function and the data. Does the estimated regression function appear to fit the data well? [4 marks] Obtain a point estimate of the mean freshman GPA for students with ACT test score X1 = 30. [2 marks] What is the point estimate of the change in the mean response when the entrance test score increases by one point? [2 marks] Obtain a 99% confidence interval for A. Interpret your condence interval. Does it include zero? Why might the director of admissions be interested in whether the condence interval includes zero? [5 marks] Test, using the test statistic t', whether or not a linear association exists between student's ACT score (X1) and GPA at the end of the freshman year (Y). Use a level of signicance of .01. State the alternatives, decision rule, and conclusion. [6 marks] What is the Pvalue of your test in part [g]? How does it support the conclusion reached in part [g]? [4 marks] Obtain a 95% interval estimate of the mean freshman GPA for students whose ACT test score is 28. Interpret your condence interval. [5 marks] Mary [ones obtained a score of 28 on the entrance test. Predict her freshman GPA using a 95% prediction interval. Interpret your prediction interval. [5 marks] Set up the AN OVA table. [4 marks] What is estimated by MSR in your ANOVA table? By MSE? Under what condition do MSR and MSE estimate the same quantity? [6 marks]