mathematics placement test is given to all entering freshman at a small college. A student who receives a grade below 35 is denied admission to the regular mathematics course and placed in a remedial class. The placement test scores and final grades for several students who took the regular course are recorded and shown below

Placement Test Course Grade
34 53
35 41
58 82
44 63
55 68

Conduct a regression analysis to predict course grade (dependent variable) on the basis of the placement test score (independent variable)

a. Determine the coefficient of determination for this regression problem and comment on its capability to predict outcome
b. Conduct an F test to determine the relationship between the two variables. Conduct the test at alpha = .05 level
c. What is the predicted grade for a placement test score of 60?
d. What is the upper and lower value for a 90% confidence interval of the grade estimate determined in part c