In considering whether to implement a program where selected entering freshmen would be required to take a precalculus refresher course before moving on to calculus, a university's business college has given mathematical proficiency tests to a sample of entering freshmen. The college hopes to use this score and the Scholastic Aptitude Test (SAT) quantitative score in predicting how well a student would end up scoring on the standardized final exam in calculus later in his or her studies. Data are available for a sample of nine entering freshmen, and their scores are shown here.

a. From these data, obtain the multiple regression equation estimating calculus final exam score on the basis of the other two variables; then determine and interpret the approximate 90% confidence interval for the mean calculus final exam score for entering freshmen who score 70 on the math proficiency test and 500 on the quantitative portion of the SAT.

b. Determine the 90% prediction interval for the calculus final exam score for an entering freshman who scored 70 on the math proficiency test and 500 on the quantitative portion of the SAT.