11.32 In planning for an initial orientation meeting with new electrical engineering majors, the chairman of the Electrical Engineering Department wants to emphasize the importance of doing well in the major courses in getting better-paying jobs after graduation. To support this point, the chairman plans to show that there is a strong positive correlation between starting salaries for recent electrical engineering graduates and their grade-point averages in the major courses.
Records for seven of last year’s electrical engineering graduates are selected at random and given in the following table:

a Find the least-squares prediction equation.
b Plot the data and graph the line as a check on your calculations. Do the data provide sufficient evidence that grade-point average provides information for predicting starting salary?
c Find a 95% prediction interval for the starting salary of a graduate whose grade-point average is 3.2.
d What is the mean starting salary for graduates with grade-point averages equal to 3.0?
Use a 95% confidence interval.

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Grade-Paint Average in Major Courses x 2.58 Starting Salary y ($ thousand) 66.5 3.27 68.6 3.85 69.5 3.50 69.2 3.33 68.5 2.89 66.6 2.23 65.6