2. Professor Farnsworth obtains SAT scores and freshman grade point averages (GPAs) for a group of n = 15 incoming students to the University of Planet Express. The SAT scores had a mean of M = 580 with SS = 22,400, and the GPAs have a mean of 3.10 with SS = 1.26, and SP = 84.

a) What is the regression equation for predicting GPA from SAT scores?

b) What GPA would you predict for someone with an SAT score of 700? How about for an SAT score of 300?

c) What proportion of the variance in GPA is accounted for in SAT scores? Interpret your answer.

d) Use the computational formula to compute and then interpret the standard error of estimate for this example:

e) Compute and compare the t-statistic for both the correlation coefficient and the slope of the regression equation.