Suppose that you are given the following information about the freshman year GPAs and the SAT scores of students entering a certain college: Mean SAT= 1125, Standard Deviation SAT= 150, Mean GPA= 2.68, St. Dev. GPA= 0.82 and r=0.65.
a)Use the above information to compute the regression line you would use to predict freshman GPAs from SAT scores.
b) Interpret the slope and the y-intercept of the regression line you obtained.
c) Predict the freshman GPA of a student who had a 1300 SAT score.
d) What is r^2(r-squared) and what does it tell you about the quality of the predictions of freshman GPA based on SAT score?
I am really lost, but have worked some of the problems out, but I'm not sure if they are correct. For part a, I got y-hat= -1.317499963 + 0.0035533333x
For part c, I got y-hat= 3.301833327
For part d, I got (0.65)^2= 0.4225 X 100= 42.45%. Therefore, quality of predictions is moderate due to moderate correlation
Any help would be greatly appreciated!