Question
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!
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!