SOLUTION: _____A regression analysis of students' college grade point averages (GPAs) and their high school GPAs found r^2 = 0.311 which of these is true ? I. High school GPA accounts for 3

Question 935398: _____A regression analysis of students' college grade point averages (GPAs) and their high school GPAs found r^2 = 0.311 which of these is true ?
I. High school GPA accounts for 31.1% of college GPA
II. 31.1% of college GPAs can be correctly predicted with this model
III. 31.1% of the variance in college GPA can be accounted for by the model
A) III Only B) II Only C) I only D) none E) I and II
*Could you please tell me step by step how to do the problem? Thank You so much for helping me !! :)
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
The value r^2 is a fraction between 0.0 and 1.0, and has no units. An r^2 value of 0.0 means that knowing X does not help you predict Y. There is no linear relationship between X and Y, and the best-fit line is a horizontal line going through the mean of all Y values. When r^2 equals 1.0, all points lie exactly on a straight line with no scatter. Knowing X lets you predict Y perfectly.
For your problem Y is college GPA's and X is high school GPA's, therefore an r^2 = 0.311 implies that there is a 31.1% correlation between X and Y.
answer is B

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