Interpreting r: Explained Variation

The value of r² is the proportion of the variation in y that is explained by the linear relationship between x and y.

1. Suppose there is a correlation of r = 0.9 between number of hours per day students study and GPAs. Which of the following is a reasonable conclusion?

(A) 90% of students who study receive high grades.

(B) 90% of students who receive high grades study a lot.

(C) 90% of the variation in GPAs can be explained by variation in number of study hours.

(D) 10% of the variation in GPAs cannot be explained by variation in number of study hours per day.

(E) 81% of the variation in GPAs can be explained by variation in number of study hours per day.