In Professor Friedman's economics course the correlation between the students' total scores before the final examination and their final examination scores isr=0.64. The pre-exam totals for all students in the course have mean289and standard deviation28. The final exam scores have mean78and standard deviation10. Professor Friedman has lost Julie's final exam but knows that her total before the exam was295. He decides to predict Julie's final exam score from her pre-exam total.

My Question:

Julie complains to Professor Friedman that her final exam score could have been much higher than what is predicted by the least squares regression line. Calculate the proportion of the variation in final exam scores that is explained by the linear relationship between pre-exam scores and final exam scores. (Express your answer as a decimal, not as a percent).