What’s my grade? In Professor Friedman’s economics course, the correlation between the students’ total scores prior to the final examination and their finalexamination scores is r = 0.6. The pre-exam totals for all students in the course have mean 280 and standard deviation 30. The final-exam scores have mean 75 and standard deviation 8. Professor Friedman has lost Julie’s final exam but knows that her total before the exam was 300. He decides to predict her finalexam score from her pre-exam total.

(a) Find the equation for the appropriate least-squares regression line for Professor Friedman’s prediction.

(b) Use the least-squares regression line to predict Julie’s final-exam score.

(c) Explain the meaning of the phrase “least squares” in the context of this question.

(d) Julie doesn’t think this method accurately predicts how well she did on the final exam. Determine r2.

Use this result to argue that her actual score could have been much higher (or much lower) than the predicted value.