In Professor Krugman\'s economics course, the correlation between the students\'

Question

In Professor Krugman's economics course, the correlation between the students' total scores prior to the final test and their final-test scores is r = 0.45. The pre-test totals for all students in the course have mean 270 and standard deviation 40. The final-test scores have mean 75 and standard deviation 8. Professor Krugman has lost Julie's final test but knows that her total before the test was 290. He decides to predict her final-test score from her pre-test total.

(1) What is the slope of the least-squares regression line of final-test scores on pre-test total scores in this course? (Round your answer to four decimal places.) What is the intercept? (Round your answer to two decimal places.)

Interpret the slope in the context of the problem:

a) Each point of pre-test total score means a loss of 0.0900 points on the final test, on average.

b) Each point of pre-test total score means a loss of 50.70 points on the final test, on average.

c) Each point of pre-test total score means an additional 0.0900 points on the final test, on average.

d) Each point of pre-test total score means an additional 50.70 points on the final test, on average. t

(2) Use the regression line to predict Julie's final-test score. (Round your answer to one decimal place.)

(3) Julie doesn't think this method accurately predicts how well she did on the final test. Use r2 to argue that her actual score could have been much higher (or much lower) than the predicted value.

a) Only 20% of the variability in final test scores is accounted for by the regression, so the estimate of y could be quite different from the real score.

b) Exactly 45% of the variability in final test scores is accounted for by the regression, so the estimate of y could be quite different from the real score.

c) Exactly 45% of the variability in final test scores is accounted for by the regression, so the estimate of y should be very close to the real score.

d) Only 20% of the variability in final test scores is accounted for by the regression, so the estimate of y should be very close to the real score.

Explanation / Answer

(a)

b= 0.45 ×8/40=0.09, and

a= 75(0.09)(270) =50.7.

Theregression equation is

y^= 50.7+0.09x

option b Each point of pre-test total score means a loss of 50.70 points on the final test, on average.

b) = 50.7+0.09(290) = 76.8

(c) option d Only 20% of the variability in final test scores is accounted for by the regression, so the estimate of y should be very close to the real score.

Julie is right. With a correlation of r =0.45 r^2=0.2025

so the regression line accounts for only 20% of the

variability in student final scores

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