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 exzamination and their final-exzamination scores is

r = 0.5.

The pre-exzam totals for all students in the course have mean 270 and standard deviation 35. The final-exzam scores have mean 73 and standard deviation 6. Professor Krugman has lost Julie's final exzam but knows that her total before the exzam was 300. He decides to predict her final-exzam score from her pre-exzam total.

(a) What is the slope of the least-squares regression line of final-exzam scores on pre-exam total scores in this course? (Round your answer to four decimal places.)
slope=...???

What is the intercept? (Round your answer to two decimal places.)
intercept=...???

Interpret the slope in the context of the problem.

Each point of pre-exzam total score means a loss of 49.86 points on the final exzam, on average. OR Each point of pre-exzam total score means an additional 49.86 points on the final exzam, on average. OR Each point of pre-exzam total score means an additional 0.0857 points on the final exzam, on average. OR Each point of pre-exzam total score means a loss of 0.0857 points on the final exzam, on average???

(b) Use the regression line to predict Julie's final-exzam score. (Round your answer to one decimal place.)
Julie's final-exzam score=...???

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

Explanation / Answer

a) slope = b = r *sd(x)/sd(y)     X - pre-exams, Y - final exams

= 0.5 * 6/35

= 0.0857142

intercept = a= ybar - b *xbar = 73 - 0.0857142*270 =49.85716

b)

y^ = 49.85716 + 0.0857142*x

= 49.85716 + 0.0857142*300

= 75.57142

c)

r^2 = 0.25

the regression only explaines 25 % of variation in the final exams , which means there is 75 % chance that julie's marks could have been more than 77

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