Question

What's my grade? 

In Professor Krugman's economics course the correlation between the students' total scores prior to the final examination and their final-examination scores is r=0.5 The pre-exam totals for all students in the course have mean 280 and standard deviation 8. Professor Krugman has lost Julie's final exam but knows that her total before the exam was 300. He decides to predict her final-exam score from her pre-exam total.  

What is the slope of the least-square regression line of final-exam scores on pre-exam total scores in this course? What is the intercept?  

Use the regression line to predict julie's final-exam score. 

 Julie doesn't think this method accurately predicts how well she did on the final exam. Use r^2 to argue that her actual score could have been much higher (or much higher) than the predicted value.

Answer 1

(a) Slope, b = r*(s_y/s_x) = 0.5*(8/40) = 0.1

Intercept = y - bx = 75 - 0.1*280 = 47

The regression equation is:

y = 47 + 0.1*x

(b) Put x = 300

y = 47 + 0.1*300

y = 77

(c) r² = 0.5*0.5 = 0.25

Since only 25% of the variability in y is explained, Julie's actual score could have been much higher than the predicted value.

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