Question

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 40. The final-exam scores have mean 75 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.

Which of the choices is the least-squares regression line of final-exam scores on pre-exam total scores in this course?

(A) y =-0.1-47x
(B) y=47-0.1x
(C) y=-47 + 0.1x
(D) y= 47 + 0.1x

Answer 1

D

Explanation:

The regression equation is

y=a+bx

Now, we have to estimate a and b.

We know that slope can be determine as

b=byx=r*(sy/sx)

=0.5*(8/40)

b=0.1

So, we have the slope of regression equation is 0.1.

Now the intercept "a" can be estimated as

y=a+bx

a=ybar-bxbar

a=75-0.1*280

a=47

So, we have the intercept of regression equation is 47.

y=a+bx

y=47+0.1x