Consider the least squares regression line between two varia

Consider the least squares regression line between two variables x and y. if the correlation coefficient between x and y doubles, how much does the coefficient of determination changes?

a. The new coefficient of variation is 4 times the old one.

b. The new coefficient of variation is the same as the old one.

c. The new coefficient of variation is 0.5 times the old one.

d. The new coefficient of variation is 0.25 times the old one

e. The new coefficient of variation is 2 times the old one.

I think the answer is a, but please confirm this answer or help me figure out the correct answer. Thanks.

Solution

a. The new coefficient of determination is 4 times the old one.

because coefficient of determination = r^2