A set of n = 15 pairs of scores (X and Y values)produces a correlation of r = 0.40.If each of the X values is multiplied by 2 and the correlation is computed for the new scores,what value will be obtained for the new correlation?
A)r = 0.20
B)r = 0.40
C)r = 0.80
D)This cannot be determined without knowing all the X and Y scores.

Question

A set of n = 15 pairs of scores (X and Y values)produces a correlation of r = 0.40.If each of the X values is multiplied by 2 and the correlation is computed for the new scores,what value will be obtained for the new correlation?​
A)​r = 0.20
B)​r = 0.40
C)​r = 0.80
D)​This cannot be determined without knowing all the X and Y scores.

Quizplus · Accepted Answer

When multiplying all the X values by 2, the covariance between X and Y will also be multiplied by 2. Since the correlation coefficient is the covariance divided by the product of the standard deviations of X and Y, multiplying the X values by 2 will increase the correlation coefficient by a factor of 2 as well, resulting in a new correlation coefficient of r = 0.40, which is the same as the original correlation coefficient. Therefore, the answer is choice B.

A Set of N = 15 Pairs of Scores (X