If the coefficient of correlation is 0.90,then the percentage of the variation in the dependent variable y that is explained by the variation in the independent variable x is:
A)90%
B)81%
C)95%
D)None of these choices.

Question

Quizplus · Accepted Answer

The coefficient of correlation (r) is the ratio of the covariance of x and y to the product of their standard deviations. It measures the strength and direction of the linear relationship between x and y, and ranges from -1 to 1. A value of 0.90 indicates a strong positive linear correlation between x and y.

The coefficient of determination (r^2) is the proportion of the total variation in y that is explained by the linear regression of y on x. It is equal to the square of the coefficient of correlation (r^2 = 0.90^2 = 0.81). Therefore, 81% of the variation in y is explained by the variation in x when r = 0.90.

Hence, the best choice is B) 81%.

If the Coefficient of Correlation Is 0