Question

Shelly found that the coefficient of determination between the age of a runner x and the runner’s finishing position y was about 0.728. What can she conclude?

72.8% of the variation in and the runner’s finishing position is explained by the runner’s age.

0.728% of the variation in and the runner’s finishing position is explained by the runner’s age.

53% of the variation in and the runner’s finishing position is explained by the runner’s age.

0.728 more variation in and the runner’s finishing position is caused by the runner’s age.

Answer 1

The answer is choice A. Roughly 72.8% of the variation in the finishing position can be explained by the runner's age.

All we do is move the decimal 2 spots to the right to convert to a percent. This is the same as multiplying by 100, so, 100*0.728 = 72.8%

There isn't any other work needed to be done because this is a useful property of the coefficient of determination.

Note: r^2 is the coefficient of determination while r itself is the correlation coefficient.