Question

shelly found that the coefficient of determination between the age of a runner x and the runners finishing position y was about 0.728. what can she conclude?

53% of the variation in the runners finishing position is explained by the runners age.
0.728 more variation in the runners finishing position is caused by the runners age.
0.728% of the variation in the runners finishing position is explained by the runners age.
72.8% of the variation in the runners finishing position is explained by the runners age.

Explanation:

The coefficient of determination ($R^{2}$) represents the proportion of the variance in the dependent - variable (runner's finishing position $y$) that is predictable from the independent variable (runner's age $x$). When $R^{2}=0.728$, we convert it to a percentage by multiplying by 100. So, $0.728\times100 = 72.8\%$. This means 72.8% of the variation in the runner's finishing position is explained by the runner's age.

Answer:

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