Interpreting the Coefficient of Determination. In Exercises 5–8, use the value of the linear correlation coefficient r to find the coefficient of determination and the percentage of the total variation that can be explained by the linear relationship between the two variables.

Weight , Waist r = 0.885 (x = weight of male, y = waist size of male)

The linear correlation coefficient between the weight and the waist size of a male is 0.885.

The square of the linear correlation coefficient between the two variables is the coefficient of determination.

Here, the linear correlation coefficient (r) between the weight and the waist size of a male is 0.885.

Thus,

\(\begin{array}{c}{\rm{Coefficient}}\;{\rm{of}}\;{\rm{determination}} = {r^2}\\ = {0.885^2}\\ = 0.783\end{array}\)

Therefore, the value of the coefficient of determination is 0.783.

Here,

\(\begin{array}{c}{r^2} = 0.783\\ = \frac{{78.3}}{{100}} \times 100\% \\ = 78.3\% \end{array}\)

Therefore, the percentage of the variation explained by the linear association between the weight and the waist size of males is 98.4%.

The rest \(100\% - 78.3\% = 21.7\% \) variation is explained by other factors and random variation.