Chapter 4.2, Problem 4.47E

To determine

To explain why we are expecting this correlation to be negative and find out the percent of the variation in BMI among girls in the study can be explained by the straight line relationship with minutes of activity.

Answer to Problem 4.47E

  $3.24\%$ of the variation is explained the straight line relationship.

Explanation of Solution

The correlation is expected to be negative because the higher the body mass index is the less you expect that they do a lot of physical activity in a day.

The square of the correlation ${\text{r}}^2$ is the fraction of the variation in the values of y the is explained by the least squares regression of $y\text{ on }x$ .

  $\begin{array}{l}{\text{r}}^2={(}^{-}\\ =0.0324\\ =3.24\%\end{array}$

This then means that $3.24\%$ of the variation is explained the straight line relationship.