Chapter 4, Problem 4.61RE

To determine

To explain how well the correlation between body weight explain brain weight for mammals and give a number and briefly explain what the number tells.

Answer to Problem 4.61RE

  $73.96\%$ is the number.

Explanation of Solution

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

  $\begin{array}{l}{r}^2={0.86}^2\\ =0.7396\\ =73.96\%\end{array}$

This then means that $73.96\%$ of the variation in the brain weight is explained by the least square regression of the brain weight on the body weight.