Chapter 8, Problem 7E

To determine

To explain what fraction of the variability in potassium is accounted for by the amount of fiber that servings contain.

Answer to Problem 7E

  $81.5\%$ .

Explanation of Solution

It is given that, an analysis of the amount of fiber in grams and the potassium content in milligrams in serving of breakfast produced the regression model:

  $\text{<mover accent="true"><mo>P</mo><mo>^</mo></mover> otassium}=38+27\text{Fiber}$

And it is given also that the correlation between a cereal’s fiber and potassium contents is $r=0.903$ . Thus, the variability in potassium is accounted for by the amount of fiber that servings contain is calculated as:

  $\begin{array}{l}{R}^2=r^2\\ ={0.903}^2\\ =0.8154\\ =81.5\%\end{array}$

Thus, $81.5\%$ of the variability in potassium is accounted for by the amount of fiber that servings contain.