Question

the correlation between a cereals fiber and potassium contents is r = 0.882. what fraction of the variability in potassium is accounted for by the amount of fiber that servings contain? (round to the nearest tenth as needed.) %

Explanation:

Step1: Recall the coefficient - of - determination formula

The coefficient of determination $R^{2}$ is used to find the fraction of variability accounted for. Given the correlation coefficient $r = 0.882$, the formula for the coefficient of determination is $R^{2}=r^{2}$.

Step2: Calculate $R^{2}$

$R^{2}=(0.882)^{2}=0.777924$.

Step3: Convert to percentage

To convert the decimal to a percentage, multiply by 100. So $0.777924\times100 = 77.7924\%$.

Step4: Round to the nearest tenth

Rounding $77.7924\%$ to the nearest tenth gives $77.8\%$.

Answer:

$77.8\%$