7.10: What fraction of the variability in potassium is accounted for by the amount of fiber that servings​ contain?

Question

The correlation between a​ cereal's fiber and potassium contents is r=0.892. 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.)

Answer 1

That variability is the coefficient of determination (r-squared) which is computed as the square of the correlation coefficient of r = 0.892: 0.796,

Answer 2

The answer is simply r^2, then convert the decimal to a percentage. The question is seeing if you recognize the coefficient of determination. The coefficient of determination (r^2) is the proportion of the variation in the response variable that is predicted by the least-squared regression line using the explanatory variable to predict the response.