Question

The correlation between the age and height of children under the age of 12 is found to be $r=0.60$. Suppose we use the age x of a child to predict the height y of the child. What can we conclude?

a. The height is generally $60\%$of a child's age.

b. About $60\%$ of the time, age will accurately predict height.

c. Thirty-six percent of the variation in height is accounted for by the linear model relating height to age.

d. For every 1 year older a child is, the regression line predicts an increase of $0.6$ foot in height.

e. Thirty-six percent of the time, the least-squares regression line accurately predicts height from age.

Short answer

The linear relationship between height and age accounts for 36% of the variation in height.

Step-by-step solution

Given information

The age and height association of children under the age of $12$is determined to be $r=0.60$.

Explanation for correct option

Consider,

$$\begin{gathered} r=0.60 \\ {R}^2=r^2=0.36 \end{gathered}$$

Because this is a simple linear regression model, the coefficient of the getting can be computed by squaring the correlation coefficient.

As a result, the best solution is (c)

Explanation for incorrect option

a. The height is generally $60\%$ of a child's age is not true.

b. About $60\%$ of the time, age will accurately predict height is not true .

d. For every 1 year older a child is, the regression line predicts an increase of $0.6$ foot in height is not true .

e. Thirty-six percent of the time, the least-squares regression line accurately predicts height from age is not true .