Chapter 7: Q. 2.14 (page 490)

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.

Expert verified

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

Step by step solution

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

Consider,

$r = 0.60 R^{2} = r^{2} = 0.36$

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)

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 .

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