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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.

Short Answer

Expert verified

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

Step by step solution

01

Given information

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

02

Explanation for correct option

Consider,

r=0.60R2=r2=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)

03

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 .

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