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Chapter 7: Q. 14 (page 463)

The correlation between the age and height of children under the age of 12is found to ber=0.60. Suppose we use the agex of a child to predict the height y of the child. What can we conclude?
(a) The height is generally60% of a child’s weight.
(b) About60% of the time, age will accurately predict height.
(c) The fraction of the variation in heights explained by the least-squares regression line of yon xis0.36.
(d) The least-squares regression line of yon xhas a slope of0.6.
(e) Thirty-six percent of the time, the least-squares regression line accurately predicts height.

Short Answer

Expert verified

The correct answer is option (c) The fraction of the variation in heights explained by the least-squares regression line of yon xis 0.36.

Step by step solution

01

Given information

The correlation between the age and height of children under the age of 12is r=0.60.Let, the age xof a child to predict the height yof the child.

02

Explanation

Utilizing the given value of the correlation, the coefficient of determination is estimated as:

Coefficient of determination=(Correlation)2=(0.60)2=0.36

The coefficient of determination indicates the variation is defined by the predictor variable on the response variable. The value of the coefficient of determination indicates the 36%of the variation on height is described by the least square line.

Hence, option (c) is correct.

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