Question

In Exercises 5–8, we want to consider the correlation between heights of fathers and mothers and the heights of their sons. Refer to the

StatCrunch display and answer the given questions or identify the indicated items.

The display is based on Data Set 5 “Family Heights” in Appendix B.

Should the multiple regression equation be used for predicting the height of a son based on the height of his father and mother? Why or why not?

Short answer

The multiple regression equation cannot be used for predicting the height of a son based on the heights of his father and mother as the measure of R-squared values is low, which suggests poor fit.

Step-by-step solution

Given information

An output for regression is known.

Analyze the regression output

Compare each measure with the provided output.

• TheP-valuein the last columnof theanalysis of variance table for the multiple regression model is low. It is less than 0.0001, which suggests that the model is overall significant.

• Each variable is significant as the P-values are less than 0.05.

• The value of the coefficient of determination (0.3249) and the adjusted value of the coefficient of determination (0.3552) are not high, which indicates a poor fit.

Therefore,the multiple regression equation fits the sample data, but it is not a good fit.

Thus, it should not be used for predicting the height of a son based on the heights of his father and mother.