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.

Identify the following:

a. The P-value corresponding to the overall significance of the multiple regression equation

b. The value of the multiple coefficient of determination\({R^2}\).

c. The adjusted value of \({R^2}\)

Short answer

The P-value is less than 0.0001.

The multiple coefficient of determinationis 0.3649.

The adjusted multiple coefficient of determinationis 0.3552.

Step-by-step solution

Given information

The multiple regression output is provided.

Determine the P-value

The p-value, which determines the overall significance of the model, is obtained for the F-test in ANOVA output.

From the provided output, the P-value can be observedin the last column oftheanalysis of variance table for multiple regression model.

Therefore, the P-value is less than 0.0001.

State the multiple coefficient of determination

The multiple coefficient of determination is the R-squared measure of the regression output.

From the provided output, themultiple coefficient of determination can be observed in the summary of fit.

Therefore, the multiple coefficient of determinationis 0.3649.

State the adjusted value of the multiple coefficient of determination

The adjusted R-squared measure is also computed for determining the accuracy of prediction in the model.

From the provided output, the adjusted value of themultiple coefficient of determination can be observed in the summary of fit.

Therefore, the adjusted multiple coefficient of determinationis 0.3552.