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 theStatCrunch 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 multiple regression equation that expresses the height of a son in terms of the height of his father and mother.

Short answer

The multiple regression equation is

\({\rm{Son}} = 18 + 0.504\;{\rm{Father}} + 0.277\;{\rm{Mother}}\).

Step-by-step solution

Given information

The analysis of the variance table for the multiple regression model is provided.

State the general equation of multiple regression

The multiple regression equation is

\(\hat y = {b_0} + {b_1}{x_1} + {b_2}{x_2} + ... + {b_n}{x_n}\), where \(\hat y\) is the predicted response variable and \({x_1},{x_2},...,{x_n}\)are the independent variables along with respective measure of coefficients \({b_0},{b_1},...,{b_n}\).

Compute the equation of multiple regression

Define the variables as follows:

Father: Height of father

Mother: Height of mother

Son: Height of son

From the output, the estimates of the variables are

\(\begin{array}{l}{b_0} = 17.96657,\\{b_1} = 0.50354896,\\{b_2} = 0.27714316.\end{array}\)

The multiple regression equation for the provided scenario is represented below:

\(\begin{array}{c}Son = {b_0} + {b_1}\;{\rm{Father}} + {b_2}\;{\rm{Mother}}\\ = 17.9666 + 0.504\;{\rm{Father}} + 0.277\;{\rm{Mother}}\end{array}\)

Therefore, the multiple regression equation is

\({\rm{Son}} = 18.0 + 0.504\;{\rm{Father}} + 0.277\;{\rm{Mother}}\).