Question

Use the following information. We have three equations. They are:

(1) Weight = a1 + 6(Height);

(2) Weight = a2 + 5(Height) + 22(Gender). Where Gender = 0 if female, 1 if male;

(3) Weight = 150 + 35(Gender).

In Equation (2), the coefficient for gender is 22. In Equation (3), the coefficient for gender is 35. Explain where the 13 extra pounds in equation (3) comes from. In other words, what is it measuring?

Answer 1

In Equation (2), the coefficient for gender is 22. In Equation (3), the coefficient for gender is 35.

Explanation of where the 13 extra pounds in equation (3) comes from:

The 13 extra pounds in equation (3) comes from: the interaction effect between the 2 Independent Variables: Height and Gender.

In Multiple Regression, Interaction Effect exists when the effect of an Independent Variable: here: Gender on a Dependent Variable: here: Weight changes, depending upon the value of other Independent Variable:here: Height.

If we include interaction term: Height X Gender to the Multiple Regression model of the dependent Variable: Weight with the 2 Independent Variables:(1) Height and (2) Gender, we can clarify the 13 extra pounds. Adding an interaction term to the Multiple Regression model drastically changes the interpretation of the slope coefficients.