12.5 Interaction Effects

Interaction effects are used when the influence of one independent variable depends on the level of another independent variable. Suppose that you want to measure time spent volunteering (\(y\)) and you think that it depends on the marital status (\(x_1\)), the number of children (\(x_2\)), and some other independent variables (\(X\)). So you could have the following regression equation \[y = \beta_1 \cdot x_1 \cdot x_2 + \beta \cdot X + \epsilon\]

\[\frac{dy}{dx}=\beta_1 x_2 + \beta_2\]