18.3 Moderation Model

A typical moderation model is represented as:

$$Y = \beta_0 + \beta_1 X + \beta_2 M + \beta_3 X \times M + \varepsilon$$

where:

• $\beta_0$: Intercept

• $\beta_1$: Main effect of $X$

• $\beta_2$: Main effect of $M$

• $\beta_3$: Interaction effect of $X$ and $M$

If $\beta_3$ is significant, it suggests that the effect of $X$ on $Y$ depends on $M$.