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 \(M\).