Failing to include interaction terms

If you fail to include for interaction terms in your model if interaction exists. Would your $R^{2}$ be less then what it would be if you included the interaction terms $R^{2}$ ?

$R^2$ will never decrease when you add more variables, and will in practice always increase, regardless of whether the added variable belongs in the model or not. So yes, adding an interaction will increase $R^2$.
• Or the adjusted $R^2$, which penalizes the addition of new variables. Dec 4, 2014 at 7:17