Eltion,

Can you say more about what you mean by "control variables?"

For interpreting any coefficient in a multiple regression, the simplest interpretation is the predicted change per unit change in the predictor with all other predictors in the model held to 0.

For a model with product-term interactions, depending on the coding, that can result in a meaningful reference group, a meaningless reference group (e.g., height = 0), or you can recode your data so that the reference group is the sample centroid. This is a common recommendation in the absence of a meaningful reference group -- mean-center your predictors before creating the product terms, then you can interpret the lower-order terms as "all other variables held to the sample mean" because the higher-order terms fall out of the prediction equation with the multiplication by one or more zeroes.

Pat

Hey Patrick,

I understand how to interpret the interaction coefficients, but my questions is this: Under an additive model with two independent variables, the coefficient for independent variable X shows the effect of X on Y while controlling for the effects of independent variable Z; and the coefficient for independent variable Z shows the effect of Z on Y, while controlling for the effects of X.

Now, under an interaction model with three independent variables (X,Z,K), do the independent variables that make up the interaction terms act as control variables at the same time? In other words, the coefficient for interaction term X*Z shows the effects of that interaction on Y. But is the independent variable K acting as a control variable under this model, even though it it is part of other interaction terms under the same model?

Eltion,

I think you're getting tripped up by the language "controlling for." It has at least two common uses.

One is that they're held at a constant.

The other is accounting for variance and rendering the coefficients as semi-partial regressions -- partialing out all of the shared variance in Y predicted by the other Xs (main effects and interactions).

Including all of the terms in the regression equation, regardless of their construction, does both for all terms except the one you're interpreting.

Does that help?

Pat

Got it! Thank you Pat!