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In regression and in analysis of variance, an interaction effect exists when the effect of an independent variable on a dependent variable changes, depending on the value(s) of one or more other independent variables.

An interaction effect is represented as the product of two or more independent variables. For example, here is a typical regression equation without an interaction:

ŷ = b0 + b1X1 + b2X2

where ŷ is the predicted value of a dependent variable, X1 and X2 are independent variables, and b0, b1, and b2 are regression coefficients.

And here is the same regression equation with an interaction:

ŷ = b0 + b1X1 + b2X2 + b3X1X2

Here, b3 is a regression coefficient, and X1X2 is the interaction.

See also:  Interaction Effects in Regression | What is a Full Factorial Experiment?