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Interactions

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?