What is the difference between "main effects" and "interaction effects"?

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The terms "interaction" and "main effects" were adopted from the analysis of variance method (ANOVA). In the context of analysis of variance an "interaction" refers to the effect of a factor averaged over another factor and the "main effect" represents the average effect of a single variable. In the case of multiple regression, this terminology is not suitable in the presence of an interaction. Typically, b1 and b2 in a nonadditive model are referred to as "main effects". It is quiet common in the case of an interactive model to refer to b 1 and b2 as "main effects". The use of this term in examining an interactive model is held here to be misleading. In the presence of an interaction these coefficients in no instance represent a constant effect of the independent variable on the dependent variable. The use of the term "main effect" implies that b1 and b2 are somehow interpretable alone when they actually represent a portion of the effect of the corresponding variable on the ...
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