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For instance, reference to an interaction term will almost always be made when Two-way ANOVA is taught. However, when considering a regression with two continuous predictors and one continuous outcome, I've found (psychology teaching context) that students are often surprised that it's possible for there to be an interaction term.

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    $\begingroup$ ANOVA is regression, mathematicall, so this has nothing to do with the methods, only with traditions of teaching. $\endgroup$ – kjetil b halvorsen Jun 9 '15 at 14:03
  • $\begingroup$ While I accept that the division between ANOVA and Regression is just a historical accident, I wondered if in this case there might be some pedagogical or other reason for the teaching tradition I have been observed. That is, is there some difference between a regression with two categorical predictors and one with two continuous predictors that justifies a more explicit consideration of interactions? $\endgroup$ – user1205901 Jun 10 '15 at 3:46
  • $\begingroup$ One difference may be that ANOVA is often used in designed experiments, with (at least close to) orthogonal predictors, so interactions might be estimated in a stable way. with regression, more often used in observational studies, colinearity is more often an issue so that estimation of interaction may be unstable. $\endgroup$ – kjetil b halvorsen Jun 10 '15 at 8:42
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I guess it depends on the field. In econometrics, interaction terms are very often included as explanatory variables in regressions, and this is taught to students.

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