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Say if we had a case:

$y=α+βmale+βeduc+ε$

$y=α+βmale+βeduc+βmale*educ+ε$

let's say that both male and educ are indicator variables. What exactly does the interactive term mean in plain English, does male*educ mean that "male and educated"

If this was the case why couldn't we just use the first regression and set male =1 and educ =1. Obviously $y$ values are different between the two models the interaction term will have extra values added to the predicted y but what exactly does this additional value mean compared to the first model?

Thank you!

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    $\begingroup$ Please search our site for plenty of information about interpreting interactions. $\endgroup$ – whuber Jun 5 '20 at 19:32
  • $\begingroup$ thank you for the link! $\endgroup$ – Wolfgang Jun 6 '20 at 3:49
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What exactly does the interactive term mean in plain English, does male*educ mean that "male and educated"?

The coefficient on the interaction term is not the effect of being "male and educated." Or, more fittingly, the coefficient does not imply the effect of being an educated man.

In simple terms, when you investigate the interaction between male and education you are saying to your audience/reader that the effect of education on $y$ depends on gender. You are now explicitly investigating if the return to education is different for men and women. Put differently, your interaction term implies that a third variable (i.e., gender) influences the relationship between education and $y$.

Obviously y values are different between the two models the interaction term will have extra values added to the predicted y but what exactly does this additional value mean compared to the first model?

The former (reduced) model with two additive binary inputs will tell you what the effect of education is on $y$ while holding gender fixed. Holding gender fixed allows you to assess the effect of the increase in education on $y$ for two individuals sharing the same gender. I assume a sizable jump (increase) in education since you entered a discretized (dummy coded) version of education into your model. The latter model, which interacts (multiplies) the two main effects for education and gender, allows you to explicitly test if that jump in education is different for men than for women.

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  • $\begingroup$ I think this clears up part of my confusion, however, when we investigate whether the effect of education on y depends on gender, instead of adding the interaction term. Why couldn't we just use a F test and test the first regression model where we define the restricted model as $βmale=0$ and use unrestricted model where we define $βmale=1$ wouldn't this hypothesis test achieve the same thing? $\endgroup$ – Wolfgang Jun 5 '20 at 19:54
  • $\begingroup$ Usually you compare the reduced model to the full model. Review the top answer here for more information and the use of the F-test. $\endgroup$ – Thomas Bilach Jun 5 '20 at 23:49
  • $\begingroup$ Thank you for the explanation and the link to the F-test it's helpful! $\endgroup$ – Wolfgang Jun 6 '20 at 2:24

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