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I have the following equation

enter image description here

and am trying to interpret the interactions. So for example, for interpreting the interaction maledemo, would I add the coefficients for the constant, male, demo and maledemo? or do I need to include coefficients for the other interactions involving male and demo as well?

Also, how would I interpret the interaction for maleage?

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    $\begingroup$ Can you clarify what you mean? In what sense do you want to interpret it? What is it you want to understand about the interaction? $\endgroup$ – gung Dec 14 '16 at 16:09
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    $\begingroup$ I think it would be easier to answer your question if you provided a more information about your predictors. I assume that age is a continuous predictor? (so they are not all dummy variables?) in that case the interaction between age and male would indicate the change in the slope with respect to age in males with respect to your baseline (I guess females). For the interactions between dummy variables, they represents a change in intercept, but the interpretations depends also on how the contrasts are coded $\endgroup$ – matteo Dec 14 '16 at 16:28
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I'm assuming age is a continuous variable. The 0.0066 maleage coefficient should be added to the coefficient of age (-0.0059 + 0.0066) and interpreted as the coefficient of the slope between fempres and age when the person is male. The coefficient of the slope for age of -0.0059 is the relationship between fempres and age when the person is female.

If demo is a dummy variable then maledemo only makes a difference for persons where demo=1 and male=1. The maledemo coefficient should be added to demo and male coefficients (and the coefficient of any other dummy variables that =1 for that person) to give the intercept when demo=1 and male=1. If male=0 or demo=0 maledemo will be 0*-0.2159 so doesn't change the intercept. If demo is continuous use the same approach as above for age.

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