# How to interpret positive interaction in regression model if I have one predictor that has positive coefficient and one that has negative coefficient?

I have a regression model with two predictors (stigma and social support), interaction (stigma*social support) and one dependent variable (depression). Stigma has positive coefficient (0.16), social support has negative coefficient (-0.23) and interaction is positive (0.13). This is a regression model: Y=11.9 + 0.16*stigma - 0.23*soc.support + 0.13 (stigma*soc.support) I would appreciate if someone could help me interpret interaction term.

• More info is needed about the "stigma" and "soc" variables (Are they continuous or binary variables? If continuous, are they mean centered?) – Umka Jun 13 '17 at 22:31
• Yes, both variables are continuous and mean are centered – AM1 Jun 13 '17 at 22:35
• Then the interaction indicates the marginal effect (+ 1 unit) of increasing one variable on the other. Example: Increasing "stigma" by 1 unit (relative to the mean) will attenuate the effect of "soc" by 0.16 point (-0.23 + 0.16 = -0.07). Alternatively, increasing "soc" by +1 unit will reinforce the effect of "stigma" (016 + 013 = 0.29). Up to you which interpretation would want to choose - The interaction effect only captures the association between these 2 variables, it says nothing about the causality of their relationship. – Umka Jun 13 '17 at 22:40
• And what can I conclude about depression? – AM1 Jun 13 '17 at 22:51
• Remember that an interaction effect implies that variation in the dependent cannot be well understood without all the variables in the interaction term. In your case the effects of soc and stigma are not independent of one another, and understanding the effect of one on Y requires also understanding the effect of the other. – Alexis Jun 14 '17 at 3:01

Here, there are two contrasting effects of social support (negative) and stigma (positive) variable on your dependent variable depression $Y$. We can see from the coefficients that the effect of the absolute effect of having social support is somewhat stronger than receiving stigma in affecting one's depression.
Holding the level of stigma constant, for every unit increase in social support, depression becomes a positive linear function with stigma. Even though social support reduces overall depression (which is $11.9$ without any social support or stigma), the interaction effect of stigma is counter-acting against it and resulting in a $0.29$ unit increase in depression with every unit increase in stigma. So if stigma is sufficiently large, it will still result in higher depression.
i.e. $Y=11.67+0.29* stigma$
i.e. $Y=12.06-0.10 *soc.support$