I'm a psychology student and trying come up with a research plan involving GLM. I'm thinking about adding an interaction term in the analysis but I'm unsure about the interpretation of it. To make things simple, I'm going to use linear regression as an example.
I'm expecting a (simplified) model like this: $$y = ax_{1} + bx_{2} + c(x_{1}*x_{2})+e$$ In my hypothesis, $x_{1}$ and $y$ are negatively correlated, and $x_{2}$ and $y$ are positiely correlated. As for correlation between $x_{1}$ and $x_{2}$, it is unknown.
Now the question is, if we make a model and get a coefficient $c$, how can we interpret it, whether it's positive or negative? The reason I'm confused is that $x_{1}$ and $x_{2}$ have different effects interms of direction (positive or negative) towards $y$. Do I have to make $x_{1}$ or $x_{2}$ into a reciprocal so that both variables have the same directional effects towards $y$?
Another possibility that I can think of is that $c$ it self does not explain the whole of interaction effect and another test needs to be run to specify that.
Thank you in advance.