Am I interpretting this interaction term correctly?

Question

I am running a model with an interaction term and I am unsure of the interpretation even after reading the other questions here in the forum.

My model looks as follows:

Where roi is the return on investment, logfreq is the log transformed trading frequency and treated is the binary treatment variable.

My interpretation of the interaction:

The interaction term is negative implying that being treated leads to lower trading frequency.

Is this the correct interpretation? Any hint would be much appreciated, and I hope this does not seem too trivial.

Answer 1

We don't know for sure how treated interacts with logfreq until we investigate that specifically. The current results may mean that if the relationship as linear as assumed (this is very unlikely), treated has a constant effect on roi when present, while logfreq has a linear relationship with roi with the coefficient 0.35369 only when treated is absent. When treated is present the linear effect of logfreq on roi is 0.35369-0.30848=0.04521, which may even be statistically non-significant.

Answer 2

You have two linear equations for roi as a function of logfreq, one for no treatment and one with treatment. To decide which one results in a larger roi, we have to know what range your logfreq values are in. In the code below, roi1 is the ROI in the treated case:

> logfreq <- seq(0, 10, .1)
> roi <- 0.11147 + 0.35369*logfreq
> roi1 <- 0.11147 + 0.35369*logfreq + 0.84900 -0.30848*logfreq
> plot(logfreq, roi, type = 'l', col = 'seagreen', panel.first = grid())
> lines(logfreq, roi1, col="steelblue") 

Here, the blue line is with treatment. Thus, if your values of logfreq are below $\approx 3$, treated will have a positive effect on roi, but above three, it will have a negative effect. Note, that this is independent of the value of the nonsignificant intercept.

More professional visualization of interactions can be achieved e.g. with the interactions R-package.