How to understand interaction effect I do research on differences in corporate tax burden by different types of enterprises (3 categories).
As we can see in the picture categorie 3 has a significant positive effect on the dependent variable (the tax burden). 
I also used some interaction effect to investigate whether some of these can mitigate the significant positive effect (I don't know for sure if I can formulate it this way). 
So let us take the interaction of categorie and WPAEX. We can observe that when categorie 3 has a higher WPAEX, this can reduce the tax burden by 8,4%. (Same holds for EQratio, however only 4,2%.) 
Can I interpret this result as for example that when categorie 3 has more WPAEX, this offsets the positive significant effect of categorie 3 on the dependent variable?

 A: Without a doubt, I would run a decision tree here. So depending on what you're using you may have to bin a continuous variable. Just go with a basic algorithm like CART and/or C4.5.
It gives you a visual of what can be going on, and also gives you ideas for interactive terms which you can then add to your model, and re-run to put this interaction "in terms" of your regression - for example, by comparing parameter estimates.
EDIT: Adding a couple links, and some general comments on decision trees.
Here is a decision tree in R. R is good enough if you're just trying to understand for yourself, but I've never been able to get quality decision tree visuals from R.
So here is another program called RapidMiner, also open source. You can get better visuals from this program - still not great but much better than R.
Any time spent learning to do them in one of the free packages will be well worth it, if you are in this field. They are not always the most powerful predictor, but they can give you much insight/ideas as to what's going on in a dataset. For example, I always do one first for any project - you don't have to fix missing values, or clean the data, or even remove fields highly correlated with your target. Run a tree and much becomes clear. Also, non-technical people will readily understand them. 
You'll want to familiarize yourself with their weaknesses. One main one is they'll group categorical values together in ways that might not make sense - for example they'll put the states CA and CT together into a group if it maximizes the splitting criteria. So you'll have to make sure in these cases such a grouping makes sense. In the example above, I might put the states into regions and use this instead of state.
So the biggest thing is you may need to apply some domain knowledge, and just make sure the tree makes sense. 
HTH
