Interpretation of interaction terms in a multiple linear regression

#1
I try to improve my statistical knowledge and right now I am working on a regression that contains interaction terms. I am currently investigating the effects of different variables (a1, a2 etc.) on the quantity of chairs sold in a transaction (dependent variable). To see if effects are different (e.g. a1 is a sales campaign) for customers who came back (comeback) I made a linear regression with interaction terms of a1 and comeback, a2 and comeback etc..

Comeback can be 0,1, 2, 3 or 4. If a customer made 2 purchases comeback equals 1 as he came back once. I also have some additional control variables for the characteristics of the customers which I include as dummies.

My results are the following: (results of dummies not shown) (*** indicate significance at the 1 percent level at * indicates significane at the 10 percent level):

Dependent variable = Quantity of chairs
a1 -12.10***
a2 -8.01
a3 6.57
a1 x comeback 50.35***
a2 x comeback 35.01*
a3 x comeback 5.01
comeback -15.30


Now my questions:

1. Is the effect of a1 on the quantity of chairs −12.10+50.35=38.25 for those that came back once and −12.10+50.35∗2=88.6 for those that came back twice?

2. Can you say because the coefficient for a1 x comeback is significant that customers who came back are affected differently by our sales campaign? Or do you have to make another test?

3. Can you say that a2 only affected customers who came back because a2 alone is not significant?

4. Can you say that because the coefficient for comeback is not significant, people that came to the shop more than once are not buying more or less chairs? Or how can you interpret the coefficient of comeback (-15.30) alone?

Maybe you can shed some light on this for me. And if you have additional comments to this method, please let me know.


Best regards
Renato