Marketing Impact Regression

#1
Hello all!

I am rather new to STATA / statistics, so I wanted to see if I can get some help from the experts that browse talkstats.com.

As the subject line implies, I am trying to find the impact of marketing spend on sales. So the model I am looking at is sales as the dependent variable, and independent variables include a number of marketing channels (TV, print, direct mailing, etc.).

I don't think a simple multiple variable linear regression would be appropriate here, as the curve here should be a bit more interesting. I presume that there will be small gains to marketing spend in the beginning, and the impact to sales should increase once the spend goes above a certain threshold. Above a certain level of spend, I think the slope will decrease again when we reach diminishing returns.

Any idea how I might tackle this?

Thank you!
 

Dason

Ambassador to the humans
#2
Do you know where these levels of spending are that you expect to see changes in the model? Or do you want to estimate them from the data as well? The first case is easier to deal with. The second case takes quite a bit more work.
 
#3
Thanks a lot for the quick reply, Dason!

Unfortunately, I do not know where I can expect to see a change, and I presume it is different for all the independent variables (for example, print advertising might become effective only after you've spent 1 million dollars, TV might require 5 million dollars before it is really effective, etc.).

If this is too complicated, I may find a way to come up with "reasonable assumptions" based on qualitative data. How would I go about it then?