This is more of a soft question, but communication is part of statistician's job.
The background: I am trained as a statistician. My boss knows little about statistics.
The problem: He wants to fit a regression model with positive coefficients only. The reason is it is good for explanation. In other words, only positive coefficients match his expectations/economic theory/common sense. The method is fit first and delete variables with negative coefficients.
I don't think this is correct.
- Explanations/expectations/economic theory/common sense are very subjective. You have your model first, then you apply your explanation to the model. You can not do it the other way around.
- You delete a variable of negative coefficient, then some of the positive coefficients may change to negative.
My question: What would you say to explain why it is wrong? It has to be easy to understand for people who have little background in statistics.