For the regression problem, we need that A must be negative to make the regression result meaningful. However, due to existence of unknown noises or unknown factors, our regression sometimes does have a positive results of coefficient A. I am struggling to find out a statistical way to force coefficient A being negative. Do you know any way to do this?

One way I am thinking is that: If the results of A is positive, I remove one point that is most influential to cause A being positive. After removing the point, then do regression again. By doing this iteratively, after removing a couple of data points, the result of A can be negative. Is there any statistical method in research literature supporting my way to remove a couple of data points to force regression coefficient A within a range we prefer (such as negative)? Appreciate your answer.