# How to prove positive effect of a variable with regression?

I am simply trying to prove that giving cash assistance to a company effects their related financial items in a good way.

I calculated the related item's mean for all companies, it's non negative and mostly positive for companies receiving cash assistance.

But when I fit a regression model (using R's lm()) with all variables that I have (amount of cash assistance, company age, all variable I think they're related etc.) cash assistance variables mostly havem negative coefficient.

I tried different combinations of variables, applying logarithmic transformation, sigmoid transformation and the others. Since I don't know too many statistics, I wanted to ask you this weak looking (maybe nonsense) question.

• first, you are not supposed to try transformations and combinations of variables until you find a result that you like. Second, the effect will be negative if the companies that got the assistance are the companies that were already doing badly, while the companies without an assistance were already doing well. Think about other possible selection biases that might affect your results. Another possible pitfall is a colider bias – rep_ho May 14 at 10:12
• @rep_ho Some people -- myself included -- are more sanguine about the value of exploratory data analysis ("try transformations and combinations..."). But if we understand your warning to mean "don't take any such result as statistically significant," then I think we are all in agreement. – whuber May 14 at 11:59
• @whuber that as well, but without even talking about statistical significance, I suppose we agree that a goal shouldn't be to prove that cash assistance works, but instead to find out if it works, or maybe how much it works – rep_ho May 14 at 12:15
• thank you both for precious answers. let me explain firstly for @rep_ho, I calculated financial items for similar companies (same industry, same amount of workers etc.) that didn't take cash assistance and calculated the company that took cash assistance and took their difference . This was my opinion to diminish the effect of bias. (If all companies go down because of economy, to diminish this kind of effects) – Samet Sökel May 14 at 12:21
• @SametSökel Your problem is basically how to show causal effect, from observational data. This is a very hard problem, there had been probably a Field's medal and a couple of Nobel prizes awarded for progress on problems like these. It's possible that with the data you have, you can't even answer that question. You would need to know and measure what causes a company to take the cash, and then correct for it, or use something like an instrumental variable. I am afraid there is no simple answer for you – rep_ho May 15 at 11:25