A question of linear regression

[ray1893]

Dear all,

I'm revising a working paper, and my coauthors and I are very confused about one issue. I will be very grateful if you can kindly give me some suggestions.

We have two variables, MF (dependent variable, defined as number of forecasts in one quarter, it could be 0, 1, 2, 3, etc) and TIGHT (one of independent variables, continuous variable). In OLS regression and fixed effects model, the coefficients of TIGHT are both significantly negative. We also define MF as dummy variable and run a logistic regression as sensitivity test. TIGHT still reveals a significantly negative association. However, when we divide whole sample into 50 equal groups according to TIGHT, and plot mean and median of MF, we cannot observe a negative tendency (it seems non-linear to me). Please refer to the attached.

I would like to know whether our model is valid. Do we have to quit linear regression results? What is the most suitable model? Are there any remedies for such situation?

Thank you very much!

Cheers,

Ray