Hi,
I am new in this forum, I read many useful comments related to panel data analysis. I am from finance background so I don't have much knowledge about econometrics so many of you may think it's a silly question.
Actually, I am working with panel data, mainly interested of the moderation effect (X and Z) which are continuous variables. My problem is can I choose OLS model instead of the Fixed effect model?

The OLS and Fixed effect models are attached:

I also ran the Random effect model, where I find the Fixed effect model is better through the Hausman test.
In my study I got expected result from the OLS model, however, it's assume that the OLS model consider the id as homogeneous where Fixed effect consider as heterogeneous. I read some paper where they select the OLS over Fixed effect model by placing F-test. Is that the correct way I can select the OLS model? If so could you please advise me some relevant materials where I can learn more about this process?

Any other advice and suggestions would be greatly appreciated.