I am trying to understand the difference between fixed and random effects modelling. The panel data I have is in the form of basic longitudinal panel time series.

I know that I can use the Hauseman test to determinate which model to use. But my problem is that in fixed effects model I have to use fixed slopes. In random effects I can use random slopes and intercept and still get a slope coefficient for the whole model.

So how can I determinate whether to use random effects model with varying intercept and coefficient or fixed effects model using only varying coefficient and fixed slope?