I understand that factors like air density, height of the air column, direction of air flow, etc have an effect on air pressure. My question is what are the relative effects? Maybe to put it another way, if there was a polynomial model, what would the relative coefficients be?

Temperature. Divergence of gradient of air flow, and its time derivative (if the air happens to be rushing toward you it is driving your atmospheric pressure up). Composition of the air column above you (e.g. water vapor is much less dense). Your altitude.

Yes, I understand the various factors, but I’m trying to get a sense of their RELATIVE effect. What’s the most important factor? Is it 10X more important than the second most important factor?