The problem with doing this is that it's usually hard to justify the ranking based purely on the size of estimated beta coefficient. Assume we regress Price of a used car (Y) on mileage, number of previous owners, and transmission type (X1, X2, X3).

The classic slope interpretation would be: For every 1 unit increase in X(n), we expect Y to increase/decrease by |beta(n)|, holding all else constant.

The issue arises because you can't easily say that increasing mileage by 1 mile is equivalent to a 1 person increase in previous owners. The units are different, so it doesn't really make sense to say which has the "most impact" on the DV. Sure, one may elicit a larger change in the DV, but that comes from a given change in X(n), which might not be equal to that same change in another X variable.

I think one (partial) solution is to standardize (at least) the predictors. This way, you can say that a 1 SD change in X1 causes a larger change in Y than a 1 SD change in X2, but again, the standard deviations have units of measure, so it's not a perfect solution, but it does help in a small way (I think, anyway, because it puts these 1 unit increases on a scale of "statistical un-usualness" within their respective distributions).

Thoughts?