3. For sparse or continuous data, you can’t really find these comparisons where v is identical, so it’s clear that regression coefficients are model-based. In that sense, I don’t mind vague statements such as “allowing for simultaneous change in the other predictors.” I’d prefer the term “comparison” rather than “change,” but the real point is that regression coefficients represent averages in a sort of smoothed comparison, a particular smoothing based on a linear model.
Understanding regression models and regression coefficients « Statistical Modeling, Causal Inference, and Social Science