# Covariance between parameters from different regression models

Is there a formula for the covariance between regression slopes from different models, fitted to the same data? For example, if I have a finite and fixed sample, $$S$$, and models:

1. $$Y = b_1X$$
2. $$Y = b_2X + b_3Z$$

...is there a general formula to characterize the covariance between $$b_1$$ and $$b_2$$, similar to how we can characterize the covariance between $$b_2$$ and $$b_3$$? Can it be generalized to an arbitrary number of regression models, including $$X$$'s effect on $$Y$$ and many potential covariates?