I find myself doing a lot of regression analysis and similar mathematics recently for the purposes of numerical modeling of kinematic systems, without really know what the fuck I'm doing. My background is in engineering/control systems and I can usually derive the least squares solutions to various multiple regression problems with constraints/etc, but as far as understanding why certain models work/fail/are unstable/etc goes I have pretty much zero idea what I'm doing.

So far I've googled various issues I've run into (things like multicollinearity, VIF, etc) and read either wikipedia articles or blog posts, the former of which tend to be too scatterbrained, and the latter of which tend to be too devoid of mathematical context and jump straight to numbers and equations.

Is there a good introductory text on the subject? Ideally something motivated by practical needs (rather than being a purely theoretical approach), but with mathematical rigor that I can follow along so as to develop an actual understanding. I know in the field of controls sometimes authors wank too hard with the mathematics of proving stability that they forget to make the results actually useful.