This is a personal guided tour of regression techniques intended for manufacturing professionals involved with quality. Starting from “historical monuments” like simple linear regression and multiple regression, it goes through “mid-century modern” developments like logistic regression. It ends with newer constructions like bootstrapping, bagging, and MARS. It is limited in scope and depth, because a full coverage would require a book and knowledge of many techniques I have not tried. See the references for more comprehensive coverage. 

To fit a regression model to a dataset today, you don’t need to understand the logic, know any formula, or code any algorithm. Any statistical software, starting with electronic spreadsheets, will give you regression coefficients, confidence intervals for them, and, often, tools to assess the model’s fit.

However, treating it as a black box that magically fits curves to data is risky. You won’t understand what you are looking at and will draw mistaken conclusions. You need some idea of the logic behind regression in general or behind specific variants to know when to use them, how to prepare data, and to interpret the outputs.