This book characterizes the field of regression analysis beyond its traditional domain of mathematics and statistics. Simply speaking, regression is a technique that relates a dependent variable to one or more independent (explanatory) variables. A regression model can show whether changes observed in the dependent variable are associated with changes in one or more of the explanatory variables. Using this definition, regression methods are extended to machine learning. Consequently, the scope of this book is to present the applications of regression using the totality of methods (totum modum) one can employ in regression analysis: Linear regression polynomial regression general linear models vector generalized linear models binomial regression logistic regression multinomial logistic regression multinomial probit ordered logit multilevel models fixed effects random effects linear mixed-effects model nonlinear mixed-effects model nonlinear regression support vector regression lasso regression ridge regression nonparametric semiparametric robust quantile isotonic principal components Using examples from the Space domain, including endoatmospheric and exoatmospheric environments, space weather, space launch, satellites, and ground sensors, many of these methods are applied. All examples are solved using the R programming language and all code and datasets are accessible from our GitHub site. Although written as a reference, the book can be adapted as an advanced textbook in regression analysis.