The course deals with a variety of statistical models and methods that generalize classical linear regression to include many others that have been found useful in statistical analysis and applications. We will first review key concepts in linear regression analysis, and expand the scope in depth to generalized linear models, then head for several important directions: nonparametric regression and generalized additive models, linear and generalized linear mixed models, generalized estimating equations for correlated data, dimension reduction and so on (if time permits). The course is a mixture of theory and applications and includes computer projects featuring R programming.