This is a course on as much of the theory and methods of regression modelling as we can reasonably cover. As a postgraduate course, it assumes knowledge of STATS 330, linear algebra, basic properties of probability and expectation, and R. The course will be delivered as three lectures and a lab each week. The course starts with generalised linear models, including parametric, semiparametric, and non-parametric views of the models, graphics for examining data and for examining models, modelling nonlinearity, and model selection for prediction and for causal inference. We will consider sampling, measurement error, missing data, censoring, and (if there is time) simple examples of longitudinal data. A solid understanding of predictive and causal inference is fundamental to Statistics and Data Science, and this course is designed for students who aim to be able to conduct statistical analyses independently.