This course offers an introduction to regression modeling with applications. The presentation begins with linear (single and multiple) models as they are simple yet tremendously useful in many applications. For these models, fitting, parametric and model inference as well as prediction will be explained. A special attention will be paid to the diagnostic strategies which are key components of good model fitting. Further topics include transformations and weightings to correct model inadequacies, the multicollinearity issue and shrinkage regression methods, variable selection and model building techniques. Later in the course, some general strategies for regression modeling will be presented with a particular focus on the generalized linear models (GLM) using the examples with binary and count response variables.

As the high-dimensional data, order of magnitude larger than those that the classic regression theory is designed for, are nowadays a rule rather than an exception in computer-age practice (examples include information technology, finance, genetics and astrophysics, to name just a few), regression methodologies which can deal with high-dimensional scenarios are presented.

The twenty-first century has been an efflorence of computer-based regression techniques which are integrated into the course based on the statistical software package R.

The overall goal of the course is twofold: to acquaint students with the athematical theory and statisical methodology of the regression modeling and to develop advanced practical skills that are necessary for applying regression analysis to a real world data analytics problem The course is lectured and examined in English.

Recommended prerequisites:

• SF1901 or equivalent course of the type 'a first course in probability and statistics'.
• Multivariate normal distribution.
• Basic differential and integral calculus, basic linear algebra.

Course literature and supplementary reading:

• D. Montgomery, E. Peck, G. Vining: Introduction to Linear Regression Analysis. Wiley-Interscience, 5th Edition (2012). ISBN-10: 978-0-470-54281-1. 645 pages. Acronym below: MPV.

• G. James, D. Witten, T. Hastie, R. Tibshirani: An introduction to Statistical Learning.Web page for the book by the publisher Springer.
• A. J. Izenman: Modern Multivariate Statistical Techniques. Regression, Classification, and Manifold Learning.Web page for the book by the publisher Springer. Acronym below: Iz.
• T. Hastie, R. Tibshirani, J. Friedman: The Elements of Statistical Learning. Web page for the book. Springer, 2ed Edition, 2017.