The goal of this course is for students to learn the basic form and methodology of linear models, including multiple regression and analysis of variance. After completing this course, students will be familiar with the matrix representation of linear models, will understand the associated methodology for estimation and inference, and will know how to apply the modeling tools for the purpose of data analysis. Emphasis will be on linear regression, but students will also learn the basic principles of experimental design as well as generalized linear models. They will understand the differences between analyzing observational and experimental data. Students will be able to fit shrinkage regression models using R and Python and will be able to communicate the methods and results to the practitioners. Students will understand alternative parameterizations for statistical models. They will gain a basic understanding of the broad class of generalized linear models and study different models for the analysis of non-normal data.

Course topics will include simple linear regression, multiple linear regression, the matrix representation of the multiple regression model, ordinary and weighted least squares estimation, prediction, confidence and prediction intervals, Gauss-Markov theorem, hypothesis testing, model building, model diagnostics, traditional and modern variable selection techniques, shrinkage regression including Ridge and Lasso, completely randomized and blocked designs, introduction to generalized linear models in canonical form, logistic and probit regression for binary data, and Poisson and Gamma regression. Relevant statistical computing packages along with advanced typesetting systems for report writing will be covered.