Statistics 230A Linear Models

Course Description

We will cover the theory and applications of linear statistical models. We will try to gain understanding and insight through algebraic and geometric approaches to the theory and by using the computer to analyze real and simulated data. Applications and computational aspects will treated using the statistical language R. I plan to cover the following topics:

Formulation of linear statistical models
Ordinary and generalized least squares
Statistical properties of least squares estimates. The Gauss-Markov theorem; second order properties; inference based on the multivariate normal distribution.
Graphical displays and diagnostic procedures
Multiple regression and analysis of variance
Model selection
Ridge regression and the lasso
Nonparametric regression
Random effects and mixed effects models
Robust procedures
Nonlinear least squares
Generalized linear models

Grades will be based on a midterm, a final exam, regular homework, and computer labs.

Pre-requisites: Statistics 135, 200B or an equivalent course in statistics at a post-calculus level. Linear algebra.

Texts: Several books will be on course reserve in the Mathematics and Statistics Library. I recommend two in particular:

Introduction to Linear Regression Analysis, 4th Edition. D. Montgomery et al. Wiley
Linear Models with R. Julian Faraway. Chapman and Hall. A free early version of this can be found in the Contributed Documentation at http://cran.us.r-project.org/