STA2005S - Linear Models

Course Outline:

This course gives an introduction to statistical modelling and the theory of linear statistical models. The material is presented from a parametric and non-parametric perspective. The course has two sections: Regression: The multivariate normal distribution; quadratic forms; the linear model; maximum likelihood; estimates of parameters in the linear model; the Gauss-Markov theorem; variable selection procedures; analysis of residuals, bootstrap sampling; principal component analysis for dimension reduction and for regression. Design and analysis of experiments: Introduction to the basic design principles, basic experimental designs (completely randomised design, the randomised block design, Latin square design) factorial experiments, analysis of variance, the problem of multiple comparisons, power and sample size calculations, introduction to random effects and repeated measures, permutation/randomization tests, nonparametric tests, bootstrapping. The students are introduced to relevant statistical software and practical data analysis through weekly computer practicals and the exposure to many datasets.