Aims & Learning Objectives:
Aims: Introduce the principles of building and analysing linear models, introduce the principles of statistical modelling.
Ability to carry out analyses using linear Gaussian models, including regression and ANOVA. Ability to manipulate joint, marginal and conditional distributions. Ability to represent normal linear models in vector and matrix form.
Regression: Estimation of model parameters, tests and confidence intervals, prediction intervals, polynomial and multiple regression. One-way analysis of variance (ANOVA): One-way classification model. Main effects and interaction, parameter estimation, F- and t-tests. Use of residuals to check model assumptions: probability plots, identification and treatment of outliers. Multivariate distributions: Joint, marginal and conditional distributions; expectation and variance-covariance matrix of a random vector; statement of properties of the bivariate and multivariate normal distribution. The general linear model: Vector and matrix notation. examples of the design matrix for regression and ANOVA, least squares estimation, internally and externally studentised residuals.