Aims

This module will provide an introduction to regression which is possibly the most widely used approach for statistical modelling. Students will learn about the use of linear and generalized linear models to build statistical descriptions of data.

Module Summary
Often a response variable Y is influenced by the value of another variable X, sometimes called a covariate – this is known as a regression problem. For instance, reaction time to a stimulus might depend on age. Two types of regression model will be introduced. First the linear regression model for responses which can be assumed to have a normal distribution will be introduced. This will start with a simple regression for a single covariate, moving to an introductory treatment of a matrix-based approach for a model with more covariates. Second the logistic regression model for binary responses will be introduced. Methods for assessing the assumptions which underlie the model will be introduced.

Outline Of Syllabus

Simple linear regression. Equivalence of least squares and maximum likelihood. Properties of estimators of regression coefficients. Introduction to multiple regression and the general linear model using matrix formulation. Conjugate Bayesian analysis of the multiple linear regression model and posterior predictive inference. Generalized linear models via logistic regression; maximum likelihood estimation. Residuals and other diagnostic tools for model checking.

Teaching Rationale And Relationship

The teaching methods are appropriate to allow students to develop a wide range of skills, from understanding basic concepts and facts to higher-order thinking. Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems. Module drop-in sessions allow students to receive learning support in areas where they may need additional guidance.

Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The format of the examination will enable students to reliably demonstrate their own knowledge, understanding and application of learning outcomes. The assurance of academic integrity forms a necessary part of the programme accreditation.

Examination problems may require a synthesis of concepts and strategies from different sections, while they may have more than one ways for solution. The examination time allows the students to test different strategies, work out examples and gather evidence for deciding on an effective strategy, while carefully articulating their ideas and explicitly citing the theory they are using.

The coursework assignments allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.