This module is not currently running in 2024 to 2025.
Regression is a fundamental technique of statistical modelling, in which we aim to model a response variable using one or more explanatory variables. For example, we might want to model the yield of a chemical process in terms of the temperature and pressure of the process. The need for statistical modelling arises because even when temperature and pressure are fixed, there will typically be variation in the resulting yield, so the model must include a random component. In this module we study the broad class of linear regression models, which are widely used in practice. We learn how to formulate such models and fit them to data, how to make predictions with associated measures of uncertainty, and how to select appropriate explanatory variables. Both theory and practical aspects are covered, including the use of computer software for regression. Outline of the syllabus: simple linear regression; the method of least squares; sums of squares; the ANOVA table; residuals and diagnostics; matrix formulation of the general linear model; prediction; variable selection; one-way analysis of variance; practical regression analysis using software; logistic regression.
36 lectures and up to 12 hours practical sessions
90% Examination, 10% Coursework
S Chatterjee, A Hadi Regression analysis by Example. (New York: Wiley, 3rd ed. 1999, 4th ed. 2006)
N R Draper, H Smith Applied Regression Analysis. (New York: Wiley. 1998) (R)
DA Freedman Statistical Models: Theory and Practice. (Cambridge, University Press, 2005)
See the library reading list for this module (Canterbury)
The intended subject specific learning outcomes
On successful completion of this module, level 5 students will be able to demonstrate:
(a) a reasonable ability to derive, from first principles and using matrix algebra, theoretical results relating to fitting regression models by least squares;
(b) a reasonable ability to fit regression models to data, and carry out related statistical inferences, using both hand calculation and appropriate computer software;
(c) a reasonable ability to use residual plots and other techniques to check the assumptions underlying regression analysis;
(d) a reasonable ability to identify outlying and influential observations;
(e) a reasonable ability to choose between alternative models for sets of data.
On successful completion of this module, level 6 students will also be able to demonstrate:
(f) a systematic understanding of the areas of simple linear and multiple regression modelling.
(g) an ability to explore the statistical literature to extend their knowledge of regression modelling to include logistic regression models.
The intended generic learning outcomes
The module provides an introduction to the theory and practice of regression. Students should emerge with an appreciation of the power of this technique, and with the ability to use it in the analysis of data.
On successful completion of the Module, level 5 students will have:
(a) developed their understanding of probability and statistics;
(b) applied a range of mathematical techniques to solve statistical problems;
(c) developed their ability to abstract the essentials of problems and to formulate them independently;
(d) improved their key skills in written communication, numeracy and problem solving;
(e) developed their ability to use statistical software;
(f) enhanced their study skills and ability to work with relatively little supervision.
On successful completion of the Module, level 6 students will also have:
(g) demonstrated an ability to extend their existing knowledge of statistics into new areas through independent study.
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