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 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. Through directed reading, students will also explore logistic regression models that are applicable when the response variable can take just two possible values. 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.
41, 36 lectures and 5 hours of computing workshops
90% Examination, 10% Coursework
Draper,N.R. and Smith, H. (1998) Applied Regression Analysis. 3rd edition, New York, Wiley. [Recommended]
Chatterjee, S and Hadi, A.S. (2012) Regression Analysis by Example. 5th edition, Hoboken, New Jersey, Wiley. [Background]
Freedman, D.A. (2005) Statistical Models: Theory and Practice, Cambridge University Press. [Background]
Collett, D. (2003) Modelling Binary Data. 2nd edition. Boca Raton, Chapman & Hall/CRC. [Recommended]
Dobson, A.J. and Barnett, A. G. (2008) An Introduction to Generalized Linear Models. 3rd edition. Boca Raton, Chapman & Hall/CRC. [Recommended]
See the library reading list for this module (Canterbury)
On successful completion of this module, 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.
(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.
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