AS2B-Linear Models

Module Provider: Mathematics and Statistics
Number of credits: 20 [10ECTS credits]
Level: 5
Terms in which taught: Autumn, Spring and Summer
Module Convenor: Mr AA Leidi
Pre-requisites: AS1E AS1F AS1G AS1H
Co-requisites:
Modules excluded:
Module version for: 2011/2

Email: A.A.Leidi@reading.ac.uk

Aims:
Linear models are used widely in applied statistics; examples of widely used linear models include linear regression and models used in analysing data from designed experiments. These models will be reviewed and their relationship to the general linear model explored.
The module will include definition of the general linear model, simple linear regression, analysis of variance, model checking, use of indicator variables, multiple regression and variable selection.
The aim of the module is to present a standard approach for fitting linear models to data and for comparing alternative linear models with one another, and to provide the student with the skills to develop and test linear models appropriate for a range of practical problems.

Assessable learning outcomes:
On completion of this module students will have acquired:
� knowledge of the basic theory associated with the general linear model and the principles of analysis of variance;
� the ability to fit regression models to data, interpret them and check their adequacy.
� an awareness of the role of regression modelling in the analysis of data from designed experiments
� the ability to use MINITAB to fit linear models and check their adequacy.

Additional outcomes:
The ability to use SAS to fit linear models and check their adequacy.

Outline content:
Introduction to the linear model.
Simple linear regression and the completely randomised design.
Fitting linear models via least-squares.
Interpreting the fitted model: properties of parameter estimates, confidence intervals and prediction intervals
Comparison of models.
Randomised block designs.
Introduction to multiple regression.
The General Linear Model: definition and matrix notation.
Model checking: residual analysis, influential observations, transformations.
More complicated models: polynomial regression, indicator variables, variable selection.
Multicollinearity.
Use of MINITAB and SAS to fit linear models.
Recommended reading:
Krzanowski, W.J. (1998). An Introduction to Statistical Modelling. London: Arnold.
Mead, R., Curnow, R.N. and Hasted, A.M. (1993). Statistical Methods in Agriculture and Experimental Biology. London: Chapman & Hall.
Montgomery, D.C. and Peck, E.A. (1992). Introduction to Linear Regression Analysis. New York: Wiley.

Brief description of teaching and learning methods:
Lectures supported by tutorials and practicals. Non-assessed exercises.

Contact hours:

Assessment:
Coursework
Two assignments.
Relative percentage of coursework: 20%
Penalties for late submission:
Penalties for late submission of course work will be in accordance with University policy.
Examination:
One paper of three hours duration
Relative percentage of examination: 80%
Requirement for a Pass
An overall mark of at least 40%
Reassessment arrangements
One examination paper of 3 hours duration

Last updated: 18 August 2011