Module Identifier MA36510  
Academic Year 2003/2004  
Co-ordinator Mr Alan Jones  
Semester Semester 1  
Pre-Requisite MA27210  
Course delivery Lecture   19 x 1 hour lectures  
  Seminars / Tutorials   3 x 1 hour example classes  
Assessment TypeAssessment Length/DetailsProportion
Semester Exam2 Hours (written examination)  100%
Supplementary Assessment2 Hours (written examination)  100%

Learning outcomes

On completion of this module, a student should be able to:

Brief description

The Linear Statistical Model encompasses all elementary statistical techniques such as one and two mean procedures, straight line fitting, etc, and much more besides. This module sets such models in a matrix formulation and shows the neatness and breadth of application of such modelling, at the same time illustrating some illuminating applications of matrices.


To introduce the scope and breadth of linear matrix modelling.


1. DISTRIBUTION THEORY: Random vectors. Multivariate Normal Distribution. Linear Forms. Brief survey of quadratic forms and their independence.
2. GENERAL LINEAR MODEL OF FULL RANK: Formulation. Least squares and the normal equations. Properties of their solution. Effect of independent homoscedastic errors. The Gauss-Markov Theorem. Consideration of the design matrix The hat matrix and leverage.
3. INFERENCE IN THE FULL RANK CASE: Confidence statements. Confidence regions. Prediction intervals. Confidence limits for ratios. Residuals and deletion statistics. Leverage.

Reading Lists

** Supplementary Text
F A Graybill (1976) Theory and application of the linear model Duxbury 0878721088
** Essential Reading
R H Myers & J S Milton (1991) A FIrst Course in the Theory of Linear Statistical Models PWS-Kent 0534916457


This module is at CQFW Level 6