Module Identifier | MA36510 | ||

Module Title | LINEAR STATISTICAL MODELS | ||

Academic Year | 2000/2001 | ||

Co-ordinator | Mr D A Jones | ||

Semester | Semester 1 | ||

Pre-Requisite | MA27010 | ||

Course delivery | Lecture | 19 x 1hour lectures | |

Seminars / Tutorials | 3 x 1hour example classes | ||

Assessment | Exam | 2 Hours (written examination) | 100% |

Resit assessment | 2 Hours (written examination) | 100% |

**General 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.

**Aims**

To introduce the scope and breadth of linear matrix modelling.

**Learning outcomes**

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

- describe the properties of the multivariate Normal distribution;
- find and identify the distributions of linear and quadratic forms in Normal variates;
- formulate a given situaton as a (matrix) linear model;
- analyse data from experiments modelled in this way;
- construct confidence intervals/regions for linear combinations of parameters and for ratios of two parameters;
- construct prediction intervals for future observations.

**Syllabus**

1. DISTRIBUTION THEORY: Random vectors. Multivariate Normal Distribution. Linear Forms. Quadratic forms. 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.

3. INFERENCE IN THE FULL RANK CASE: Confidence statements. Confidence regions. Prediction intervals. Confidence limits for ratios.

**Reading Lists**

**Books**
**** Supplementary Text**

F A Graybill.
*An Introduction to the General Linear Model*. Duxbury
**** Essential Reading**

R H Myers and J S Milton.
*A FIrst Course in the Theory of Linear Statistical Models*. PWS-Kent