# Module Information

Module Identifier
MA36510
Module Title
LINEAR STATISTICAL MODELS
2009/2010
Co-ordinator
Semester
Semester 1
Pre-Requisite
MA27210

#### Course Delivery

Delivery Type Delivery length / details
Lecture 19 Hours. (19 x 1 hour lectures)
Seminars / Tutorials 3 Hours. (3 x 1 hour example classes)

#### Assessment

Assessment Type Assessment length / details Proportion
Semester Exam 2 Hours   (written examination)  100%
Supplementary Assessment 2 Hours   (written examination)  100%

### Learning Outcomes

On completion of this module, a student should be able to:
1. describe the properties of the multivariate Normal distribution;
2. find and identify the distributions of linear and quadratic forms in Normal variates;
3. formulate a given situati5on as a (matrix) linear model;
4. analyse data from experiments modelled in this way;
5. construct confidence intervals/regions for linear combinations of parameters and for ratios of two parameters;
6. construct prediction intervals for future observations.
7. consider and analyse a design matrix with respect to leverage.

### 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.

### Aims

To introduce the scope and breadth of linear matrix modelling.

### Content

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.