|| MA36510 |
|| LINEAR STATISTICAL MODELS |
|| 2004/2005 |
|| Mr Alan Jones |
|| Semester 1 |
|| MA27210 |
| Course delivery
|| Lecture || 19 x 1 hour lectures |
|| Seminars / Tutorials || 3 x 1 hour example classes |
|Assessment Type||Assessment Length/Details||Proportion|
|Semester Exam||2 Hours (written examination) ||100%|
|Supplementary Assessment||2 Hours (written examination) ||100%|
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 situati5on 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.
consider and analyse a design matrix with respect to leverage.
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.
** Supplementary Text
F A Graybill (1976) Theory and application of the linear model
** Essential Reading
R H Myers & J S Milton (1991) A FIrst Course in the Theory of Linear Statistical Models
This module is at CQFW Level 6