Module Information
Course Delivery
Assessment
| Assessment Type | Assessment length / details | Proportion |
|---|---|---|
| Semester Exam | 2 Hours (Written Examination) | 100% |
| Supplementary Exam | 2 Hours (Written Examination) | 100% |
Learning Outcomes
On successful completion of this module students 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 situation 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 unknown population variance.
6. carry out simple linear hypothesis tests based on ANOVA.
7. calculate leverages and residuals, and use them for outlier detection.
Brief description
The Linear Statistical Model encompasses a variety of elementary statistical techniques such as linear regression, design models, ANOVA, etc, and much more besides. This module introduces the general matrix formulation of the linear model, and demonstrates the neatness of its systematic application to a wide range of statistical problems.
Aims
To introduce the scope and breadth of linear matrix modelling.
Content
2. GENERAL LINEAR MODEL OF FULL RANK: Formulation. Ordinary Least Squares estimator and normal equations. The assumption of independent homoscedastic errors. The BLUE and Gauss-Markov Theorem. Consideration of the design matrix. The hat matrix and leverage.
3. FURTHER INFERENCE IN THE FULL RANK CASE: Estimation of population variance. Confidence regions and intervals. Consideration of outliers: residuals and leverage. Tests of linear hypotheses.
Module Skills
| Skills Type | Skills details |
|---|---|
| Adaptability and resilience | Students are expected to develop their own approach to time-management and to use the feedback from marked work to support their learning. |
| Co-ordinating with others | Students will be encouraged to work in groups to solve problems. |
| Creative Problem Solving | The assignments will give the students opportunities to show creativity in finding solutions and develop their problem solving skills. |
| Digital capability | Use of the internet, Blackboard, and mathematical packages will be encouraged to enhance their understanding of the module content and examples of application |
| Professional communication | Students will be expected to submit clearly written solutions to set exercises. |
| Subject Specific Skills | Broadens exposure of students to topics in mathematics, and an area of application that they have not previously encountered. |
Notes
This module is at CQFW Level 6