# MMath Mathematics with Financial Mathematics

Year of entry: 2023

## Course unit details:Regression Analysis

Unit code MATH38141 10 Level 3 Semester 1 Department of Mathematics No

### Overview

In many areas of science, technology and medicine one often wishes to explore the relationship between one observable random response and a number of explanatory variables, which may influence simultaneously the response. The required statistical principles and techniques are established and used to select a suitable model for a given dataset.

### Pre/co-requisites

Unit title Unit code Requirement type Description
Probability 2 MATH20701 Pre-Requisite Compulsory
Statistical Methods MATH20802 Pre-Requisite Compulsory

None.

### Aims

• To familiarise students with the methodology and applications of standard techniques of regression analysis and analysis of variance.
• To explore some of the wide range of real-life situations occurring in different fields that can be investigated using regression statistical models.

### Learning outcomes

On successful completion of this course unit students will be able to:

• formulate, estimate, use and test for lack of fit regression linear models that are suitable for relevant statistical studies;
• formulate statistical hypotheses in terms of the model parameters and test such hypotheses;
• obtain confidence intervals for linear combinations of the model parameters;
• state the implications of orthogonality and collinearity between regressors;
• obtain a best-fitting model in a systematic and pragmatic way;
• use R to implement methods covered in the course.

### Syllabus

• Regression models. Assumptions. Matrix representation. Least squares estimators and their properties. Fitted values. Residuals. Estimating 2. [4]
• Vector random variables. Gauss-Markov theorem. Multivariate normal distribution. [3]
• Distribution of estimators and residuals. [3]
• Orthogonality. Multicolinearity. Indicator variables. Overparameterisation. [2]
• Estimating variance from replication. Weighted least squares. Testing model fit with and without replication. Checking model assumptions. Plots of residuals.[3]
• Model building and model selection. Deleting predictor variables. The general linear hypothesis. Stepwise regression. Penalised likelihood. AIC, AICc, BIC. Comparison of nested and not nested models. [3]
• One and two way analysis of variance. [4]

### Assessment methods

Method Weight
Other 30%
Written exam 70%
• Coursework: weighting 30%
• End of semester examination: weighting 70%

### Feedback methods

Feedback tutorials will provide an opportunity for students' work to be discussed and provide feedback on their understanding.  Coursework or in-class tests (where applicable) also provide an opportunity for students to receive feedback.  Students can also get feedback on their understanding directly from the lecturer, for example during the lecturer's office hour.

• Draper, D. N. R. and Smith, H., Applied Regression, (third edition).  Wiley.
Faraway, J. J. (2015). Linear Models with R., (second edition). Chapman and Hall/CRC.Montgomery,
D. C. and Peck, E. A., (2011). Introduction to Linear Regression Analysis, Wiley.
Weisberg, S., (2013). Applied Linear Regression (fourth edition). Wiley.
All are both recommended and further reading.

### Study hours

Scheduled activity hours
Lectures 11
Practical classes & workshops 11
Independent study hours
Independent study 78

### Teaching staff

Staff member Role
Alexander Donev Unit coordinator

The independent study hours will normally comprise the following. During each week of the taught part of the semester:

·         You will normally have approximately 60-75 minutes of video content. Normally you would spend approximately 2-2.5 hrs per week studying this content independently

·         You will normally have exercise or problem sheets, on which you might spend approximately 1.5hrs per week

·         There may be other tasks assigned to you on Blackboard, for example short quizzes or short-answer formative exercises

·         In some weeks you may be preparing coursework or revising for mid-semester tests

Together with the timetabled classes, you should be spending approximately 6 hours per week on this course unit.

The remaining independent study time comprises revision for and taking the end-of-semester assessment.

The above times are indicative only and may vary depending on the week and the course unit. More information can be found on the course unit’s Blackboard page.