University of Essex

MA317-7-SP-CO:
Linear Regression Analysis

The details

Year: 2023/24

Department: Mathematics, Statistics and Actuarial Science (School of)

Campus: Colchester Campus

Term: Spring

Level: Postgraduate: Level 7

Status: ReassessmentOnly

Start date: Monday 15 January 2024

End date: Friday 22 March 2024

Credits: 15

Last updated: 10 October 2022

Requisites for this module

Pre-requisites: (none)

Co-requisites: (none)

Pre and / or co-requisites: (none)

Prohibited modules: (none)

Key module (requisite for): (none)

Key module for

(none)

Module description

This module is concerned with the application of linear models to the analysis of data.

The underlying assumptions are discussed and general results are obtained using matrices. The standard approach to the analysis of normally distributed data using ANOVA is introduced. Methods for the design and analysis of efficient experiments are introduced. The general methodology is extended to logistic regression and the analysis of multidimensional contingency tables.

Module aims

The aim of this module is to provide the essential foundations of linear models by studying important topics of statistical modelling. This is achieved by an in-depth study of the main methods to analyse experimental data.

Module learning outcomes

On completion of the module students should be able to:

1. calculate confidence intervals for parameters and prediction intervals for future observations;
2. understand how to represent a linear model in matrix form;
3. check model assumptions and identify influential observations;
4. identify simple designed experiments;
5. construct factorial experiments in blocks;
6. adapt linear models to fit growth curves;
7. carry out logistic regression;
8. analyze cross-tabulated data using log linear models;
9. analyse linear models using R.

Module information

Syllabus

Simple linear regression
1. Link between maximum likelihood and least Squares. OLS for linear regression.
2. Pythagoras and the ANOVA table. The estimation of $rc2.
3. Confidence intervals for parameters and prediction intervals for future observations.

General results using matrices
4. Matrix formulation. Normal equations. Solution. Moments of estimators.
5. Gauss-Markov theorem. Estimability.
6. Generalised and weighted least squares.

Multiple regression
7. Multiple regression. Subdividing the regression sum of squares. Lack of fit and pure error.
8. Regression diagnostics. Leverage, Residual plots. Multicollinearity, Serial correlation.
9. Model selection. Stepwise methods. Cp plots.
10. Curvilinear regression. Orthogonal polynomials.
11. ANCOVA

Designed experiments
12. Completely randomised experiment. Replication. ANOVA. Contrasts.
13. Randomized blocks. Latin squares. Multiple comparison tests.
14. ANOVA with random effects
15. Balanced incomplete blocks. ANOVA (relation to bivariate regression)
16. Factorial experiments: notation. ANOVA. Model selection.
17. Factorials and blocks: confounding and partial confounding.
18. Fractional replicates. Aliases.

Non-linear models
20. The Newton-Raphson procedure. Application to growth curves.
21. Estimation, confidence intervals, tests.

Learning and teaching methods

Teaching in the department will be delivered using a range of face to face lectures, classes and lab sessions as appropriate for each module. Modules may also include online only sessions where it is advantageous, for example for pedagogical reasons, to do so.

Bibliography

Montgomery, D.C., Peck, E.A. and Vining, G.G. (2021) Introduction to linear regression analysis. Sixth edition. Hoboken: John Wiley & Sons, Inc. Available at: https://app.kortext.com/Shibboleth.sso/Login?entityID=https://idp0.essex.ac.uk/shibboleth&target=https://app.kortext.com/borrow/914905.
Krzanowski, W.J. (1998) An introduction to statistical modelling. London: Arnold.
Verbeek, M. (2017) A guide to modern econometrics. 5th edition. Hoboken: John Wiley & Sons. Available at: https://ebookcentral.proquest.com/lib/universityofessex-ebooks/detail.action?docID=6488280.
Faraway, J.J. (2015) Linear Models with R. Second edition. Boca Raton, FL: CRC Press. Available at: https://app.kortext.com/Shibboleth.sso/Login?entityID=https://idp0.essex.ac.uk/shibboleth&target=https://app.kortext.com/borrow/87267.

The above list is indicative of the essential reading for the course.
The library makes provision for all reading list items, with digital provision where possible, and these resources are shared between students.
Further reading can be obtained from this module's reading list.

Assessment items, weightings and deadlines

Coursework / exam	Description	Deadline	Coursework weighting
Exam	Main exam: In-Person, Open Book (Restricted), 180 minutes during Summer (Main Period)
Exam	Reassessment Main exam: In-Person, Open Book (Restricted), 180 minutes during September (Reassessment Period)

Exam format definitions

Remote, open book: Your exam will take place remotely via an online learning platform. You may refer to any physical or electronic materials during the exam.
In-person, open book: Your exam will take place on campus under invigilation. You may refer to any physical materials such as paper study notes or a textbook during the exam. Electronic devices may not be used in the exam.
In-person, open book (restricted): The exam will take place on campus under invigilation. You may refer only to specific physical materials such as a named textbook during the exam. Permitted materials will be specified by your department. Electronic devices may not be used in the exam.
In-person, closed book: The exam will take place on campus under invigilation. You may not refer to any physical materials or electronic devices during the exam. There may be times when a paper dictionary, for example, may be permitted in an otherwise closed book exam. Any exceptions will be specified by your department.

Your department will provide further guidance before your exams.

Overall assessment

Coursework	Exam
20%	80%

Reassessment

Coursework	Exam
20%	80%

Module supervisor and teaching staff

Supervisor: Dr Stella Hadjiantoni, email: stella.hadjiantoni@essex.ac.uk.

Teaching staff: Dr Stella Hadjiantoni and Dr Oludare Ariyo

Contact details: stella.hadjiantoni@essex.ac.uk

Availability

Available to incoming Essex Abroad / Exchange students: No

Available to Outside Option: No

Available to Audit: No

External examiner

Name: Dr Yinghui Wei

Institution: University of Plymouth

Name: Dr Murray Pollock

Institution: Newcastle University

Academic role: Director of Statistics / Senior Lecturer

Resources

Teaching materials: Available via Moodle

Lecture recording: Of 1702 hours, 10 (0.6%) hours available to students:
1692 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).

Further information

Department website: Mathematics, Statistics and Actuarial Science (School of)

Disclaimer: The University makes every effort to ensure that this information on its Module Directory is accurate and up-to-date. Exceptionally it can be necessary to make changes, for example to programmes, modules, facilities or fees. Examples of such reasons might include a change of law or regulatory requirements, industrial action, lack of demand, departure of key personnel, change in government policy, or withdrawal/reduction of funding. Changes to modules may for example consist of variations to the content and method of delivery or assessment of modules and other services, to discontinue modules and other services and to merge or combine modules. The University will endeavour to keep such changes to a minimum, and will also keep students informed appropriately by updating our programme specifications and module directory.

The full Procedures, Rules and Regulations of the University governing how it operates are set out in the Charter, Statutes and Ordinances and in the University Regulations, Policy and Procedures.

Module Directory

MA317-7-SP-CO:Linear Regression Analysis