Modelling Experimental Data
Undergraduate: Level 6
Sunday 17 January 2021
Friday 26 March 2021
16 July 2020
Requisites for this module
MA114 and MA200
BSC 5B43 Statistics (Including Year Abroad),
BSC 9K12 Statistics,
BSC 9K13 Statistics (Including Placement Year),
BSC 9K18 Statistics (Including Foundation Year),
BSC G1F3 Mathematics with Physics,
BSC G1F4 Mathematics with Physics (Including Placement Year),
BSC GCF3 Mathematics with Physics (Including Year Abroad),
BSC I1G3 Data Science and Analytics,
BSC I1GB Data Science and Analytics (Including Placement Year),
BSC I1GC Data Science and Analytics (Including Year Abroad),
BSC I1GF Data Science and Analytics (Including Foundation Year)
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.
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.
On completion of the module students should be able to:
- calculate confidence intervals for parameters and prediction intervals for future observations;
- understand how to represent a linear model in matrix form;
- check model assumptions and identify influential observations;
- identify simple designed experiments;
- construct factorial experiments in blocks;
- adapt linear models to fit growth curves;
- work efficiently in small groups to analyse data;
- analyse linear models using R.
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. H, Q, V.
7. Generalised and weighted least squares.
8. Multiple regression. Subdividing the regression sum of squares. Lack of fit and pure error.
9. Regression diagnostics. Leverage, Residual plots. Multicollinearity, Serial correlation.
10. Model selection. Stepwise methods. Cp plots.
11. Curvilinear regression. Orthogonal polynomials.
13. Completely randomised experiment. Replication. ANOVA. Contrasts.
14. Randomized blocks. Latin squares. Multiple comparison tests.
15. ANOVA with random effects
16. Balanced incomplete blocks. ANOVA (relation to bivariate regression)
17. Factorial experiments: notation. ANOVA. Model selection.
18. Factorials and blocks: confounding and partial confounding.
19. Fractional replicates. Aliases.
20. The Newton-Raphson procedure. Application to growth curves.
21. Estimation, confidence intervals, tests.
Teaching will be delivered in a way that blends face-to-face classes, for those students that can be present on campus, with a range of online lectures, teaching, learning and collaborative support.
- Faraway, Julian James. (©2015) Linear models with R, Boca Raton, FL: CRC Press. vol. Chapman & Hall/CRC texts in statistical science series
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
||180 minutes during Summer (Main Period) (Main)
Module supervisor and teaching staff
Dr Stella Hadjiantoni, email: firstname.lastname@example.org.
Dr Stella Hadjiantoni & Dr Joseph Bailey
Dr Stella Hadjiantoni (email@example.com), Dr Joseph Bailey (firstname.lastname@example.org)
No external examiner information available for this module.
Available via Moodle
No lecture recording information available for this module.
* Please note: due to differing publication schedules, items marked with an asterisk (*) base their information upon the previous academic year.
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.