# Module Directory

## MA317-6-SP-CO:Modelling Experimental Data

The details
2020/21
Mathematical Sciences
Colchester Campus
Spring
Current
Sunday 17 January 2021
Friday 26 March 2021
15
16 July 2020

Requisites for this module
MA114 and MA200
(none)
(none)
(none)

MA321

## Key module for

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)

## 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.

## 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:

- 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.

## 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. H, Q, V.
7. Generalised and weighted least squares.

Multiple regression

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.
12. ANCOVA

Designed experiments

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.

Non-linear models

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

## Learning and teaching methods

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.

## Bibliography

• 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 Description Deadline Weighting
Coursework   Assignment 1  19/02/2021
Coursework   Assignment 2  26/03/2021
Exam  240 minutes during Summer (Main Period) (Main)

Coursework Exam
20% 80%

### Reassessment

Coursework Exam
20% 80%
Module supervisor and teaching staff
Dr Stella Hadjiantoni & Dr Joseph Bailey

Availability
Yes
Yes
No

## External examiner

Prof Fionn Murtagh
University of Huddersfield
Professor of Data Science
Resources
Available via Moodle
Of 1817 hours, 0 (0%) hours available to students:
1817 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).

Further information
Mathematical Sciences

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