Modelling Experimental Data
Undergraduate: Level 6
Thursday 03 October 2019
Saturday 14 December 2019
01 October 2019
Requisites for this module
MA114 and (MA200 or MA207)
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.
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.
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.
No additional information available.
The module has 28 contact hours in total. These consist of 20 lectures, 4 labs and 4 classes during the spring term, together with 3 revision lectures in the summer term.
- 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
Professor Berthold Lausen (email@example.com). Dr Stella Hadjianto (firstname.lastname@example.org), Dr Joe Bailey (email@example.com)
Professor Berthold Lausen (firstname.lastname@example.org)
Prof Fionn Murtagh
Professor of Data Science
Available via Moodle
Of 35 hours, 33 (94.3%) hours available to students:
2 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).
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