MA317-6-AU-CO:
Linear Regression Analysis
2023/24
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Autumn
Undergraduate: Level 6
Current
Thursday 05 October 2023
Friday 15 December 2023
15
09 February 2024
Requisites for this module
MA114 and MA200
(none)
(none)
(none)
(none)
BSC N233 Actuarial Science (Including Placement Year),
BSC N323 Actuarial Science,
BSC N323DF Actuarial Science,
BSC N324 Actuarial Science (Including Year Abroad),
BSC N325 Actuarial Science (Including Foundation Year),
BSC 5B43 Statistics (Including Year Abroad),
BSC 9K12 Statistics,
BSC 9K13 Statistics (Including Placement Year),
BSC 9K18 Statistics (Including Foundation Year),
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),
MSCIN399 Actuarial Science and Data Science,
BSC N333 Actuarial Studies,
BSC N334 Actuarial Studies (Including Placement Year),
BSC N335 Actuarial Studies (Including Year Abroad)
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 aim of this module is:
- To provide the essential foundations of linear models by studying important topics of statistical modelling achieved by an in-depth study of the main methods to analyse experimental data.
By the end of this module, students will be expected to 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.
- Work efficiently in small groups to analyse data.
- Analyse linear models using R.
Syllabus
- Simple linear regression
- The link between maximum likelihood and least Squares. OLS for linear regression.
- Pythagoras and the ANOVA table. The estimation of $rc2.
- Confidence intervals for parameters and prediction intervals for future observations.
- General results using matrices
- Matrix formulation. Normal equations. Solution. Moments of estimators.
- Gauss-Markov theorem. Estimability.
- Generalised and weighted least squares.
- Multiple regression
- Multiple regression. Subdividing the regression sum of squares. Lack of fit and pure error.
- Regression diagnostics. Leverage, Residual plots. Multicollinearity, Serial correlation.
- Model selection. Stepwise methods. Cp plots.
- Curvilinear regression. Orthogonal polynomials.
- ANCOVA.
- Designed experiments
- Completely randomised experiment. Replication. ANOVA. Contrasts.
- Randomised blocks. Latin squares. Multiple comparison tests.
- ANOVA with random effects.
- Balanced incomplete blocks. ANOVA (relation to bivariate regression).
- Factorial experiments: notation. ANOVA. Model selection.
- Factorials and blocks: confounding and partial confounding.
- Fractional replicates. Aliases.
- Non-linear models
- The Newton-Raphson procedure. Application to growth curves.
- Estimation, confidence intervals, tests.
Teaching in the School 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.
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 |
| Coursework |
Test |
|
|
| 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
Reassessment
Module supervisor and teaching staff
Dr Danilo Petti, email: d.petti@essex.ac.uk.
Dr Danilo Petti
d.petti@essex.ac.uk
Yes
Yes
No
Dr Yinghui Wei
University of Plymouth
Dr Murray Pollock
Newcastle University
Director of Statistics / Senior Lecturer
Available via Moodle
Of 34 hours, 32 (94.1%) hours available to students:
0 hours not recorded due to service coverage or fault;
2 hours not recorded due to opt-out by lecturer(s), module, or event type.
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