## MA317-6-AU-CO:Linear Regression Analysis

The details
2024/25
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Autumn
Current
Thursday 03 October 2024
Friday 13 December 2024
15
23 May 2024

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

MA322

## Key module for

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)

## 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.

## Module aims

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.

## Module learning outcomes

By the end of this module, students will be expected to 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. Work efficiently in small groups to analyse data.

7. Analyse linear models using R.

## Module information

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.

## Learning and teaching methods

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.

## Bibliography*

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.

## 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.

Coursework Exam
30% 70%

### Reassessment

Coursework Exam
30% 70%
Module supervisor and teaching staff
Dr Danilo Petti, email: d.petti@essex.ac.uk.
Dr Danilo Petti
maths@essex.ac.uk

Availability
Yes
Yes
No

## External examiner

Dr Yinghui Wei
University of Plymouth
Dr Murray Pollock
Newcastle University
Director of Statistics / Senior Lecturer
Resources
Available via Moodle
Of 33 hours, 32 (97%) hours available to students:
1 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s), module, or event type.

Further information

* Please note: due to differing publication schedules, items marked with an asterisk (*) base their information upon the previous academic year.

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