MA717-7-AU-CO:
Applied Regression and Experimental Data Analysis

The details
2023/24
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Autumn
Postgraduate: Level 7
Current
Thursday 05 October 2023
Friday 15 December 2023
15
07 November 2023

 

Requisites for this module
(none)
(none)
(none)
(none)

 

(none)

Key module for

MSC G30412 Data Science,
MSC G30424 Data Science,
MSC G304PP Data Science with Professional Placement,
DIP G30009 Statistics,
MSC G30012 Statistics,
MPHDG30048 Statistics,
PHD G30048 Statistics,
MPHDG30448 Data Science,
PHD G30448 Data Science,
MSCIG199 Mathematics and Data Science

Module description

This module is concerned with the application of regression 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 nonlinear regression, generalised regression and the analysis of multidimensional contingency tables.

Module aims

The aims of this module are:



  • To build on the essential foundations of regression models by studying important topics of statistical modelling.

  • To enable students to engage with an in-depth study of the main methods to analyse experimental data.

Module learning outcomes

By the end of this module, students will be expecting to be able to:



  1. Calculate confidence intervals for parameters and prediction intervals for future observations.

  2. Understand how to represent a linear regression model in matrix form.

  3. Check model assumptions and identify influential observations.

  4. Identify advanced designed experiments.

  5. Construct factorial experiments in blocks.

  6. Understand basic nonlinear regression.

  7. Carry out generalised linear regression analysis.

  8. Analyse cross-tabulated data using log linear models.

  9. Analyse linear models using R.

Module information

There will be a recap on basic statistics and simple linear regression in the first week.


Syllabus


General results using matrices



  • Matrix formulation. Normal equations. Solution. Moments of estimators.

  • Gauss-Markov theorem. Estimability.


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. Cp plots, LASSO.

  • Curvilinear regression. Orthogonal polynomials.

  • Weighted least squares.


Designed experiments



  • Completely randomised experiment. Replication. ANOVA. Contrasts.

  • Randomised blocks. Latin squares. Multiple comparison tests.

  • ANOVA with random effects.

  • Missing values in Experimental Data.

  • Balanced incomplete blocks. ANOVA (relation to bivariate regression).

  • Factorial experiments: notation. ANOVA. Model selection.

  • Factorials and blocks: confounding and partial confounding.

  • Fractional replicates. Aliases.

  • ANCOVA.


Non-linear models



  • The Newton-Raphson procedure. Application to growth curves.

  • Estimation, confidence intervals, tests.

  • Generalised Linear Regression (Logistic regression, Poisson regression, link function, exponential families, contingency table).

Learning and teaching methods

This module will be delivered via:

  • One 2-hour lecture per week.
  • One 1-hour class per fortnight.
  • One 1-hour lab per fortnight.

There will also be 5 hours of lectures to recap basic statistics and simple linear regression in the first week There will also 3 hours of revision lectures for the summer exam.

Bibliography

This module does not appear to have a published bibliography for this year.

Assessment items, weightings and deadlines

Coursework / exam Description Deadline Coursework weighting
Coursework   Assignment     
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

Coursework Exam
20% 80%

Reassessment

Coursework Exam
20% 80%
Module supervisor and teaching staff
Dr Yanchun Bao, email: ybaoa@essex.ac.uk.
Dr Yanchun Bao; Dr Oludare Ariyo
ybaoa@essex.ac.uk

 

Availability
Yes
No
Yes

External examiner

Dr Murray Pollock
Newcastle University
Director of Statistics / Senior Lecturer
Resources
Available via Moodle
Of 65 hours, 65 (100%) hours available to students:
0 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

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