What will I learn on this module?

This module covers the three important areas of experimental design, multivariate techniques and regression. Experimental design will be developed using analysis of variance techniques to compare treatments meaningfully using replication, factorial experiments and balanced incomplete block designs. You will then move on to multivariate techniques including multivariate inference, data reduction using principal component analysis and classification with linear discriminant analysis. You will also learn how to extend regression models to the case where there are several explanatory variables including indicator variables. The models will subsequently be scrutinised using variable selection criteria and regression diagnostics to improve the model. Curvilinear and non-linear regression models cover the important aspect where different types of curves are appropriate for the data. The generalised linear model will be introduced and the specific case of a count response variable is developed.

Outline Syllabus
Experimental Design: design and analysis of 2n factorial experiments with replication, a full replicate and balanced
incomplete block designs.
Multivariate techniques: the multivariate normal distribution and its properties. Hotellings T2 test for one, two and paired
samples. Manova, linear discriminant analysis and principal component analysis.
Multiple linear regression: least squares estimation of the parameters of the model and their properties. The analysis of variance
and the extra sum of squares method. Variable selection techniques and regression diagnostics.
Non-linear and generalised linear models: Non-linear regression models, estimation of parameters and testing the model. Analysis of deviance and the Poisson regression model.

How will I learn on this module?

You will learn on this module via a combination of lectures and laboratory sessions involving the use of appropriate statistical packages such as R and SPSS. Classes will be scheduled in our modern computer laboratories enabling you to apply the techniques presented in the lecture part of the session and, in this way, gain a deeper understanding of the material and develop your practical skills. The bespoke laboratory sessions will take place broadly every other week.

Assessment involves an assignment and a laboratory examination. You will receive both written and oral feedback from the assignment. Oral feedback will be given concurrently during the laboratory sessions. Further to this, you will also receive exam feedback after the end of year exam in the summer, particularly relevant if you are on the MMath degree programme.

In addition, we operate an open door policy where you can meet with your module tutor to seek further advice or help if required. Your ability to analyse germane data and convey results in a concise report will be assessed via an individual assignment with individualised data, and your ability to choose the appropriate analysis for a range of problems will be tested in a laboratory exam at the end of the module.

How will I be supported academically on this module?

You will be supported academically chiefly through participation in the hands-on laboratory sessions, where you will be analysing data with appropriate software. This provides you with the opportunity to receive support on both the theory and technical components of the module simultaneously as well as offering experience of conditions representative of the final assessment.

You can engender further feedback and discussion with the teaching team at any time through our open door policy. In addition, all teaching materials, selected R commands, and supplementary material (such as interesting articles) are available through the e-learning portal.

What will I be expected to read on this module?

All modules at Northumbria include a range of reading materials that students are expected to engage with. The reading list for this module can be found at: http://readinglists.northumbria.ac.uk

What will I be expected to achieve?

Knowledge & Understanding:
1. Use an appropriate statistical package to apply multivariate and regression techniques
2. Appraise problems in order to select and apply the appropriate method for statistical analysis

Intellectual / Professional skills & abilities:
3. Develop appropriate multivariate and regression techniques to build models for data analysis, implementing such models using statistical software.
4. Critically evaluate statistical models based on real-life data

Personal Values Attributes (Global / Cultural awareness, Ethics, Curiosity) (PVA):
5. Research and cite information appropriately, in order to analyse data and present findings effectively

How will I be assessed?

SUMMATIVE
1. Coursework in the form of an individual assignment (30%) – 1, 2, 3, 4, 5
2. Laboratory examination (70%) – 1, 2, 3, 4

FORMATIVE
Formative assessment will be available on a broadly fortnightly basis in the laboratory sessions via normal lecturer-student interactions, allowing them to extend, consolidate and evaluate their knowledge.

Formative feedback will be provided on your work, and errors in understanding will be addressed reactively using one-to-one discussion. Solutions for laboratory tasks will be provided after you have attempted the questions, allowing you to receive feedback on the correctness of their solutions and to seek help if matters are still not clear.

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Module abstract

This module is designed to introduce advanced statistical methods with a dual focus on multivariate techniques and applied regression models. These topics will develop methods to analyse large, complex and multi-faceted data with real-life case studies drawn from finance, medicine and sport used to illustrate. Skills in using statistical software will be developed throughout the module to analyse data. In part one of the module the primary focus is on the data reduction techniques of principal components analysis and linear discriminant analysis. Regresssion models form the second part of the module, considering cases where we have multiple explanatory variables, indicator variables, polynomial and non-Gaussian relationships. Assessment of the module is by one individual assignment (30%) and one formal laboratory examination (70%). The module is designed to provide students with a useful preparation for employment or postgraduate study in an applied statistical environment where knowledge of appropriate software is key.

What will I learn on this module?

This module covers the three important areas of experimental design, multivariate techniques and regression. Experimental design will be developed using analysis of variance techniques to compare treatments meaningfully using replication, factorial experiments and balanced incomplete block designs. You will then move on to multivariate techniques including multivariate inference, data reduction using principal component analysis and classification with linear discriminant analysis. You will also learn how to extend regression models to the case where there are several explanatory variables including indicator variables. The models will subsequently be scrutinised using variable selection criteria and regression diagnostics to improve the model. Curvilinear and non-linear regression models cover the important aspect where different types of curves are appropriate for the data. The generalised linear model will be introduced and the specific case of a count response variable is developed.

Outline Syllabus
Experimental Design: design and analysis of 2n factorial experiments with replication, a full replicate and balanced
incomplete block designs.
Multivariate techniques: the multivariate normal distribution and its properties. Hotellings T2 test for one, two and paired
samples. Manova, linear discriminant analysis and principal component analysis.
Multiple linear regression: least squares estimation of the parameters of the model and their properties. The analysis of variance
and the extra sum of squares method. Variable selection techniques and regression diagnostics.
Non-linear and generalised linear models: Non-linear regression models, estimation of parameters and testing the model. Analysis of deviance and the Poisson regression model.

Course info

UCAS Code G101

Credits 20

Mode of Study 4 years full-time or 5 years with a placement (sandwich)/study abroad

Department Mathematics, Physics and Electrical Engineering

Location City Campus, Northumbria University

City Newcastle

Start September 2020 or September 2021

Mathematics MMath (Hons)

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