# MAS3903 : Linear Models

• Offered for Year: 2024/25
• Module Leader(s): Dr Pete Philipson
• Owning School: Mathematics, Statistics and Physics
• Teaching Location: Newcastle City Campus
##### Semesters

Your programme is made up of credits, the total differs on programme to programme.

 Semester 1 Credit Value: 10 ECTS Credits: 5.0 European Credit Transfer System

#### Aims

To achieve an understanding of linear models, and how regression, Analysis of Variance (ANOVA) and Analysis of Covariance (ANCOVA) models arise as special cases. To understand the problem of identifiability in ANOVA, and the role played by parameter constraints and dummy variables in solving it.

Module summary

This module is concerned with building and applying statistical models for data. How does a mixture of quantitative and qualitative variables affect the body mass index of an individual? Suppose we find an association between age and body mass index, how can we study if this association varies between men and women, or between those with different educational backgrounds? In this course we consider the issues involved when we wish to construct realistic and useful statistical models for problems which can arise in a range of fields: medicine, finance, social science, sport and environmental issues being some of the main areas.

We revise multiple linear regression models, and see how they are special cases of a general linear model. We move on to consider Analysis of Variance (ANOVA) as another special case of a general linear model – this is the problem of investigating contrasts between different levels of a factor in affecting a response and then we generalize to the case of several factors. We consider Analysis of Covariance (ANCOVA) which involves mixing linear regression and factor effects, and the idea of interaction between explanatory variables in the way they affect a response. The module provides a comprehensive introduction to the issues involved in using statistics to model real data, and to draw relevant conclusions. There is an emphasis on hands-on application of the theory and methods throughout, with extensive use of R.

#### Outline Of Syllabus

The general linear model: maximum likelihood in the multi-parameter case; estimation of parameters; prediction; model adequacy; regression, ANOVA and ANCOVA as special cases. Model choice. Analysis of designs with 1, 2 or 3 factors. Model identifiability, parameter constraints and dummy variables. Use of transformations. Various extended examples of statistical modelling using R.

#### Teaching Methods

##### Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture51:005:00Problem classes
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision lectures
Scheduled Learning And Teaching ActivitiesLecture201:0020:00Formal lectures
Guided Independent StudyAssessment preparation and completion151:0015:00Completion of in course assessments
Guided Independent StudyIndependent study581:0058:00Preparation time for lectures, background reading, coursework review
Total100:00
##### Teaching Rationale And Relationship

The teaching methods are appropriate to allow students to develop a wide range of skills, from understanding basic concepts and facts to higher-order thinking.

Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems.

#### Assessment Methods

The format of resits will be determined by the Board of Examiners

##### Exams
Description Length Semester When Set Percentage Comment
Written Examination1201A80N/A
##### Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises1M5Problem-solving exercises assessment
Prob solv exercises1M5Problem-solving exercises assessment
Prob solv exercises1M5Problem-solving exercises assessment
Prob solv exercises1M5Problem-solving exercises assessment
##### Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The format of the examination will enable students to reliably demonstrate their own knowledge, understanding and application of learning outcomes. The assurance of academic integrity forms a necessary part of programme accreditation.

Examination problems may require a synthesis of concepts and strategies from different sections, while they may have more than one ways for solution. The examination time allows the students to test different strategies, work out examples and gather evidence for deciding on an effective strategy, while carefully articulating their ideas and explicitly citing the theory they are using.

The problem solving exercises are expected to consist of two exercises of equal weight: the exact nature of assessment will be explained at the start of the module. The exercises and the group project allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.