# GENERAL LINEAR MODELS - 2022/3

Module code: MAT2002

## Module Overview

This module introduces least squares fitting, methods of inference based on normal theory, diagnostics and analysis of data from simple designs.

### Module provider

Mathematics

GODOLPHIN Janet (Physics)

## Overall student workload

Independent Learning Hours: 76

Lecture Hours: 33

Laboratory Hours: 8

Captured Content: 33

Semester 1

## Prerequisites / Co-requisites

MAT1033 Probability and Statistics

## Module content

Indicative content includes:

• Review of one and two sample normal-based methods

• revision of R and further use of R

• Covariance and correlation

• The simple linear regression model – least squares estimation, prediction

• Multiple regression and selection of variables

• Completely randomised and randomised block experiments – one-way and two-way analyses with interaction

• Contrasts

• General regression approach to analysis, residual analysis and diagnostics

## Assessment pattern

Assessment type Unit of assessment Weighting
Coursework Coursework 20
Examination Exam (2 hours) 80

N/A

## Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate:

·         Understanding of and ability to interpret and manipulate mathematical statements.

·         Subject knowledge through the recall of key definitions, theorems and their proofs.

·         Analytical ability through the solution of unseen problems in the coursework, test and exam.

Thus, the summative assessment for this module consists of:

·         One two hour examination at the end of the Semester; worth 80% module mark.

·         One Coursework, worth 20% module mark.

Formative assessment and feedback

Students receive written feedback via marked coursework assignment over an 11 week period. In addition, verbal feedback is provided by lecturer at practicals.

## Module aims

• Introduce basic concepts of statistical modelling
• study model fitting and selection for simple linear regression, polynomial regression and multiple regression models
• consider and analyse simple experimental design models
• use linear models in prediction and problems that may arise
• use of R to apply theory to practical data analysis, using data from various areas of business and economics, science and industry

## Learning outcomes

 Attributes Developed 001 Express regression models as linear equations or in matrix form KC 002 Calculate estimates of the parameters of simple linear regression (SLR) models by least squares . KC 003 Calculate confidence intervals and carry out tests for parameters of SLR models . KC 004 Calculate confidence and predictive intervals for predictions KC 005 Explain methods for selecting variables in multiple regression models KCPT 006 Explain the meaning of outliers and influential observations and apply methods to identify them. KCPT 007 Carry out the analysis of a completely randomised design (calculate the Analysis of Variance Table, table of means, standard errors of means and standard errors of differences) KCPT 008 Perform tests for fixed effects, use contrasts for equi-replicate designs and methods for unplanned comparisons KC 009 Analyse a randomised block design (calculate the Analysis of Variance Table, test for fixed effects and least squares estimates) KCPT 010 Analyse data, using these methods and write up the results in a report KCPT 011 Interpret computer output of the above methods. KCPT

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

## Methods of Teaching / Learning

The learning and teaching strategy is designed to provide:

A detailed introduction to the theory behind linear models using least squares estimation

Experience (through data analysis and R practicals) of the methods used to interpret, understand and solve problems in analysis

The learning and teaching methods include:

• lectures with additional notes on white board to supplement the module handbook and Q + A opportunities for students

• practical sessions using R to analyse data using the techniques learnt with lecturer/tutor walking around to support learning.

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.