# GENERAL LINEAR MODELS - 2019/0

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

Module Leader

GODOLPHIN Janet (Maths)

Number of Credits: 15

ECTS Credits: 7.5

Framework: FHEQ Level 5

JACs code: G100

Module cap (Maximum number of students): N/A

Module Availability

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 |
---|---|---|

Examination | EXAMINATION | 80 |

Coursework | 1 COURSEWORK | 20 |

Alternative Assessment

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

Overall student workload

Independent Study Hours: 117

Lecture Hours: 23

Seminar Hours: 10

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:

- 3 x 1 hour lecture the first week and then 2 x 1 hour lectures per week x 10 weeks, with additional notes on white board to supplement the module handbook and Q + A opportunities for students
- 1 x 1 hour practical session using R per week x 10 weeks 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.

Programmes this module appears in

Programme | Semester | Classification | Qualifying conditions |
---|---|---|---|

Mathematics and Computer Science BSc (Hons) | 1 | Optional | A weighted aggregate mark of 40% is required to pass the module |

Mathematics with Statistics BSc (Hons) | 1 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Mathematics BSc (Hons) | 1 | Optional | A weighted aggregate mark of 40% is required to pass the module |

Mathematics MMath | 1 | Optional | A weighted aggregate mark of 40% is required to pass the module |

Mathematics with Music BSc (Hons) | 1 | Optional | A weighted aggregate mark of 40% is required to pass the module |

Financial Mathematics BSc (Hons) | 1 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2019/0 academic year.