# MAS2902 : Introduction to Regression and Stochastic Modelling

• Offered for Year: 2024/25
• Module Leader(s): Dr Daniel Henderson
• 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 2 Credit Value: 10 ECTS Credits: 5.0 European Credit Transfer System

#### Aims

This module will provide an introduction to ways of mathematically describing processes that exhibit variability. Students will learn about the use of linear models to build statistical descriptions of data and about the use of simple probability distributions to provide useful models for many applications. Students will be able to use regression analysis in some simple cases; they will be able to apply Poisson Processes to model relevant random processes

Module summary

The module will introduce students to two distinct areas of stochastic modelling. One part will broaden the students' knowledge of statistical inference gained in MAS2901 by introducing the linear model. This will start with a simple regression for a scalar covariate, moving to an introductory treatment of a matrix-based approach for a model with more covariates. The other part will be to use the Poisson process as an example of a model for a process of events occurring randomly in time. The main properties of the homogenous Poisson process will be derived, and necessary tools, such as probability and moment generating functions, will be studied.

#### Outline Of Syllabus

Simple linear regression, i.e. E(Y) = β0 + β1 x for scalar x with Normal errors with unknown variance. Equivalence of least squares and maximum likelihood. Properties of estimator of β = (β0 β1). Introduction of the general linear model using matrix formulation; demonstration of formula for the estimator of β; use of formula for the variance of the estimator of β but no proof. Examples using regression with two or three continuous covariates.

Introduction to PGFs and MGFs. Formal definition of the homogenous Poisson Process. Distribution of number of events in an interval. Distribution of inter-arrival times and time to nth event. Reinforcement of results using simulation.

#### Teaching Methods

##### Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture51:005:00Problems 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
Scheduled Learning And Teaching ActivitiesDrop-in/surgery51:005:00drop-in sessions
Guided Independent StudyIndependent study531:0053:00Preparation time for lectures, background reading, coursework review, revision for exam
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 Examination1202A80N/A
##### Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises2M5Problem-solving exercises assessment
Prob solv exercises2M5Problem-solving exercises assessment
Prob solv exercises2M5Problem-solving exercises assessment
Prob solv exercises2M5Problem-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 the programme accreditation.

Exam 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 coursework assignments 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.