# LINEAR STATISTICAL MODELS - 2024/5

Module code: MAT2053

## Module Overview

Statistical modelling provides a means of extracting information from data, enabling informed decisions to be made. It is a versatile and powerful tool with widespread applications contributing to advancements in research, business, technology, and society. Students will be introduced to the basic concepts of statistical modelling via linear regression models, which are fundamental in statistics and serve as the basis for more complex modelling techniques. Model fitting, selection and evaluation are covered for: Simple Linear Regression; polynomial regression and multiple regression models. The module concludes with the introduction of simple models in the Design of Experiments, covering the use of  such experiments and the analysis of data arising from them. The statistical software R is fully integrated with the module. Students will reinforce their understanding of concepts of statistical modelling and develop their digital capabilities by using R to conduct analyses of real data sets from business, science and industry.

### Module provider

Mathematics & Physics

GODOLPHIN Janet (Maths & Phys)

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

Independent Learning Hours: 53

Lecture Hours: 33

Laboratory Hours: 8

Guided Learning: 23

Captured Content: 33

Semester 2

None.

## Module content

Indicative content includes:

• 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, model selection and evaluation

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

• Orthogonal contrasts

• General regression approach to analysis, residual analysis and diagnostics.

## Assessment pattern

Assessment type Unit of assessment Weighting
Coursework Assessed Coursework 20
Examination End-of-Semester Examination (2 hours) 80

NA

## Assessment Strategy

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

• Understanding and knowledge of the theory underlying linear regression models.

• The ability to apply this knowledge to unseen models and to previously unseen data sets in the coursework and the examination.

Thus, the summative assessment for this module consists of:

• One coursework involving analysis of a set of data using R, with the results written up in the form of a report. This assessment is worth 20% of the module mark and corresponds to Learning Outcomes 3 and 5,

• A synoptic examination (2 hours), worth 80% of the module mark, corresponding to Learning Outcomes 1, 2, 3 and 4.

Formative assessment

There are two formative unassessed courseworks over an 11 week period, designed to consolidate student learning.

Feedback

Individual written feedback is provided to students for both formative unassessed courseworks and assessed coursework. Any issues with the unassessed courseworks are discussed in lectures. Likewise, verbal feedback on the exercise sheets is given in lectures. Students receive verbal feedback during computer lab sessions: this is particularly useful in providing guidance for the assessed coursework which is submitted after the final computer lab session.

## Module aims

• Introduce students to the basic concepts of statistical modelling.
• Give students an understanding of the method of least squares for parameter estimation and familiarity with the derivation and properties of the estimators for Simple Linear Regression.
• Extend the concepts covered in Simple Linear Regression to polynomial models and multiple linear regression models.
• Facilitate understanding of methods of model selection and diagnostic techniques.
• Provide students with experience in using fitted models to make predictions.
• Develop resourcefulness and resilience amongst students in data analysis through skills in use of R.
• Equip students with practical model fitting and evaluation skills and skills to report on their findings that will enhance their employability.

## Learning outcomes

 Attributes Developed 001 Students will demonstrate the ability to calculate estimators and confidence intervals for Simple Linear Regression and calculate confidence and predictive intervals. KCP 002 Students will be able to represent models in matrix and non-matrix form. They will demonstrate resourcefulness and resilience by application of the method of least squares to obtain estimators and predictors for models not previously seen. KC 003 Students will develop understanding and practical skills of the key tasks associated with fitting and selecting models for a given data set, and in the role and use of diagnostic procedures. KCPT 004 Students will be able to analyse data arising from completely randomised designs and from complete block designs both by hand and using R, and will be able to conduct tests for fixed effects and contrasts for equi-replicate designs. KCPT 005 In completing the assessed coursework, students will demonstrate problem-solving resourcefulness and digital capabilities by using R to analyse a set of data arising from a linear model. They will demonstrate their ability to interpret the R output and present their findings in a comprehensive report. 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 and to equip students with the knowledge and digital skills to interpret, understand and solve problems in data analysis.

The learning and teaching methods include:

• Three one-hour lectures per week for eleven weeks, with typeset notes to complement the lectures. The lectures provide a structured learning environment with opportunities for students to ask questions and to practice methods taught.

• Eight one-hour computer lab sessions in which students gain practical experience of analysing data sets using R.

• Students are provided with weekly exercise sheets aimed at reinforcing their learning. These sheets allow students to tackle questions at their own pace outside of scheduled teaching sessions. Dedicated lecture time is assigned to help students tackle any challenges they might face. Model solutions are provided one week after the initial distribution.

• There are two unassessed courseworks to provide students with further opportunity to consolidate learning. Students receive individual written feedback on these as guidance on their progress and understanding.

Lectures may be recorded. Lecture recordings are intended to give students the opportunity to review parts of the session that they might not have understood fully and should not be seen as an alternative to attendance at lectures.

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.

Upon accessing the reading list, please search for the module using the module code: MAT2053

## Other information

The School of Mathematics and Physics is committed to developing graduates with strengths in Digital Capabilities, Employability, Global and Cultural Capabilities, Resourcefulness and Resilience and Sustainability. This module is designed to allow students to develop knowledge, skills, and capabilities in the following areas:

Digital Capabilities: The computer lab sessions and assessed coursework are specifically designed to help students cultivate digital data manipulation and modelling skills using the statistical software R.

Employability: Students gain practical skills in the analysis of data; model fitting and report writing. These skills have broad applications across almost every industry. The ability to make data-driven decisions, build predictive models, and to communicate findings effectively is becoming increasingly valuable in the workplace.

Global and Cultural Capabilities: Data sets used in the module arise from a range of countries, cultures and environments. Investigating such data sets and fitting appropriate models aids students in the development of their cultural awareness.

Resourcefulness and Resilience: The lectures and computer laboratory sessions form the foundations of a learning journey in which students develop the skills of model fitting, model evaluation and report writing. In particular, the computer laboratory sessions are designed to foster active participation and reflective engagement with less scaffolding provided as the module advances, enabling students to develop confidence in handling data sets independently. The investigative style of the assessed coursework gives students scope to demonstrate thinking and decision-making processes developed during the module.

Sustainability: Students use simulated data relating to sustainability issues. For example, the focus of a data set might be on the purification of water or the extraction of metal from ores. In such cases, the aim is to develop models which best describe the water quality or metal yield, enabling water quality to be optimized or metal yield to be maximised, and their performance is evaluated.

## Programmes this module appears in

Programme Semester Classification Qualifying conditions
Mathematics with Statistics BSc (Hons) 2 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics with Statistics MMath 2 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics with Music BSc (Hons) 2 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics BSc (Hons) 2 Optional A weighted aggregate mark of 40% is required to pass the module
Financial Mathematics BSc (Hons) 2 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics MMath 2 Optional A weighted aggregate mark of 40% is required to pass the module
Economics and Mathematics BSc (Hons) 2 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 2024/5 academic year.