ST23110 Linear Statistical Modelling with R
Introductory description
This module builds from ideas introduced in Year 1 Statistical
Modelling and embeds them into the framework of linear models. Linear regression
models are widely used in statistical practice and aim to explain or predict a
continuous response variable using a collection of explanatory variables. Students will
learn the theoretical background of such models, how to fit linear models to a given
data set using R and how to interpret and evaluate the results.
Prerequisistes:
 First Year Statistics Core (including ST117 Introduction to Statistical Modelling, ST118 Probability 1, and ST119 Probability 2) or equivalents.
AND
 Statistics students. Both ST229 Probability for Mathematical Statistics and ST230 Mathematical Statistics; or
 External students: ST232/ST233 Introduction to Mathematical Statistics.
Leads to
 ST340 Programming for Data Science
 ST344 Professional Practice of Data Analysis
 ST346 Generalised Linear Models for Regression and Classification.
Other thirdyear statistics modules.
Module aims
 Introduce the application of statistical modelling and statistical model exploration.
 Use of R software and its use as a tool for statistical modelling, specifically for working with linear models in a variety of different scenarios.
Outline syllabus
This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.
This module introduces the theory of normal linear models and their practical application in R.
 Normal linear models: definition and model assumptions.
 Estimators for normal linear models and their sampling distributions.
 Diagnostics and model building.
 Confidence intervals and ttests for normal linear models.
 Ftests and analysis of variance; model selection and diagnostics.
 Variable selection.
Learning outcomes
By the end of the module, students should be able to:
 Define a (normal) linear model and describe its modelling assumptions;
 Derive the properties of estimators for normal linear models; compute confidence intervals and perform hypothesis tests for normal linear models;
 Fit, diagnostically check, improve and compare regression models in R;
 Interpret and critically evaluate various linear models;
 Communicate solutions to problems accurately with structured and coherent arguments.
Indicative reading list
Sheather, S (2009) A modern approach to regression with R. Springer Science and Business Media.
View reading list on Talis Aspire
Research element
Students complete guided exploration of data sets as part of the coursework which provides a foundation for applied statistics research in later years.
Interdisciplinary
While not explicitly interdisciplinary, students are exposed to dataset from a variety of application contexts.
Subject specific skills
Demonstrate facility with advanced mathematical and probabilistic methods.
Demonstrate knowledge of key mathematical and statistical concepts, both explicitly and by applying them to the solution of mathematical problems.
Select and apply appropriate mathematical and/or statistical techniques
Create structured and coherent arguments communicating them in written form.
Select and apply appropriate computational techniques in a statistical programming language (for example, R) to build and evaluate linear models.
Transferable skills
Problem solving skills: The module requires students to solve problems presenting their conclusions as logical and coherent arguments.
Written communication skills: Students complete written assessments that require precise and unambiguous communication in the manner and style expected in mathematical sciences.
Verbal communication skills: Students are encouraged to discuss and debate formative assessment and lecture material within smallgroup tutorials sessions.
Students can continually discuss specific aspects of the module with the module leader. This is facilitated by statistics staff office hours.
Team working and working effectively with others: Students are encouraged to discuss and debate formative assessment and lecture material within smallgroup tutorials sessions.
Professionalism: Students work autonomously by developing and sustain effective approaches to learning, including timemanagement, organisation, flexibility, creativity, collaboratively and intellectual integrity.
Study time
Type  Required  Optional 

Lectures  20 sessions of 1 hour (20%)  2 sessions of 1 hour 
Practical classes  10 sessions of 1 hour (10%)  
Private study  45 hours (45%)  
Assessment  25 hours (25%)  
Total  100 hours 
Private study description
Weekly revision of lecture notes and materials, wider reading and practice exercises, working on problem sets and preparing for examination.
Costs
No further costs have been identified for this module.
You do not need to pass all assessment components to pass the module.
Assessment group D1
Weighting  Study time  

Lab. Report  20%  18 hours 
You will use the statistical programming language R to carry out calculations and fit models on provided data sets in response to a set of questions. You will present, discuss, and evaluate the results. The length of the report will not exceed 18 pages, including figures, tables, code and R output, The preparation and completion time noted below refers to the amount of time in hours that a wellprepared student who has attended lectures and carried out an appropriate amount of independent study on the material could expect to spend on this assignment. 

Set of short lab reports.  10%  5 hours 
There will be approximately weekly problem sets. Each set will contain a number of individual questions based on the material delivered in the lectures. Problem sheets are supported by practical classes, including analytical, computational tasks and computerbased work. Assessment is based on solutions to the problems and engagement with inclass practical classes. The preparation and completion time noted below refers to the amount of time in hours that a wellprepared student who has attended lectures and carried out an appropriate amount of independent study on the material could expect to spend on this assessment. 

Linear Statistical Modelling with R examination  70%  2 hours 
You will be required to answer all questions on this examination paper.

Assessment group R1
Weighting  Study time  

Inperson Examination  Resit  100%  
You will be required to answer all questions on this examination paper.

Feedback on assessment
Individual feedback will be provided on problem sheets by class tutors.
Solutions and cohort level feedback will be provided for the examination
Students are actively encouraged to make use of office hours to build up their understanding, and to view all their interactions with lecturers and class tutors as feedback.
Courses
This module is Core for:

USTAG302 Undergraduate Data Science
 Year 2 of G302 Data Science
 Year 2 of G302 Data Science

USTAGG14 Undergraduate Mathematics and Statistics (BSc)
 Year 2 of GG14 Mathematics and Statistics
 Year 2 of GG14 Mathematics and Statistics

USTAY602 Undergraduate Mathematics,Operational Research,Statistics and Economics
 Year 2 of Y602 Mathematics,Operational Research,Stats,Economics
 Year 2 of Y602 Mathematics,Operational Research,Stats,Economics
This module is Option list B for:

UCSAG4G1 Undergraduate Discrete Mathematics
 Year 2 of G4G1 Discrete Mathematics
 Year 2 of G4G1 Discrete Mathematics
 Year 2 of UCSAG4G3 Undergraduate Discrete Mathematics