Introductory description

This module builds from ideas in statistical modelling introduced in Year 1 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.

Pre-requisistes:

• Statistics Students:

  • First Year Statistics Core (including ST117 Introduction to Statistical Modelling, ST118 Probability 1, and ST119 Probability 2) AND
  • ST229 Probability for Mathematical Statistics and ST230 Mathematical Statistics.

• External Students:

  • ST120 Introduction to Probability, ST121 Statistical Laboratory and ST232 Introduction to Mathematical Statistics.

Leads to

• ST340 Fundamentals of Machine Learning
• ST344 Professional Practice of Data Analysis
• ST346 Generalised Linear Models for Regression and Classification.

Other third-year statistics modules.

Module web page

Module aims

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.

1. Normal linear models: definition and model assumptions.
2. Estimators for normal linear models and their sampling distributions.
3. Diagnostics and model building.
4. Confidence intervals and t-tests for normal linear models.
5. F-tests and analysis of variance; model selection and diagnostics.
6. 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

Reading lists can be found in Talis

Specific reading list for the module

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 small-group 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 small-group tutorial sessions.
• Professionalism: Students work autonomously by developing and sustain effective approaches to learning, including time-management, organisation, flexibility, creativity, collaboration and intellectual integrity.