Mathematics

Linear Statistical Models (L6)

Module code: G1107
Level 6
15 credits in autumn semester
Teaching method: Lecture, Practical
Assessment modes: Unseen examination, Coursework

Linear modelling concerns the situation where a response variable depends on one or several variables. Despite its simplicity, it is extremely useful. Applications include:

• determining factors affecting the length of hospital stay 
• estimating the reproduction number of an epidemic
• identifying elements that influence sales.

In the first part of this module, we will develop the theory of general linear models. We will be concerned with problems of estimating model parameters, finding confidence intervals as well as carrying out various statistical tests.

We will then move on to some specific models: quadratic models, analysis-of-variable models; they all belong to the family of linear models, so it is handy to have the general theory first. 

The module will also help you to develop your modelling skills. While fitting models to various data sets, Questions may include: 

• How is the model fitted?
• Which variables should be included in the model? 
• How well does the model predict? 

The module includes practical classes in the use of the statistical software R, which is used to fit models and produce statistics which help answer important practical questions. No prior knowledge of R is assumed. 

Module learning outcomes

• Understand the theory of the general linear model and derive distributional results relating to estimators.
• Apply the general linear model of full rank to a variety of applications, using transformations and variable selection techniques.
• Understand the benefits of designed experiments, select and carry out statistical analyses and report conclusions clearly.
• Use statistical software to fit regression and analysis of variance models, compute additional statistics and construct diagrams.