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School of Mathematics

# MATH68341 - 2012/2013

General Information
• Title: Linear and Generalised Linear Models
• Unit code: MATH68341
• Credits: 15
• Prerequisites: None
• Co-requisite units: None
• School responsible: Mathematics
• Members of staff responsible: Dr C. Charalambous
Page Contents
Other Resources
• Online course materials

## Specification

### Aims

This course unit aims to familiarise students with the methodology and practical applications
of regression analysis, analysis of variance and analysis of covariance within the class of
linear and generalized linear models.

### Brief Description of the unit

As an important modelling strategy, regression analysis is concerned with investigating whether, and how, one or more so-called explanatory variables, such as age, sex, blood pressure, etc., influence a response variable, such as a patient's diagnosis, by taking random variations of data into account. In Linear Models, the Normality assumption of the response and the linear relationship imposed between the response and the explanatory variables could sometimes be inappropriate to model certain data. An extension of Linear Models to Generalized Linear Models can help overcome this issue, by extending linearity to non-linearity and normality to a commonly encountered distribution family, called the exponential family of distributions. The course starts with an introduction to the concepts of Linear Models, Generalized Linear Models and the exponential family of distributions. It then continues on to study model fitting, assessing (model diagnostics, variable selection) and inference (hypothesis testing, confidence intervals) in the Linear Model setting. An extension of the aforementioned processes to Generalized Linear Models is also considered.

### Learning Outcomes

Students should be able to:

• understand the methods for fitting linear and generalized linear model to data and the
relevant statistical assumptions
• have the ability to interpret a statistical model
• fit data to a given linear or generalized linear model and comment on the adequacy of the fit
• produce confidence intervals for linear combinations of the model parameters
• formulate hypotheses in terms of the model parameters and construct test procedures for
testing such hypotheses
• interpret the results of such analyses
• use the model to predict outcomes of new but related data sets
• perform statistical calculations using SPlus/R
• communicate and discuss the results of the statistical analysis of data

None

### Syllabus

1. Linear Model and its specification, least squares estimators and maximum likelihood
estimators and their statistical properties, residuals and residual sum of squares, their
statistical properties and their use in assessing the goodness of fit of the model. Model
comparison and model building. Multicollinearity.
2. Confidence intervals and t-tests involving a parametric function, prediction. The general
linear hypothesis and its test using the likelihood ratio test, Ftests. Linear regression problems using dummy variables.
3. Generalized linear model, the exponential family of distributions, linear predictor, link
function, canonical link, mean-variance relationship, maximum likelihood estimation,
iteratively weighted least square (IWLS) estimation, asymptotic properties of the model
estimators, Fisher information matrix, Wald statistic and its use in hypothesis testing and
confidence interval construction, deviance function, general linear hypothesis and its test
based on analysis of deviance.
4. Applications to Binary, Binomial, Multinomial data and Poisson data arising in medicine
and public health.

### Teaching and learning methods

Three lectures and one exercise class a week

### Assessment

End of semester examination: two and a half hours, 80%
Coursework 20%

## Arrangements

Online course materials are available for this unit.