## MAS273 Statistical Modelling

Note: This is an old module occurrence.

You may wish to visit the module list for information on current teaching.

 Semester 2, 2014/15 10 Credits Lecturer: Dr Mathew Joseph uses MOLE Timetable Reading List Aims Outcomes Assessment

This unit develops the idea of constructing simple statistical models to describe processes in the real world, for example patient responses to different treatments, or the effects of class sizes on examination results. In the presence of uncertainty, modelling can be used to infer relationships between different variables in the process and make predictions about future observations. A single class of models known as linear models will be considered, and it will be shown how these models are applicable in a wide variety of circumstances. Modelling and data analysis will be performed on practical examples using the software package R.

Prerequisites: MAS201 (Linear Mathematics for Applications); MAS202 (Advanced Calculus); MAS205 (Statistics Core)

The following modules have this module as a prerequisite:

 MAS360 Practical and Applied Statistics MAS361 Medical Statistics MAS363 Linear Models MAS370 Sampling Theory and Design of Experiments MAS372 Time Series MAS461 Medical Statistics MAS463 Linear Models

## Outline syllabus

• The general linear model: Matrix representation of a linear model. Linear regression, polynomial regression and ANOVA models as examples of linear models.
• Least squares: Parameter estimation using least squares; least squares estimators in matrix notation.
• Straight line regression: Fitting linear models in R and interpreting the output. Illustrate the use of distributional relationships between Normal, χ2 and f distributions. Distributional properties of least squares estimators and the residual sum of squares. Hypothesis testing via model comparisons; the f-test for comparing nested linear models and relationship with ANOVA tables. Confidence intervals and prediction intervals. Model checking using standardized residuals; transformations; R2. Introduction to polynomial and multiple regression.
• One-way Analysis of Variance: Indicator variables. Fitting into general theory.
• Introduction to two-way Analysis of Variance: Balanced two-way data (blocks and treatments or 2-factors) with replicates and interactions.

## Aims

• To consider linear regression models in detail.
• To extend the comparison of means from two to several groups through ANOVA models.
• To give students experience in the use of R for fitting linear models.

## Learning outcomes

• have an understanding of regression and ANOVA models as examples of linear models;
• be able to estimate parameters in a linear model;
• be able to make inferences about model parameters through appropriate model comparisons;
• be able to develop a 'best-fitting' model in a systematic and pragmatic way;
• be able to undertake model checking procedures through the use of residuals;
• be able to use R to implement methods covered in the course;
• have experienced the task of preparing a structured word processed report of the statistical analysis of an open-ended problem.

22 lectures, 3 tutorials, 3 practicals

## Assessment

One formal 2 hour closed book examination [85%]. Practical file [15%].