## MAS293 Statistical Modelling (NJTech)

 Semester 1, 2016/17 10 Credits Lecturer: Dr Keith Harris Reading List Aims Outcomes Assessment Full Syllabus

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.

There are no prerequisites for this module.
No other modules have this module as a prerequisite.

## 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.

32 lectures, 22 tutorials, 10 practicals

## Assessment

One formal 2 hour written examination. All questions compulsory.

## Full 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.

## Reading list

Type Author(s) Title Library Blackwells Amazon
B Draper and Smith Applied Regression Analysis Blackwells Amazon
B Faraway Linear models with R Blackwells Amazon
B Kleinbaum, Kupper, Muller and Nizam Applied Regression Analysis and Other Multivariable Methods Blackwells Amazon

(A = essential, B = recommended, C = background.)

Most books on reading lists should also be available from the Blackwells shop on Mappin Street.