MAS273 Statistical Modelling

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:

MAS360Practical and Applied Statistics
MAS361Medical Statistics
MAS363Linear Models
MAS370Sampling Theory and Design of Experiments
MAS372Time Series
MAS461Medical Statistics
MAS463Linear 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%].

Reading list

Type Author(s) Title Library Blackwells Amazon
B D.G. Kleinbaum, L.L. Kupper, K.E. Muller and A. Nizam Applied Regression Analysis and Other Multivariable Methods 519.536 (A) Blackwells Amazon
B Julian J. Faraway Linear models with R 519.538 (F) Blackwells Amazon
B N. Draper and H. Smith Applied Regression Analysis 519.536 (D) Blackwells Amazon

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

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

Timetable

Tue 09:00 - 09:50 lecture   Arts Tower Lecture Theatre 3
Wed 09:00 - 09:50 lecture   Hicks Lecture Theatre 7
Wed 10:00 - 10:50 tutorial (group 61) (even weeks) Hicks Seminar Room F20
Wed 10:00 - 10:50 lab session (group 61) (even weeks) Hicks Room G25
Wed 10:00 - 10:50 lab session (group 62) (even weeks) Arts Tower Computer Room 1012
Wed 10:00 - 10:50 tutorial (group 62) (even weeks) Hicks Seminar Room F24
Thu 10:00 - 10:50 tutorial (group 63) (even weeks) Hicks Seminar Room F28
Thu 10:00 - 10:50 lab session (group 63) (even weeks) Hicks Room G25