Athena SWAN Bronze Award

Supporter of LMS Good Practice Award

Statistical Theory III

Course category: 
2nd year
Module code: 
Professor Jian Zhang


To continue the development of statistical concepts and techniques learnt in Statistical Theory I and Statistical Theory II and to provide students the necessary background for advanced third year statistics modules.

Learning objectives

At the end of the module you should be able to:

  • have an understanding of multiple regression and polynomial regression models as examples of linear models. Understand the least squares principle for model estimation.
  • know how to apply the multiple linear regression technique to real data by using the software R.
  • understand the main properties of least squares estimators for a general linear model.
  • understand the concepts of model check and variable selection. Be able to perform stepwise variable selection based on the software R.
  • have some idea about ridge regression.


  • Introduction and preliminaries
  • Linear models and least squares estimators
  • Tests and confidence sets
  • Collinearity, variable selection
  • Coefficient shrinkage and ridge regression
  • Residual analysis and model check
  • Influence observations
  • Dummy variables

Recommended texts

  • ***Weisberg, S. Applied Linear Regression (3rd Edition), Wiley (SF 2.5 WEI).
  • ***N R Draper and H Smith, Applied regression analysis (3rd edn), Wiley (SF 2.5 DRA).
  • *** G A F Seber and A J Lee, Linear regression analysis  (2nd edn), Wiley (SF 2.5 SEB)
  • ***J Fox, Applied regression analysis, linear models, and related methods, Sage Publications (SF 2 FOX).
  • **A C Atkinson, Plots, transformations, and regression : an introduction to graphical methods of diagnostic regression analysis, Oxford (SF 2.5 ATK).
  • *W J Krzanowski, An introduction to statistical modelling, London ; New York : Arnold (SF 1 WOJ).
  • *D C Montgomery, E A Peck, Introduction to linear regression analysis (2nd edn), Wiley (SF 2.5 MON). 


  • Summer Term
  • 3 lectures per week
  • Weekly seminar


One and a half hour closed examination in weeks 8 or 9 of Summer Term (90%)

Coursework (10%)

Note that coursework submitted after the advertised deadlines will be given a mark of zero.

Elective information

Add elective information here.

Please check prerequisites carefully before asking to take this module as an elective.



Edited 9 Sep 2010 - 13:54 by admin

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