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# Statistical Theory III

Course category:
2nd year
Module code:
0590038
Year:
2009/10
Term:
Summer
Credits:
10
Lecturer:
Professor Jian Zhang

## Aims

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.

## Syllabus

• 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).

## Teaching

• Summer Term
• 3 lectures per week
• Weekly seminar

## Assessment

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.