Statistical Theory III
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.
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
- ***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%)
Note that coursework submitted after the advertised deadlines will be given a mark of zero.
Add elective information here.
Please check prerequisites carefully before asking to take this module as an elective.
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