Outline Description of Module
Regression analysis is arguably the most widely used in practice statistical tool. Fundamentals of regression analysis are thus the must for every student who will be seeking a statistics -related job. In a similar vein, the methods and principles of designing experiments are extremely important and regularly used by practitioners in a variety of disciplines. All the theoretical discussions are accompanied with solving practical problems.
Prerequisite Modules: MA1501 Statistical Inference
On completion of the module a student should be able to
- Demonstrate knowledge of the main properties of LSE, and numerical properties of this estimator
- Construct confidence intervals, and hypothesis tests concerning the parameters of the linear regression model
- Formulate and solve normal equations to generate least square estimators
- Generate and use the properties of various estimators (unbiased and biased) of the parameters of the linear regression model
- Describe the principles of experimental design in a statistical context
- Extend the ideas of analysis of variance to factorial experiments with two or more factors
- Be familiar with the basic construction schemes of experimental designs and their properties
- Compare designs with respect to their efficiency
How the module will be delivered
Modules will be delivered through blended learning. You will be guided through learning activities appropriate to your module, which may include:
- On-line resources that you work through at your own pace (e.g. videos, web resources, e-books, quizzes),
- On-line interactive sessions to work with other students and staff (e.g. discussions, live streaming of presentations, live-coding, group meetings)
- Face to face small group sessions (e.g. tutorials, exercise classes, feedback sessions)
Skills that will be practised and developed
Facility with regression techniques, residual analysis and ANOVA analysis.
Facility with the most common types of experimental designs.
Ability to apply regression analysis in other areas.
Ability to apply the basic ideas and methods of experimental design in engineering, medicine and other applied areas.
- Fitting a straight line
- Normal equations and standard least squares estimators (LSE)
- Solution of the normal equations for orthogonal regression
- Solution of the normal equations for the models of incomplete rank
- LSE as the best linear unbiased estimators (Gauss-Markov theorem)
- LSE as the maximum likelihood estimator
- Weighted LSE
- Construction of confidence intervals for the unknown parameters and regression forecast
- Testing general statistical hypothesis in linear regression models, ANOVA
- Residual analysis; Further topics in regression. Links between experimental design and regression
- Experimental Design
- A general scheme of experiment, application areas
- Full and fractional 2-level factorial designs, defining and generating contrasts, aliasing
- Multilevel fractional factorial designs
- Latin designs, orthogonal Latin squares, magic squares, Youden rectangles, ANOVA for Latin designs
- Balanced incomplete block designs
- Exact and approximate designs in regression, information matrices of a designs and their properties;
- Comparison of designs, optimality criteria
- Optimality theorems for regression designs (without proofs), examples
- Response surface methodology
- Search designs, entropies of partitions of the set of hypotheses, applications to blood testing and finding false coins problems
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