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: MA0152 Statistical Inference I

• 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

54 - 50 minute lectures

Some handouts will be provided in hard copy or via Learning Central, but students will be expected to take notes of lectures.

Students are also expected to undertake at least 100 hours private study including preparation of solutions for selected exercises.

Skills:

Facility with regression techniques, residual analysis and ANOVA analysis.

Facility with the most common types of experimental designs.

Transferable Skills:

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.

Formative assessment is carried out by means of regular tutorial exercises.  Feedback to students on their solutions and their progress towards learning outcomes is provided during examples lectures and material on Learning Central.  

The in-course element of summative assessment consists of assessed exercises (some to be attempted at home, some in examination conditions) similar in form to the tutorial exercises. This allows students to demonstrate a level of knowledge and skills appropriate to that stage in the module.

The major component of summative assessment is the written examination at the end of the module.  This gives students the opportunity to demonstrate their overall achievement of learning outcomes.  It also allows them to give evidence of the higher levels of knowledge and understanding required for above average marks.

The examination paper has a choice of four from six equally weighted questions.

• Regression
  • 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

Please see Background Reading List for an indicative list.

Applied regression analysis, Draper, N.R., & Smith, H., New York: Chichester, Wiley

Modern regression methods, Ryan, T. P., New York: Wiley, 1997.

Applied regression analysis: a research tool, Rawlings, J. O. , California: Wadsworth & Brooks

Applied regression analysis and other multivariable methods (2nd ed), Kleinbaum, D. G., Kupper, L. L., & Muller, K. E., Boston: PWS-Kent Pub. Co., 1988

Optimum experimental designs, Atkinson A.C., & Donev, A.N., Oxford University Press, 1992.

Quality through design: experimental design, off-line quality control and Taguchi's contributions, Logothetis, N., & Wynn, H.P., Oxford: Clarendon, 1989

Design and analysis of experiments, Montgomery, D. C., New York: Wiley

Fundamental concepts in the design of experiments, Hicks, C. R., London: Holt, Rinehart, and Winston

Statistics for experimenters: an introduction to design, data analysis, and model building, Box, G.E.P., Hunter, W.G., &  Hunter, J.S., New York: Wiley, 1978.