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

• 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

Modules will be delivered through blended learning. You will be guided through learning activities appropriate to your module, which may include:

• Weekly face to face classes (e.g. labs, lectures, exercise classes)
• Electronic resources that you work through at your own pace (e.g. videos, exercise sheets, lecture notes, e-books, quizzes)

Students are also expected to undertake self-guided study throughout the duration of the module.

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.

• 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