Linear Statistical Modelling

Course Coordinator: Dr Tony M T Chan, Grad Dip, MPhil (CUHK); PhD (CityU)

Course Developer: The Open University, UK, Course Team

MATH S346 is one of the compulsory higher-level courses for BSc and BSc (Hons) in Statistics and Decision Science programme, and an optional course for the BSc and BSc (Hons) in Mathematical Studies programmes.

MATH S346 forms an excluded combination with MATH S345.

Advisory prerequisite(s)
You are advised to have already studied MATH S245 / MATH S246 /MATH S248 or to have already acquired a basic knowledge of the ideas of statistical science at the level of MATH S245 / MATH S246 / MATH S248.

A theoretical background in those topics is not necessary, but you are expected to have a conceptual understanding and to be able to apply the ideas and interpret the answers.

Aims
This course aims to:

• Offer a practical treatment of an important area of statistical methodology, linear modelling, applicable in a wide variety of situations;
• Understand the statistical methods about the statistical modelling of situations in which a response variable depends on at least one explanatory variable;
• Analyse problems and solve them appropriately;
• Interpret the results of computer printouts.

Contents
The course covers the following topics:

• Review of statistical concepts — normal distribution; confidence intervals; hypothesis testing; Chi-squared and F distributions; Bernoulli, binomial and Poisson distributions; maximum likelihood estimation;
• Introduction to Genstat — getting started; loading, storing, retrieving and manipulating data; summaries and graphics;
• Linear regression with one explanatory variable — the simple linear regression model; fitting lines and making inferences; confidence intervals and prediction; checking assumptions; transformations; comparing slopes; correlation;
• One-way analysis of variance — regression with a continuous response variable and a categorical explanatory variable; one-way ANOVA: data and model; testing for quality of means; checking the model; differences between treatments;
• Multiple linear regression — using the model; choosing explanatory variables; parallels with the case of one explanatory variable; using indicator variables in comparing regression lines; using indicator variables to analyse variance;
• The analysis of factorial experiments — two-way factorial analysis of variance; more than two factors; using regression; factorial ANOVA without replication;
• Experiments with blocking — blocking; more complicated blocking; factorial experiments with incomplete blocks; designing experiments;
• Binary regression — the logistic function; the logistic regression model; using the logistic regression model; exercise in logistic regression;
• Generalized linear models — Poisson regression; the generalized linear model; inference for GLMs; a short history of GLMs;
• Diagnostic checking — leverage; the Cook statistic; diagnostics for generalized linear models; recommended use of model diagnostics;
• Loglinear models for contingency tables — two-way contingency tables; sampling models; loglinear models in practice; logistic and loglinear models;
• Futher data analyses.

Learning support
There will be ten two-hour tutorials and four two-hour surgeries throughout the course.

Assessment
There will be four assignments (from which the best three scores will be used to determine the final grade) and a final examination. Students are required to submit assignments via the Online Learning Environment (OLE).

Online requirement
This course is supported by the Online Learning Environment (OLE). You can find the latest course information from the OLE. Through the OLE, you can communicate electronically with your tutor and the Course Coordinator as well as other students. To access the OLE, students will need to have access to the Internet. The use of the OLE is required for the study and assessment of the course.

Equipment
The course contains a substantial computing component. You will need access to a computer system capable of running the Genstat software package. A computer system suitable for connecting to the Internet is also required for accessing the OLE.

A calculator with basic statistical functions will also be required.

Software
This course will make use of the software package Genstat.

Limited access to Genstat may be available in the HKMU computer laboratory.

Set book(s)
There are no set books for this course.

Students with disabilities or special educational needs
If you have difficulty with manual operations, the computing component could be a problem.