Department of Probability and Statistics

MAS465 Multivariate Data Analysis

Material relating to MAS465 Multivariate Data Analysis is available from this course web page. This course was previously designtated MAS465 and PAS 6011. Material for the parallel course MAS6011 is available via the University's Blackboard (MOLE) system. Lecture notes etc are in .pdf form and may be read and printed with Adobe Acrobat. The data sets are in R, Minitab, SPSS, SAS or S-plus form as indicated. It is recommended that you use Microsoft Internet Explorer (and not Netscape) to access these, clicking on them gives the option of downloading or running from the web sources. Downloading is recommended and is necessary for R data sets.

Some of the material in the courses Statistical Modelling in R and Further Multivariate Analysis may also be of interest to those wanting to go further on topics such as Multidimensional Scaling, Cluster Analysis and Neural Networks although much of this material is contained in the appendices to this course.

There is a guide to basic matrix algebra available here. As well as describing the basics of matrix algebra, including numerical calculations ‘by hand’, for example of matrix multiplication and inversion, the notes give guidance on how to do numerical calculations in R and S-plus.

The computer package for the course is R. A brief introduction to R is given here. More information is given on the CRAN home page. Detailed information on using R for matrix calculations is given in the notes Basics of Matrix Algebra.

Corrections and Clarifications
[updated 15/11/2011]

Lecture notes:

Study Guide for Multivariate Data Anlysis

Syllabus for MAS465 (Multivariate Data Analysis)
Syllabus for MAS6011 (Dependent Data: Multivariate Data Analysis and Time Series)

Complete lecture notes, one page to the sheet version (5.8MB)

Click here for links to lecture podcasts, vodcasts and rich media recordings of lectures.

The lecture notes are given in a complete Acrobat .pdf file with a hyperlinked table of contents immediately following the title page.
To print just one of the chapters note that the printed pages numbers in the contents list and in the notes do not correspond with those of the .pdf file. Instead, use the contents list to move to the start of the chapter and note the page number given at the bottom of the Acrobat window. This will allow you to issue a print instruction for the appropriate number of pages starting at that point.

Lecture Slides for Multivariate Data Anlysis: Chapters 0 & 1(printing version)
Lecture Slides for Multivariate Data Anlysis: Chapter 2
Lecture Slides for Multivariate Data Anlysis: Chapter 3
Lecture Slides for Multivariate Data Anlysis: Chapter 4
Lecture Slides for Multivariate Data Anlysis: Chapters 5 to 7
Lecture Slides for Multivariate Data Anlysis: Chapter 8
Lecture Slides for Multivariate Data Anlysis: Chapter 9

Additional Informal Lecture notes:

Eigen analysis of special matrices

Numerical example of projections (.pdf)

Numerical example of projections (PowerPoint)

Biscuit Face

29/10/07 & 1/11/07: Outlier displaying components

Article on Outlier displaying components

Further example of interpretation of loadings (facial identification) (.pdf)

Weekly Tasks and Exercises:

Tasks for Week 1
Tasks for Week 2
Tasks for Week 3
Tasks for Week 4
Tasks for Week 5
Tasks for Week 6
Tasks for Week 8
Tasks for Week 9
Tasks for Week 10
Tasks for Week 11

Exercise Sheet 1
Exercise Sheet 2
Exercise Sheet 3

Solutions to task sheets:

Task sheets are intended for self-assessment of understanding of course material.
Outline solutions will only be provided three to four weeks after the
relevent material has been covered in lectures (see Study Guide).
This is to allow plenty of time to go back to check the relevant sections
of the lecture notes & slides if you cannot see immediately how to do the tasks.

Weekly Tasks: Solutions to Weeks 1-3

Weekly Tasks: Solutions to Weeks 4 & 5

Weekly Tasks: Solutions to Weeks 6-9

Weekly Tasks: Solutions to Weeks 10 & 11

Solutions to Exercises:

Solutions to exercises will be provided shortly after the submission date.

Solutions to Exercise Sheet 1       Feedback on Exercise Sheet 1
Solutions to Exercise Sheet 2       Feedback on Exercise Sheet 2
Solutions to Exercise Sheet 3       Feedback on Exercise Sheet 3

Guide to Course Work Grading

R Script Files for Task Sheets and Exercises etc:

Scree Plot		Scaling Scree Plot
Improved Identify Function

[Partially seen] Quiz on interpretation of PCA coefficients

Preliminary background information
PowerPoint slides with questions (slides) Printing version of slides
For recording click here

Past Exam Papers

Copies of previous exam papers are available here.

Rubric and Allowed material in open book examinations

The rubric on the examination papers is
RESTRICTED OPEN BOOK EXAMINATION.
Candidates may bring to the examination lecture notes and associated lecture material (but no textbooks) plus a calculator that conforms to University regulations. All answers will be marked but credit will be given for only the best THREE answers.
All questions carry equal marks. Total marks 75.
Definition of "lecture notes and associated lecture material": This consists of anything that you have downloaded and printed from this course page, including example sheets and solutions, examination papers and solutions to the past two years' of examination papers (i.e. for 2009/10 and 2010/11 andONLY) together with any personal notes you have made and any annotations you have personally made on material printed from this course page and any material distributed in the MAS465 lectures. It does not include any material printed from other module pages nor any examination papers and solutions for years other than the previous two years nor any text books (even if listed as recommended texts within the course material).

Solutions to past exam papers:

Solutions to PAS470, 2009/10, are available here
Solutions to MAS465, 2010/11, are available here

Brian Everitt's Data Sets and Functions:

Click here to access Brian Everitt's webpage containing functions and data sets
from his book An R and S-Plus Companion to Multivariate Analysis.
Note: it is best to download all of the files in one zipped file
using the link highlighted in blue towards the top of the page.