Business 41912: Applied Multivariate Analysis

Spring Quarter of 2014

Instructor: Ruey S. Tsay

Office: HPC 455
Tel:      773-702-6750
Fax:     773-702-0458

Office hour: (a) Friday: 1:30 pm to 2:30 pm.
                    (b) By appointment
You may e-mail me questions. E-mail is the easiest way
to make contact with me.

Teaching Assistant: Mr. Yongning Wang, e-mail:

Text: Applied Multivariate Statistical Analysis
         by R.A. Johnson and D.W. Wichern
         6th ed. Prentice Hall, 2007.
         ISBN 0-13-187715-1

Grading: Midterm 30% + Final Exam 45% + Homework 25%
where total credits of each component are normalized to be 100.

New focus of the course: Recent developments in high-dimensional data analysis,
including dimension reduction, Lasso and related sparse regressions, and
independent component analsyis.

Syllabus: of the course.


R is the main package, but students can use any other programs.
Instructions for R will be given. The following R packages are useful for the
course: mvtnorm, fastICA, CCA, lars, gamlr, leaps, rgl (3D plot), mvoutlier

Lecture: (Will be posted weekly before the lectures)
Week1: Review Chapters 1 to 3, and the first half of Chapter 4:
lec1  Data set: T1-2.DAT, Baker.dat, lec2 & Data set: m-ba4c9807.txt, T5-1.DAT, T4-1.DAT
Week2: Random sample from a multivariate normal distribution & Inference about mean
Lec2 (continued) Data set:

             Matlab program to obtain Chi-square QQ-plot: qqchi2.m
             Matlab program to compute Hotelling T^2: hotelling.m
             Matlab program for transformation: boxcox.m
            Matlab program to compute various confidence intervals for means of
              components: cfinterval.m
            Matlab programs to handle missing values in a Gaussian random sample:
              (a) EM-algorithm: emmiss.m    (b) MCMC method: mcmcmiss.m   

R package: mvoutlier has some new tools for detecting multivariate outliers
             R program to compute Chi-square QQ-plot: qqchi2.R
             R program to compute beta-disribution QQ-plot: qqbeta.R
             R program to compute statistics for outlier detection: outlier.R  
             R program to compute Hotelling T^2: Hotelling.R 
             R program to compute various confidence intervals for means:
             Use data: confreg.R,   Use summary statistics: confrega.R  
R programs for two multivariate control charts: t2chart.R & t2future.R

Week 3: Multivariate Analysis of Variance (MANOVA)
Lec3 Data sets used:T6-1.DAT, T6-2.DAT, t6-9.dat, t6-14.dat, t6-5.dat, t6-6.dat
R programs: contrast.R, Behrens.R , Box_M.R , profile.R, growth.R
R demo: r-manova
Week 4: Multivariate Analysis of Variance (MANOVA) & Linear Regression
Lec4 Data sets used: T7-5.DAT

Week 5: Multivariate Linear Regression & Principal Component Analysis
 Lec5: Data set used: T7-4.dat
R example for regression models with time series errors: mlreg-ts 
R program for multivariate multiple linear regression analysis: mmlr.R
       R commands: princomp
       R demonstration: r-pca   data: m-pca5c-9003.txt 

Week 7: Dimension Reduction: sliced inverse regression, independent components,
and factor models.
Lec7: R script: sir.R Data set used: T8-4.DAT R demonstration: r-factor

Week 8: Canonical correlation analysis and applications.
Lec8 & Data set used: T9-12.DAT & m-pca5c-9003.txt

Week 9: Discriminant analysis and classification, clustering analysis
Lec9 & Lec10
       R program: discrim.R (allows for more than 2 populations)
       Data sets used: T11-1.DAT, T11-2.DAT t12-3a.dat

Week 10: Hierarchical clustering, multidimensional scaling and visualization of high-dimensional data
Lec11&Data sets used: T12-4.DAT, T12-5.DAT, T12-7m.DAT, T12-9.DAT

Reading materials for high dimensional data analysis:
(a) Sliced inverse regression approach: 

Homework assignment:

HW#1:  Data sets used:
Solutions: hw1s
HW#2: Data sets used:
Solutions: hw2s
HW#3: Data sets used:
Solutions: hw3s
HW#4: Data sets used:
Solutions: hw4s
HW#5: Data sets used:
Solutions: hw5s

Old exams
(a) Year 2010: Midterm & solutions; final & solutions
(b) Year 2012: Midterm & solutions;

Midterm: Week 6, Friday, May 9
Exam and solutions

Final Exam: Exam week, Friday, June 13, 8:00 am to 11:00 am.
Exam and Solutions