STA 4702 – Multivariate Statistical Methods – Section 19D9

STA 5701 – Applied Multivariate Methods – Section 1961

Spring 2017

**MWF - 4 ^{th}
Period - Anderson 134**

** Instructor:** Dr. Larry Winner

** Office:** 228 Griffin/Floyd Hall

** Instructor Webpage:** http://www.stat.ufl.edu/~winner/

** TA: **Minji Lee, Office: FLO 115B, e-mail:
mlee9@ufl.edu

** Office Hours:** Instructor: M 12:30-1:30, Th 11:00-12:00 TA: Tu 2:00-4:00, W 9:00-10:00

** Course Objectives:** STA 4702/5701 is an
introductory course in statistics when responses are more than one
characteristic or variable is observed on units (thus multivariate). We begin
with a review of the relevant matrix theory/applications and common statistical
distributions as well as the Multivariate Normal Distribution. Methods of inference
regarding multivariate means will include: Hotelling’s T

__Tentative Course Topics/Exam
Schedule: __

·
Introduction to Multivariate Analysis (1.5 Lectures)

o Applications (1.2)

o Data organization (1.3)

o Graphing (1.4)

o Distance (1.5)

·
Review of Matrix Algebra and Random Vectors/Matrices (1.5 Lectures)

o Vectors: Addition, Length,
Angle, Inner Product, Projection (2.2)

o Matrices: Multiplication,
Square Matrices, Orthogonal Matrices, Eigenvalues/Eigenvectors (2.2)

o Positive Definite Matrices
(2.3), Square Root Matrix (2.4)

o Random Vectors and Matrices
(2.5), Mean Vectors and Covariance Matrices (2.6)

·
Geometry of the Sample and Random Sampling (1 Lecture)

o **X**
matrix, means vector, deviations, sample variance-covariance and correlation
matrices (3.2)

o Random sampling, Expectations
of Sample mean vector and variance-covariance matrix (3.3)

o Matrix form of Mean vector
and variance-covariance and correlation matrices (3.5)

o Linear Combinations of
Random Variables (3.6)

·
Probability and Sampling Distributions (1 Lecture)

o Univariate: Normal,
Student’s *t*, c^{2}, *F* (Supplementary Course Notes)

o Multivariate Normal (4.2)

o Sampling Distribution of
Sample Mean Vector and variance-covariance matrix (4.4)

o Large-Sample results for
Sample Mean Vector and variance-covariance matrix (4.5)

·
Inferences for a Population Mean Vector (3 Lectures)

o Hypothesis test for a
population mean (scalar or vector) – Hotelling’s *T*^{2} (5.2)

o Confidence Regions and
Simultaneous Comparisons of Individual Means (5.4)

o Large Sample Inference for a
Population Mean Vector (5.5)

·
Comparing Several Population Mean Vectors (8 Lectures)

o Repeated Measures on
Subjects under 2 Different Conditions/Treatments (6.2)

o Repeated Measures of
Subjects with a single response and several Treatments (6.2)

o Comparing Mean Vectors for 2
Populations (6.3)

o Comparing Mean Vectors for *g* ≥ 2 Populations (6.4)

o Simultaneous Confidence
Intervals for Treatment Means (6.5)

o Test of Equality of
Variance-Covariance Matrices (6.6)

o 2-Way Multivariate Analysis
of Variance (6.7)

o Profile Analysis (6.8)

o Repeated Measures and Growth
Curves (6.9)

·
Multivariate Linear Regression Model (5 Lectures)

o Classical Univariate
(Response) Multiple (Predictor) Linear Regression Model (7.1)

o Least Squares Estimation
(7.2)

o Inferences for the
Regression Model Parameters (7.3)

o Inferences for the Estimated
Regression Function (7.4)

o Multivariate (Response)
Multiple (Predictor) Regression (7.7)

·
Principal Components (3 Lectures)

o Population Principal
Components (8.2)

o Principal Components for
Sample Covariance/Correlation Matrices (8.3)

o Graphing Principal
Components (8.4)

o Large-Sample Inferences
(8.5)

·
Factor Analysis (3 Lectures)

o Orthogonal Factor Model
(9.2)

o Methods of Estimation (9.3)

o Factor Rotation (9.4)

·
Canonical Correlation Analysis (2 Lectures)

o Canonical Variates and
Canonical Correlations (10.2)

o Interpreting Population
Canonical Variables (10.3)

o Sample Canonical Variates
and Canonical Correlations (10.4)

·
Discriminant Analysis (4 Lectures)

o Classifying 2 Populations
(11.2)

o Classifying with 2
Multivariate Normal Populations (11.3)

o Evaluating Classification
Functions (11.4)

o Classifying More than 2
Populations (11.5)

·
Cluster Analysis (3 Lectures)

o Similarity Measures (12.2)

o Hierarchical Methods (12.3)

o Nonhierarchical Methods
(12.4)

·
Exam 1 – February 3 Exam
2 – March 17 Exam 3 – April 17

·
Assignment 1 – (Posted 1/13 – Due 2/3) Assignment 2 – (Assigned 2/10 – Due 2/24)

·
Assignment 3 – (Posted 3/13 – Due 3/27) Assignment 4 – (Assigned 3/31 – Due 4/14)

** Grading:** Exams will count 28% each, and Homework
Assignments will count 4% each to the Final total of 100%

__Course Grade Cut-offs:__

** Attendance/Exam/Assignment
Policies:** While attendance is not taken, students are expected to
attend lectures and participate in class. Make-up exams will only be considered
with documented medical event or conference attendance (graduate students).
Early exams will be given under no circumstances. Assignments are to be handed
in during class on the date the assignment is due in paper format. Electronic
submission of assignments will not be accepted. Turn off cell phones during classes.
Students can bring 1 hand-written formula sheet (8.5”x11”) to exams, and any
calculator without internet access.

__Academic Accommodations:__** **If you have a documented disability and wish to
discuss academic accommodations with me, please contact me as soon as possible.

** Textbook:** R.A. Johnson and D.W. Wichern (2007).

__University
Grading Points:__

** Online Course
Evaluations:** The University has an online course evaluation system.
Late in each semester (after final withdrawal date), students can go to the
GATORRATER portal and evaluate courses. The website is located at: https://evaluations.ufl.edu/evals/Default.aspx.

__University Policies:__

**Academic Dishonesty: **All members of the University Community share the
responsibility to challenge and make known acts of apparent academic
dishonesty. Acts of academic dishonesty will not be tolerated and will be
referred to the Student Honor Council.

__Campus Resources:__

Counseling
and Wellness Center: http://www.counseling.ufl.edu/cwc/

Academic
Resources: http://www.ufl.edu/academics/resources/

Disability
Resource Center: https://www.dso.ufl.edu/drc/

Student
Health Care Center: http://shcc.ufl.edu/