**Course Announcement**

**Time:**Monday, Wednesday, Friday at 11:00 a.m. - 11:50 a.m.

**Location:**Addams Hall 302 (830 S Halsted St, Chicago, IL 60607)**Instructor:**Jie Yang

**Office:**SEO 513

**Phone:**(312) 413-3748

**E-Mail:**jyang06 AT uic DOT edu

**Office Hours:**Monday, Wednesday, Friday at 10:00 a.m. - 11:00 a.m.**Textbook:**Richard A. Johnson, Dean W. Wichern,*Applied Multivariate Statistical Analysis*, Pearson Prentice Hall, 6th edition, 2007

**Reference Books:**- C. Radhakrishna Rao,
*Linear Statistical Inference and its Applications*, 2nd edition, Wiley, 1973 (Reprinted in 2001).

- T. W. Anderson,
*An Introduction to Multivariate Statistical Analysis*, 3rd edition, Wiley, 2003. - Brian Everitt, Torsten Hothorn,
*An Introduction to Applied Multivariate Analysis with R*, Springer, 2011.

**Content:**Multivariate normal distribution, estimation of mean vector and covariance matrix, Hotelling's T-square test, confidence regions and simultaneous confidence intervals, multivariate analysis of variance (MANOVA), multivariate linear regression models, principal components, factor analysis, canonical correlation analysis, discrimination and classification

**Prerequisite:**Grade of C or better in STAT 521**Homework:**Turn in every Wednesday before class via UIC Blackboard; half of the grade counts for completeness; half of the grade counts for correctness of one selected problem

**Exams:**This course will require students to be on campus for in-person exams on February 8th and March 15th, Wednesdays, 11:00 a.m. - 11:50 a.m.

**Project:**Students are required to work by themselves or in groups on course projects and submit their final reports before April 28th, 2023, Friday, 11:00am. Each group should consist of at most three students. The projects may come from the project problems assigned by the instructor or be proposed by the students themselves upon the approval of the instructor.

**Grading:**Homework 20%, Two Exams 25% each, Project 30%

**Grading Scale:**90% A , 80% B , 70% C , 60% D**Format of All Exams:**Each exam is based on the homework and the examples discussed in class. The last class session before each exam is a review session. Please prepare any questions that you may have.*No makeup exam will be given without a valid excuse*.

- C. Radhakrishna Rao,
**Course Syllabus****WEEK****SECTIONS****BRIEF DESCRIPTION**01/09 - 01/13 1.1, 1.2, 1.3; 2.1, 2.2, 2.3; 2.5, 2.6 Aspects of Multivariate Analysis; Some Basics of Matrix and Vector Algebra, Positive Definite Matrices; Random Vectors and Matrices, Mean Vectors and Covariance Matrices 01/16 - 01/20 Holiday; 3.3, 3.5, 3.6; 4.1, 4.2 Sample Geometry and Random Sampling; Multivariate Normal Density and Its Properties 01/23 - 01/27 4.3; 4.4, 4.5; 4.6 Sampling from a Multivariate Normal Distribution and Maximum Likelihood Estimation; Sampling Distribution of Xbar and S, Large-Sample Behavior of Xbar and S; Assessing the Assumption of Normality 01/30 - 02/03 5.1, 5.2; 5.3; 5.4 Plausibility of mu0 as a Value for a Normal Population Mean; Hotelling's T^2 and Likelihood Ratio Tests; Confidence Regions and Simultaneous Comparisons 02/06 - 02/10 Review; Exam-I; 5.5 Large Sample Inferences about a Population Mean Vector 02/13 - 02/17 6.1, 6.2; 6.3; 6.4 Paired Comparisons and a Repeated Measures Design; Comparing Mean Vectors from Two Populations; Comparing Several Multivariate Population Means 02/20 - 02/24 6.5, 6.6; 6.7; 7.1, 7.2, 7.3 Simultaneous Confidence Intervals for Treatment Effects, Testing for Equality of Covariance Matrices; Two-Way Multivariate Analysis of Variance; Classical Linear Regression Model, Least Squares Estimation 02/27 - 03/03 7.4; 7.6; 7.7 Inferences about the Regression Model; Model Checking and Other Aspects of Regression; Multivariate Multiple Regression 03/06 - 03/10 7.7; 7A; 7.10 Multivariate Multiple Regression; Distribution of the Likelihood Ratio; Multiple Regression Models with Time Dependent Errors 03/13 - 03/17 Review; Exam-II; 8.1, 8.2 Population Principal Components 03/27 - 03/31 8.2; 8.3; 8.5, 8A Population Principal Components; Summarizing Sample Variation by Principal Components; Large Sample Inferences, Geometry of Sample Principal Component Approximation 04/03 - 04/07 9.1, 9.2; 9.3; 9.3 Orthogonal Factor Model; Methods of Estimation; Methods of Estimation 04/10 - 04/14 10.1, 10.2; 10.3; 10.4 Canonical Variates and Canonical Correlations; Interpreting the Population Canonical Variables; Sample Canonical Variates and Sample Canonical Correlations 04/17 - 04/21 11.1, 11.2; 11.3; 11.4 Introduction, Separation and Classification for Two Populations; Classification with Two Multivariate Normal Populations; Evaluating Classification Functions 04/24 - 04/28 11.6; 11.7; 11.7 Fisher's Method for Discriminating, Logistic Regression and Classification

**Homework**- Homework #1, due 01/18/2023

- Homework #2, due 01/25/2023

- Homework #3, due 02/01/2023

- Homework #4, due 02/06/2023

- Homework #5, due 02/22/2023

- Homework #6, due 03/01/2023

- Homework #7, due 03/08/2023

- Homework #8, due 03/13/2023

- Homework #9, due 04/05/2023

- Homework #10, due 04/12/2023

- Homework #11, due 04/21/2023

- Homework #1, due 01/18/2023
**Using R**- Download
**R**for Free -- the most popular software used by statisticians

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- Use R to Compute Numerical Integrals

- Downloadable Books on R:
*An Introduction to R*, by William N. Venables, David M. Smith and the R Development Core Team

*Using R for Data Analysis and Graphics - Introduction, Code and Commentary*, by John H. Maindonald

**More R Books in Different Languages ...**

- Download
**COVID-19 Impacts on Instruction**- UIC fall COVID-19 guidance -- COVID-19 vaccination required, Masks required, COVID-19 saliva testing, etc.

- Lecture Recording Privacy FAQ

We will be recording the class sessions, or portions of the class, for students who are unable to attend synchronously. The recording feature for others is disabled so that no one else will be able to record this session through Zoom, Blackboard Collaborate, Webex, or Echo360. Recording by other means is not permitted. The recorded class sessions will be posted on our Blackboard class website unless otherwise notified.

If you have privacy concerns and do not wish to appear in the recording, turn OFF your video and notify me in writing (via email) prior to the next class session. If you prefer to use a pseudonym instead of your name, please let me know what name you will be using, so that I can identify you during the class session. If you would like to ask a question, you may do so privately through the chat feature by addressing your question to me or your TA only (and not to “everyone”), or you may contact me or your TA by another private method, which we will agree upon in advance of class. If you have questions or concerns about this video recording policy, please contact me before the end of the first week of class.

- UIC fall COVID-19 guidance -- COVID-19 vaccination required, Masks required, COVID-19 saliva testing, etc.
## Disability Accommodations Statement

UIC is committed to full inclusion and participation of people with disabilities in all aspects of university life. Students who face or anticipate disability-related barriers while at UIC should connect with the Disability Resource Center (DRC) at drc.uic.edu, drc@uic.edu, or at (312) 413-2183 to create a plan for reasonable accommodations. In order to receive accommodations, students must disclose disability to the DRC, complete an interactive registration process with the DRC, and provide their course instructor with a Letter of Accommodation (LOA). Course instructors in receipt of an LOA will work with the student and the DRC to implement approved accommodations.

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