Stat 430/Math 468 Notes #1
Aspects of Multivariate Analysis
Introduction
Chapter 1
We will analyze the data which include simultaneous measurement on many variables, and the methodology is called multivariate analysis. We will try to provide explanations
Notes 01: Correlation
E. Bokhari
Spring 2015
STAT 420: Spring 2015
This is an R Markdown document. Markdown is a simple formatting syntax for authoring web pages, and a
very nice way of distributing an analysis. It has some very simple syntax rules.
<! He
Notes 04: Regression Diagnostics
E. Bokhari
STAT 420: Spring 2015
Several packages are used within this script, so it is necessary to ensure the packages are installed beforehand.
if (!require(broom) cfw_ # install broom package, if not already installed
STAT 420
Notes 01: Correlation
Ehsan Bokhari
University of Illinois at Urbana-Champaign
Spring 2015
Bokhari, E. (UIUC)
STAT 420
Spring 2015
Outline of Notes
Pearsons Correlation
Important Properties
Sampling Distribution
Inferences with Correlations
Hypot
Notes 07: ANOVA
E. Bokhari
STAT 420: Spring 2015
This R Markdown file supplements the class notes on analysis of variance.
Several packages are used within this script, so it is necessary to ensure the packages are installed beforehand.
if (!require(dplyr
STAT 420
Notes 00: Introduction to R and Programming
Ehsan Bokhari
University of Illinois at Urbana-Champaign
Spring 2015
Bokhari, E. (UIUC)
STAT 420
Spring 2015
Outline of Notes
Introduction to R
Downloading R
Basic Calculations
Using R Functions
Object
STAT 420
Notes 07: Analysis of Variance
Ehsan Bokhari
University of Illinois at Urbana-Champaign
Spring 2015
Bokhari, E. (UIUC)
STAT 420
Spring 2015
Outline of Notes
Analysis of Variance
ANOVA Models
One-Way ANOVA Model
Two-Way ANOVA Model
Balanced Design
STAT 420
Notes 00: Linear Algebra and Normal Distribution
Ehsan Bokhari
University of Illinois at Urbana-Champaign
Spring 2015
Bokhari, E. (UIUC)
STAT 420
Spring 2015
Outline of Notes
Linear Algebra
Some Basics
Matrix Definiteness
Matrix Decompositions
De
STAT 420
Notes 04: Model Diagnostics
Ehsan Bokhari
University of Illinois at Urbana-Champaign
Spring 2015
Bokhari, E. (UIUC)
STAT 420
Spring 2015
Outline of Notes
Normality Assumption
Visualizing Nonnormality
Diagnostics for Nonnormality
Remedial Measures
Notes 02: SLR
E. Bokhari
STAT 420: Spring 2015
This R Markdown file supplements the class notes on simple linear regression.
Several packages are used within this script, so it is necessary to ensure the packages are installed beforehand.
if (!require(ggp
THE BINOMIAL DISTRIBUTION
In statistics we often consider repeated independent performances of a chance experiment in which an event of interest may or may not occur. Each repetition of the experiment is usually called a trial. We are often interested in
Stat 430/Math468 Notes #2
Matrix Algebra and Random Vectors
Chapter 2
SAS code for histogram, normality test and normal Q-Q plot (dataset is in table 1.5 on page 39.).
options formdlim="*"; data table1_5; infile 'F:\teachingS2010\T1-5.dat'; input wind sol
Stat 430/Math468 Notes #3
Matrix Algebra and Random Vectors (continued)
Chapter 2
Orthogonal Matrix The square matrix Q is called an orthogonal matrix if Q ' Q = QQ ' = I , where I is the identity matrix of the same dimension. Remark: 1. From the definiti
Stat 430/Math468 Notes #4
Random Vectors and Matrices
Chapter 2
A random vector (or matrix) is a vector (or matrix) whose elements are random variables. Suppose X = ( X 1 ,., X p ) ' is a random vector with joint PDF/PMF f ( x1 ,., x p ) and each element
Stat 430/Math468 Notes #5
Sample Geometry and Random Sampling
Chapter 3
A single multivariate observation is the collection of measurements of p different variables taken on the same item or trial. If n observations have been obtained, the entire data set
Stat 430/Math468 Notes #6
The Multivariate Normal Distribution
Chapter 4
Univariate Normal Distribution Recall the univariate normal distribution N ( , 2 ) has probability density function (PDF)
1 f ( x) = e 2 ( x )2 2 2
=
1 2 ( 2 ) 2
1
e
1 ( x )( 2 )1 (
Stat 430/Math468 Notes #7
The Multivariate Normal Distribution (Continued)
Chapter 4
If a random vector X has multivariate normal distribution, then it has the following properties: 1. Linear combinations of the components of X are normally distributed. 2
Stat 430/Math468 Notes #8
The Multivariate Normal Distribution (Continued)
Chapter 4
Result: (Conditional distribution) Suppose X ~ N p ( , ) . Make the following
12 partitioning X = X1 , = 1 , and = 11 . Assume that | 21 22 2 X2 conditional distribution
Stat 430/Math468 Notes #10
Inference about a Mean Vector
Chapter 5
Suppose X1 ,., Xn are random sample from a normal population N p (, ) . The sample mean and sample variance-covariance matrix are, respectively,
X = 1 ( X1 + X 2 + . + X n ) and S = n
1 n
Stat 430/Math 468 Notes #11
Chapter 5: Inference about a Mean Vector (Continued)
Simultaneous Confidence Interval for a ' (i.e. for ai i )
i =1 p
Chapters 5, 8
Result: Let X1 ,., Xn be random sample from a normal population N p (, ) . The sample mean and