Matrix Algebra Basics
Khalil Shafie
UNC
1
2
Rows
Rows are the number of horizontal lines in
the matrix
Example: This matrix has 3 rows
1 2 3 4
5 6 7 8
9 8 7 6
3
Column
Columns are the number of vertical lines in
a matrix
Example: This matrix has 4 col
SRM 502
Chapter 9
Regression
K. Shafie
UNC
Regression
Use of Regression Equations
Estimating ( Predicting ) Y from X
Error of Estimate ( Residual )
Proportion of Predictable variance, r2
The least-squares criterion
Association does not imply causation
Cau
SRM 502
Chapter 18
Analysis of Covariance
K. Shafie
UNC
0
Review of Simple Linear Regression and
Analysis of Covariance
ANCOVA Model
ANCOVA Assumptions
ANCOVA Computations
1
ANCOVA
In all ANOVA models we have had
One numerical DV
One or more categoric
SRM 502
Chapter 12
One-way Classifications:
Analysis of Variance
K. Shafie
UNC
One-way Classifications: Analysis of Variance
Comparing several means
ANOVA terminology
Fixed Effect Model
The analysis of variance F test
Conditions for ANOVA
F distribution a
SRM 502
Chapter 15-1
Failures in the Assumptions
K. Shafie
UNC
0
Assumptions
When you choose to analyze your data using
an ANOVA model or SLM, part of the
process involves checking to make sure that
the data you want to analyze can actually be
analyzed us
SRM 502
Chapter 14
Two- Way Classification
K. Shafie
UNC
0
Two- And Three-Factor ANOVA
Two -Factor ANOVA
The Meaning of Interaction
A model for the data
Two Factor ANOVA with one observation per cell
Randomized Block Design
Two Factor ANOVA one rand
SRM 502
Chapter 13
Analysis of Variance:
The Random Effects Model
K. Shafie
UNC
Expected Mean Squares in One-way
ANOVA
Mean square error (aka MS within) is a pooled variance.
It is an unbiased estimate of the population variance.
i.e.
= 2
The expectati
SRM 502
Chapter 17-2
Multiple Linear Regression
K. Shafie
UNC
Indicator Variables
The General Concept of Indicator Variables
Some Comments on Indicator Variables
Regression Approach to Analysis of
Variance
2
The General Concept of Indicator Variables
1. We wish to evaluate a new textbook for a statistics class. There are seven sections; four are chosen at random
to receive the new book, three receive the old book. At the end of the semester, student evaluations show the
following percentages of studen
SRM 502
Chapter 11
Analysis of Frequencies
K. Shafie
UNC
Analysis of Frequencies
The
distributions
test for goodness of fit
The
test for independence
The
test for homogeneity
1
Example: Fair die
A die is rolled 60 times, with the following results:
1
2
SRM 502
Chapter 16-3
Repeated-Measures ANOVA
K. Shafie
UNC
0
Repeated-Measures ANOVA
Repeated-Measures (Within-subjects )ANOVA
R-M ANOVA with a Between Subjects factor
Repeated-Measures with two Within-subjects and
one Between-Subjects factor
1
Repeate
SRM 502
Chapter 10
Correlation
K. Shafie
UNC
Relationships: Scatterplots and correlation
Explanatory and response variables
Displaying relationships: scatterplots
Interpreting scatterplots
Measuring linear association: correlation, r
The use of
r
Facts ab
SRM 502
Chapter 16-2
Nested Designs
K. Shafie
UNC
0
Nested Designs
In some two-factor experiments the level of one
factor , say B, is not cross classified with the other
factor, say A, but is NESTED within it.
The levels of B are different for different
SRM 502
Simple Regression and One-way ANOVA
In matrix form
K. Shafie
UNC
1
Simple linear regression model
2
Simple linear regression model
3
Simple linear regression model
4
Estimating Parameters by Least Squares
Normal equations obtained from:
n
Q Q
,
an
SRM 502
Chapter 15-2
Unbalanced Designs
K. Shafie
UNC
0
Common unbalanced data situations
In designed experiments: equipment failure, error
in data entry, missing data.
More observations can be taken for treatments of
greater importance
The data were s
SRM 502
Chapter 17
Multiple Linear Regression
K. Shafie
UNC
Multiple Linear Regression
Multiple Regression Models
Estimation of the Model Parameters
Hypothesis Testing in Multiple Linear Regression
Confidence Intervals on the Regression Coefficients
SRM 502
Chapter 16-1
Factorial Experiments
K. Shafie
UNC
0
Higher- Order Classification
The basic concepts of a two-way classification
can be extended to more complex designs
involving three or more factors.
Such designs are referred to as higher- order
SPECIAL COMMUNICATIONS
Exercise and Hypertension
POSITION STAND
This pronouncement was written for the American College of
Sports Medicine by Linda S. Pescatello, Ph.D., FACSM, (Co-Chair),
Barry A. Franklin, Ph.D., FACSM, (Co-Chair), Robert Fagard, M.D.,
1
CARDIOVASCULAR RESPONSE TO EXERCISE
A
s exercise physiologists, we not only need to understand the basics of physiology but we
also must understand how these physiological systems respond to the stresses of exercise.
It is during exercise that we observ
8/22/2016
Introduction
chapter
1
INTRODUCTION TO THE
CARDIOVASCULAR
SYSTEM
Why do we need a cardiovascular system?
What organs engage in exchange with the outside
environment?
Arrangement of the CVS
Three components
Heart
Blood vessels
Lymphatic sys
Journal of Sports Sciences
ISSN: 0264-0414 (Print) 1466-447X (Online) Journal homepage: http:/www.tandfonline.com/loi/rjsp20
Effects of high-intensity interval training on
cardiometabolic risk factors in overweight/obese
women
Abbie E. Smith-Ryan, Eric T.
RESULTS: Participants attended 83.3% 16% of total prescribed sessions. Post-program CRF significantly increased (27.5 7.3 to 30.4 7.4 ml.kg-1.min-1) despite no
significant increase in HRpeak (149.5 19.8 to 148.5 21.9 bpm) and respiratory exchange ratio (1
Original Research
Carotid Artery IMT, Blood Pressure, and Cardiovascular Risk
Factors in Males and Females
CHRISTINA M. CROMWELL, KRISTIN R. AICHELE*, JOYANN E. OAKMAN,
MICHAEL P. NEAL*, JESSICA M. LENZO*, AVERY N. PEREZ*, NAOMI L.
BYE, ERICA L. SANTANIEL
SRM 602
Assignment 2
Note: You only need to submit Part II.
Part I: Problems from the text : Solve problems 4.3, 4.9, and 4.35 from the text.
You may ignore the questions related to the omitted parts.
Part II: Questions
1. Assume the IQ scores of the stud
SRM 602
Assignment 1
Note: You only need to submit Part II by the due date.
The EXERCISE and OECD data sets and also the HSB data set and its description,
a readme file, are available in Blackboard. You can also download the SAS code for
questions 4,5, 6,
SRM 602
Assignment 3
Note: You only need to submit Part II by the due date.
The HSB data set and its description, a readme file, are available in Blackboard.
You can also download the SAS code for question 4 from Blackboard.
Part I: Problems from the text
SRM 502
Homework Assignment 7
Answer the following questions. For hand calculations feel free to use anything like Excel to
make the calculations easier and quicker. Use SAS only when directed.
1. An anesthesiologist studied the effects of codeine and acu
SRM 502
Homework Assignment 6
Answer the following questions. For hand calculations feel free to use anything like Excel to
make the calculations easier and quicker. Use SAS only when directed.
1. The number of pounds of steam used per month at a plant is