2. SIMPLE REGRESSION MODEL
You guys are just like this lion cub. You look innocent.
Simple means there are only one variable on the right hand side.
One variable on the left hand side[RHS]
One variable on the right hand side[LHS
= 1 + 2 +
is called a
Thomas A. Trabold
Associate Professor, Golisano Institute for Sustainability
CoDirector, Center for Sustainable Mobility
Rochester Institute of Technology
Building 78, Room 2412
111 Lomb Drive, Rochester, NY 146235608
(585) 4754696.v / (585) 4757370.f
22 Hidden Meadow
Penfield, NY 14526
Phone: (716) 3777450
Email: twssch@rit.edu
Curriculum Vitae  Thomas W. Smith, Ph.D.
Research/Technology Interests:
Design and synthesis of functional polymers (ionbinding polymers, block
copolymers and liquid ionic
Michael G. Thurston
Research Faculty and Technical Director, The Sustainability Institute
Rochester Institute of Technology
133 Lomb Memorial Drive
Rochester, New York 146235608
(585) 4756550.v (585) 4755455.f
mgtasp@rit.edu
Professional Preparation
Ro
THE NICENE CREED ON THE CHURCH
* We believe in one holy catholic and apostolic Church.
[J.S. Bach, a devout Lutheran, wrote a musical setting for the
Liturgy known as the Bminor Mass. In his setting for the words
printed above, there are two melody lines
THE NICENE CREED
The Nicene Creed is the most widely accepted and used brief
statements of the Christian Faith. In liturgical churches, it is
said every Sunday as part of the Liturgy. It is Common Ground to
East Orthodox, Roman Catholics, Anglicans, Luthe
THE FILIOQUE CLAUSE
This essay is an Appendix to the essay called CREED NICENE. It deals
with one particular line of the Nicene Creed.
The Creed as formulated at Nicea in 325 ended with the words
* And we believe in the Holy Spirit.
When the Council of Co
THE COUNCIL OF ORANGE
The Council of Orange was an outgrowth of the controversy between
Augustine and Pelagius. This controversy had to do with degree to
which a human being is responsible for his or her own salvation, and
the role of the grace of God in
THE APOSTLES' CREED VERSUS GNOSTICISM
A creed generally emphasizes the beliefs opposing those errors
that the compilers of the creed think most dangerous at the time.
The Creed of the Council of Trent, which was drawn up by the Roman
Catholics in the 1500
THE ANATHEMAS OF THE SECOND COUNCIL OF CONSTANTINOPLE (553 AD)
The Second Council of Constantinople was called to resolve certain
questions that were raised by the Definition of Chalcedon, the most
important of which had to do with the unity of the two na
Seminario Teologico Northwestern
Mdulo Tres de Apredizaje
Sus Libros de Texto para estas asignaciones son los 66 libros de la Santa Biblia.
Es recomendado esto usted compra una Biblia de estudio. La Biblia de Estudio de
Ryrie es una Biblia excelente para
Paul H. Stiebitz
Rochester Institute of Technology
133 Lomb Memorial Drive, Rm. 2400
Rochester, NY 14623
5854752602
phseie@rit.edu
Experience
Rochester Institute of Technology
1984present
Currently Interim Academic Director at RITs Sustainability Insti
Thomas A. Trabold
Associate Professor, Golisano Institute for Sustainability
CoDirector, Center for Sustainable Mobility
Rochester Institute of Technology
Building 78, Room 2412
111 Lomb Drive, Rochester, NY 146235608
(585) 4754696.v / (585) 4757370.f
Show us the straight way,
the way of those whom Thou hast favored,
not the way of those who earn Thine anger
or of those who go astray.
Ummil Quran, 57
Questions Raised
The recent attacks on the World Trade
Center have affected everyone who
lives in Amer
1. Review of statistics
11 What is probability?
Throwing a coin.
What is the probability of getting a head?
How do we know?

Assuming a fair coin. 1/2

Throw a coin for many many times.
12 Probabilistic Event
a. Coin Toss
Outcome:
head or tail
Head cf
We have a simple regression model
yi 1 2 xi ei and the assumptions of the Gauss
Markov theorem hold. The variance of eis are
2.
1.
Now you have done the estimation. What you need to do next? Explain why you need to do that.
2.
When discussing the unbias
10. Heteroskedasticity
Heteroscedasticity or heteroskedasticity?
Heteroscedasticity
Pronunciation: screen vs scene
It is published in Econometrica 1985.
Nowadays heteroskedasticity is more popular.
101 What is Heteroskedasticity?
Definition. Simple varia
5. Modeling Issues
51 Scaling
Use data collected from Econometrics and Macroeconomics class. 2012 Fall
y= 1 + 2 x +
Data
Weight measured in kg,
Height
measured in cm
Dependent Variable: WT
Method: Least Squares
Date: 12/04/12 Time: 12:03
Sample: 1 58
In
We have a simple regression model yi 1 2 xi ei and the assumptions of the
GaussMarkov theorem hold.
The variance of eis are 2 .
1.
Derive the least squares estimators b1 and b2 for the true parameters 1 and 2 .
2.
Calculate the sample covariance between
4. INFERENCE IN REGRESSION MODEL
So far we tried to get the estimate of the true parameter.
In other words, we tried to find the candidate for the true parameter value which
is a unknown nonrandom constant
Now we want to get the range of the true value
4
3 Measuring Goodness of Fit & Prediction
31 Fitted value and residual
Fitted value :
= 1 + 2
Residual i :

= 1 2
Using fitted value and the residual, we can write
= +

Square both sides,
2 = 2 + 2 + 2

Sum both sides,
2 = 2 + 2 + 2
since = 0
=
Homework #2
1. Let be a continuous random variable with probability density function given by
() = .5 + 1
0 2
=0
< 0, > 2
(a) Calculate the mean of the random variable X.
(b) Calculate the variance of the random variable X.
2. Let be a continuous random
Curriculum Vitae
Eric David Williams
Contact Information
School of Sustainable Engineering and the Built Environment &
The School of Sustainability
Arizona State University
Tempe, Arizona 852875306
Phone: (480) 7276259 Fax: (480) 9650557
Email: ericwil
The Worldwide Church of Jesus Christ
OUR DOCTRINAL POSITION
We believe that the Bible is the inspired, infallible, eternal Word of God.
1 Cor. 2:13; 2 Tim. 3:16
We believe in one God, eternally existent in three persons: Father, Son and Holy Spirit.
Matt.
Seminario Teologico Northwestern
y
Ministerios Alianza Cristiana Mundial
El Prospecto del Programa de Seminario de Rama
La Vision
El personal y el mando del Seminario Teolgico Northwestern reconoce
nuestro objetivo primario como la educacin de creyentes e
Dr. Thomas P. Seager
Rochester Institute of Technology, Sustainability Institute
111 Lomb Memorial Dr., Rochester NY 14623
Thomas.Seager@rit.edu
5854756612
Professional Appointments
Jun 2007 present
Associate Professor, Sustainability Institute, RIT
Jan
Seminario Teologico Northwestern
PROCESO DE MATERIAL DE ENTREGA
Para Uso En Papeles, Tesis, y Disertaciones
LOS TEMAS Y SU PRESENTACIN.
Introduccin:
Una de las tareas que con mayor asiduidad realiza el estudiante
cristiano es la investigacin. La preparaci
Michael H. Haselkorn
Senior Staff Engineer and Research Faculty
Rochester Institute of Technology
111 Lomb Memorial Drive
Rochester, New York 146235608
(585) 4755408.v (585) 4755455.f
mhhasp@rit.edu
Professional Preparation
Alfred University, Alfred, N
Mario Waldor Gomes
(585) 4752148 (work)
mwgeme@rit.edu
2189 Gleason Hall
76 Lomb Memorial Drive
Rochester, NY 14623
EDUCATION:
Jan. 2005
PhD
Committee:
Thesis:
Honors:
Cornell University, Theoretical and Applied Mechanics
Andy Ruina(adviser), Steven Stro