Multicollinearity
Lecture Note #8
This note is based on Prof. Yoon-Jae Whangs lecture notes series.
1. Perfect Multicollinearity
Definition : Existence of exact linear relationship(s) among independe
DESCRIPTIVE
STATISTICS
Objective
:
To
present
statistical
data
in
such
a
way
that
the
important
characteristics
of
the
data
could
be
easily
understood.
Our
aim
is
to
survey
Interval
Estimation
II
5.
Condence
Intervals
for
the
Variance
of
a
Normal
Population
Suppose
that
we
have
a
sample
of
n
observations
from
a
normal
population
with
mean
an
Sampling
Distribution
\A
sample
should
be
representative
of
the
population":
Random
Sampling
.
Some
denitions
.
We
want
to
know
the
properties
of
a
large
group
of
objects,
Families
of
Distributions
We
have
discussed
properties
of
discrete
and
continuous
random
variables.
Now,
we
are
going
to
consider
some
important
examples
of
discrete
and
conti
Random
Variables
(Distribution
Theory)
This
note
is
based
on
Prof.
Joon
Y.
Park's
lecture
notes
series.
1.
Random
Vectors
and
Joint
Distribution
(1)
A
Random
Vector
.
Random
Hypothesis
Testing
6.
Tests
of
the
Population
Variance
In
this
section,
we
develop
procedures
for
testing
the
population
variance
2
based
on
a
random
sample
of
n
observation
Inference
in
the
Simple
Regression
Lecture
Note
#4
This
note
is
based
on
Prof.
Yoon-Jae
Whang's
lecture
notes
series.
We
have
learned
how
to
get
OLS
estimates
(point
estima
1
Linear
Regression
Model:
Basic
Results
1
The
Linear
Regression
Model
.
Model:
yi
=
1
+
2xi2
+
+
kxik
+
ui
for
i
=1,
2,
:,
n.
In
a
matrix
form,
it
can
be
written
Linear
Regression
Model:
Inference
Why
Study
Hypothesis
Testing?
.
Examples:
(i)
To
evaluate
the
prediction
of
an
economic
theory,
e.g.
interest
elasticity
of
money
demand
=
Multiple
Regression
Lecture
Note
#6
This
note
is
based
on
Prof.
Yoon-Jae
Whang's
lecture
notes
series.
.
General
Model
Yi
=
1
+
2X2i
+
+
K
XKi
+
ui
There
may
be
mo
Dummy
Variables
Lecture
Note
#7
This
note
is
based
on
Prof.
Yoon-Jae
Whang's
lecture
notes
series.
.
Dummy
Variable
:
Explanatory
variables
take
only
one
of
two
values,
1
Simple
Regression
2
Lecture
Note
#3
This
note
is
based
on
Prof.
Yoon-Jae
Whang's
lecture
notes
series.
Once
we
get
the
OLS
estimator
in
a
simple
regression
model,
next
ste
Autocorrelation
Lecture
Note
#10
1.
The
Nature
of
Autocorrelation.
.
In
classical
assumptions,
regression
errors
are
assumed
to
be
uncorrelated,
that
is,
Cov
(ui;uj)=
0
for
i
Inference
in
the
Simple
Regression
II
Lecture
Note
#5
This
note
is
based
on
Prof.
Yoon-Jae
Whang's
lecture
notes
series.
In
this
chapter,
we
consider
the
following
problems
Heteroscedasticity
Lecture
Note
#9
1.
The
Nature
of
Heteroscedasticity
.
Consider
the
following
simple
regression
Yi
=
1
+
2X2i
+
ei
to
explain
household
expenditure
on
food
Generalized
Linear
Models
1.
Model
y
=
X
+
u,
where
Eu
=0
Euu.
=
V
.
6
:
Nonspherical
errors
2
=
2I
2.
Sources
of
nonspherical
errors
Non-spherical
errors
are,
most
no
Multicollinearity
Lecture
Note
#8
1.
Perfect
Multicollinearity
.
Denition
:
Existence
of
exact
linear
relationship(s)
among
independent
variables
.
Example
:
Yi
=
1
+
2X2i
+
Point
Estimation
This
note
is
based
on
Prof.
Joon
Y.
Park's
lecture
notes
series.
1.
Statistical
Inference
General
Remarks
:
Suppose
that
we
are
given
n-numbers
x1;:;xn,
whi
Probability
Distributions
This
note
is
based
on
Prof.
Joon
Y.
Park's
lecture
notes
series.
1.
Continuous
Probability
Distributions
In
fact,
there
are
lots
of
continuous
probab
Multiple Regression
Lecture Note #6
This note is based on Prof. Yoon-Jae Whangs lecture notes series.
General Model
Yi = 1 + 2 X2i + + K XKi + ei
There may be more than one explanatory variable that
Inference in the Simple Regression
Lecture Note #4
This note is based on Prof. Yoon-Jae Whangs lecture notes series.
We have learned how to get OLS estimates (point estimates) in the simple regression
Heteroscedasticity
Lecture Note #9
This note is based on Prof. Yoon-Jae Whangs lecture notes series.
1. The Nature of Heteroscedasticity
Consider the following simple regression
Yi = 1 + 2 X2i + ei
t
Inference in the Simple Regression II
Lecture Note #5
This note is based on Prof. Yoon-Jae Whangs lecture notes series.
In this chapter, we consider the following problems in a linear regression model
1
Autocorrelation
Lecture Note #10
This note is based on Prof. Yoon-Jae Whangs lecture notes series.
1. The Nature of Autocorrelation.
In classical assumptions, regression errors are assumed to be un
Simple Regression 1
Lecture Note #2
This note is based on Prof. Yoon-Jae Whangs lecture notes series.
1. The Regression Problem
Let
Y : Dependent Variable (or Explained) Variable
X : Independent (or E
Simple Regression 2
Lecture Note #3
This note is based on Prof. Yoon-Jae Whangs lecture notes series.
Once we get the OLS estimator in a simple regression model, next step is to investigate
the proper
Dummy Variables
Lecture Note #7
This note is based on Prof. Yoon-Jae Whangs lecture notes series.
Dummy Variable : Explanatory variables take only one of two values, 1 or 0.
Qualitative variables ma
What subjects are covered in this course?
Literal Interpretation:
Econo + Metrics = Economic Measurement
Purpose: Econometrics gives empirical content to a priori reasoning in economics.
Economic Th
10. Two-Sample Tests
-SCENARIO 10-15
-The table below presents the summary statistics for the
starting annual salaries (in thousands of dollars) for
individuals entering the public accounting and fina