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Econometrics note

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Tue
°"^
Exam
no
•
3- 4
c.
Multi choices
questions
( entry level )
questions
open
email
a
-
Book
90 mini mites
•
write
.
.
Syllabus
Linear
•
Regression
Regression model
•
•
•
•
•
⑥
Panel data model
:
series
using gretl
in 2
problem
Circle intncment
→
one
( Stata
f
:
( population
observed
?
Time
dependent
CI variable
:
individual
,
direction
main
variable
has
snuffed )
different time )
observed
?
assumption
→
+
observed overtime
limitation
on
Tinie
series
)
co
-
variance to
How
to
detect
→
in
consistence
solve
problem and de
fix the
day
13
Apr
Difference approach of
1) Statistics
theoretical model
do not have
ra
[( exploring
④
test the data without
Dm
Econometrics
•
?
idea of 1
the
having
dataset using techniques
?
about magnitude t I
coefficient
a
not
-104113121
statistics and Econometrics
care
2)
Test
score
a)
⇐a
I
"
i
/
STR
Ba
t
i
t
f.
Mi
)
*
-
=
!
it
STR i
la
COV ( STR i ; Test score i
pg,
*
-
Mm
have theoretical
test
wi
( pg
:
Ia
it EI
( STR;
( STR;
.
STR ) ( test score ;
-
-
STR
)
the
as
;
VAR ( STR i )
f-
regressor
:
-
care
student
→
estimators og Bi
2
support
economic
o
idea works )
(
B1
-
teacher ratio
-
model
statistics tool to test if the
coefficient
about
How
b)
•
The
the
•
•
error
term
is
residual of
Focus
on
Research
B,
pi
precise
?
Otp
not observed
f-
=
,
However
.
VAR
[
when
,
( Gi
-
Mx) ni
VAR Cx; )
we
)
knowing
-2.2g
question
:
B
,
Is
is
crucial
,
estimated
coefficient in
and
different from
p, negative
order to
↳
Performing
Test
&
Xi
woo
↳ My
Bo Pa and y then
OLS estimators
because
)
-
Hypothesis
0 ?
support
or
=
=
)
'
:
E. sin
↳TJ
number of observations
mean
:
:
mean
g
student
test
g
-
teacher ratio
score
-
is
45 : 00
)
n
,
using
*
term
error
Fs )
model
whether data
research question
.
his
Po
=
;
( i.e
:
SIR
SIR
we can
not
our
use
the
swbsiheteion
to
research question
calculate
Test
Hypothesis
Ho
:
Ht
Based
•
0
(
goes
to
-
tail test
is
Opp
Opp
÷p
pi
either go
:
or
so
µ?
)
,
OLS
that
Given
to the true
value
( pg
Epa )
this is
N
Under Ho
t
=
;
poi
-
-
using
t statistics
-
"
;
a
consistent estimator
of
variance
t
-
-
of
converge in
estimator
OLS
Be
Bijan
→
→
•
B
-
estimator of Pa converges in distribution
in
the true value
population
of parameter
infinity
normal variable
Loa
two
Central Himit theorem
on
n
=
Be 40
:
"
when
of
Be
normal variable
to
probability
Nco ;D
standard
error
:
SE
( RT )
O
Biff
→
,
/ raesnpetftoalmnoermisae
"
Nco ;D
*
=
-
If value of tis
distribution
drawing graph and
There
ist located ?
-
o
belong
o.o ,
to
E.
-
-
:
reject
µJ
•
•
Nco ;D
-
determine location
g
t
on
the
graph
where
expected
value
a.
variable biased
g
inside
Estimator standard
=
0.05
ggpyqgqpgpffpfq-h.lt#
-1.96
-
t
=
2.28
-
-
O
I
-
4
1.96
E
L
-
o
,
-1*96 )
a
-
reject
0.52
→
a
-
adjust
The
↳m
↳
'
R
Be
analysis hypothesis
is
There
cannot
be
significant different from
support
the
data
zero
core and STR
isnrelation between testes
,
negative
linear
d) whether
the
model
what is the amount
of
↳
R2
pi
I
is
complete
variability
or
of the
not ?
Performance of student
give information about which party van biting y
explained sum of square
of
'
:
=
⇐
efgs-g-f.I.gg
0.049
B.
-
¥
only
total
.
5%
95%
irs
of
.
left
I
be captured
Test score )
dependent variable
by the chimention oydasses
can
Rest
:
.
can
sum
of
square
variability of
to
test
the error term
score
explained by
STR
be
explained
?
by regressor
Gir
whether
Problem :
some
variable
is in
term also correlated
error
the
regressor
included
omitted biased variable pig when
Biao
infinity
to
produces
n
.→
solution
New model
instead
b.
using
of
:
test score
:
using
vector
P
the omitted
introduce
Po
=
→
1-
biased
Siri
P,
+
T
T
Bo
Bi
Bi
=/% )
estimator
OLS
p,
v¥o*
-
min
UH
µ
,
( Yy )
Man .ua)
.
bill
=
this bias e-does not vanish neither
asymptotically
Percentage English
:
residuals
of square
sum
learner
is
minimized
U
(Y
nxt
At
'
+
µ,
-
pz PEREEL ;)
'
+
"
Ma
]
get minimum
§
-11
xp) ( y xp )
-
cdgimlely)
quadratic function
fa s t
/
-
"
Smi
Mi
+
+
=
-
un
n
min
PEREEL
STR
p•
Pillai
p
X
"n
as
+
Po P,
-
Iif
not
=
Bakri
=
Be
min
Mi
( Test score
i=1
Pot
=
E
=
,
T
transpose
y
→
in
n
E Ñ?
yin
+
.
to
goes
value of data such that the
the
:
n
i= -1
B
ble into the model
Pj Peretti
t
,
OLS
'
van
biased estimate of
→
1
derivative
=
Boise (
0
✗
→
'
✗
check whether
5- X'
Y
minimum
( ¥pF§
Variance
co
-
irañana
included
in
Epi
Epi
=
É
"
Eri
,
Ho
Hi
:
P
,
:p,
t=
=
:)
:b Ñp
,
Ep:p
-
,
→
sy matric matrix
main
Em
diagonal
variances
:
µ
?
:
co
-
variances
,
0
=/ 0
BASEL
PD
Comment
y
-
2)
12 regressor
,
3)
:
2.28
→m
increase
Goodness
of fit
0.049
☒
t
=
-
:
adjust
increase
-11=-2,56
-1.1
→
R
'
(
have
0.424
→
L -196
A
-
have better result
:
more 1
regress
tors
)
much better
:
reject
0.43
↳• even
and
↳
including
variable / cause? omitted biased variable) ,
t
significantly different
0
although coefficient
t=
✗
a
-1%-3
x2
is
I
co
,
a
and
model
significantly different
-20,9
still negative
.
the
4) Does Xs enter into
( Is
tis
a
fundamental
-196
=/ 0
,
the
impact
significantly
than 0
→
variable
in
or
or
is
much
less
not ?
not ? )
significantly
extremely different than 0
✓
explaining
the
performance y students
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