Summary of Regression for Quantitative Research Methods

Correlation




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DATA

Cross Section uits of interest
# pointin time period kumulative




!
#independent observations
o
Pooled Cross Sections multiple
# cross sections independentcross sections



Time Series Avariables of interestperiod recurring) seriallycorrelated
frends
#




el/Longitudinal #units of interest opened recurring time-invariant unobservables

lagged responses
#




DICTIONARY

Leter's Paribus all other factors equal

, GAUSS-MARKOV/ CLASSIC LINEAR MODEL ASSUMPTIONS
1 -
5 1 -
6



1 yB
= +


3x,+... Bx,4- the relationship between
+

xx, and y
is linear in the population ofparameter linearity


2 [j,y,: =1,...,n3 -

the sample from the population is random random sampling

3 X X; the independentvariables are not constant and theyare not collinear
perfectly of collinearity


Eij-; 8 -

the values of the independent variables are all
not equal sample variation (explanatoryvariable)

4
E(4,lij 0 the independentvariable not contain information the mean unobserved factors
=

must about the
-


of



zero conditional the correlation
#
mean between 4 and x
Hexogeneity
E(4) 8
=




all independentvariables must notbe correlatedwith the error term weak exogeneity
COV/X;,4) 0 =




=B UNBLASEDNESS
↳




5-
VAR/4,/x) 02 = -
the value of the independentvariable not
must contain information
# homoskedasficity
variabilityof the unobserved factors
about the


Iconstantdistribution

or robust SE

↳
plim - =
CONSISTENCY -




the probability thatthe estimate is arbitrarilyclose to the tune value

the sample
can be arbitrarilyincreasedby
increasing
size



L
VARI) -, jike, jek
=
-




~4, -N10,02 unobserved factors of the function
the are normallydistributed normality

or
large n



L
⑤
-
NI, VARI), then, siken, jai -