Formula Sheet Econometrics.pdf
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By: Kaleem
Formula Sheet Econometrics
Percentage Change
1
1
% 100t t
t
Y Ychange
Y
(1.1)
1% [ln( ) ln( )] 100t tchange Y Y (1.2)
Mean
1
N
iiY
YN
(1.3)
Standard Deviation
2( )
1
iY Ys
N
(1.4)
Variance
2
2 ( )
1
iY Ys
N
(1.5)
Mean of the probability distribution for X, expected value, mathematical expectation of X
( ) ( )E X Xp X (1.6)
Variance of probability distribution
2 2 2( ) ( ) ( )E X X p X (1.7)
Standard Deviation
2( ) ( ) ( )E X X p X (1.8)
Covariance
1( )( )
( , )1
N
i iiY Y X X
COV Y XN
(1.9)
Correlation
( , )
Y X
COR Y Xr
s s (1.10)
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By: Kaleem
( 1)
M variable possibe correlations 2
M MFor
(1.11)
Regression Model
i i iY X (1.12)
Error term
i i iY X (1.13)
Fitted Regression Line
ˆˆ ˆi iY X (1.14)
Regression Residuals
ˆˆ ˆi i iY X (1.15)
Sum of Squared Residuals
2
1
ˆN
i
i
SSR
(1.16)
2
1
ˆˆ( )N
i i
i
SSR Y X
(1.17)
2
1
ˆ( )N
i i
i
SSR Y Y
(1.18)
R2
2
1
( )N
i
i
TSS Y Y
(1.19)
2
1
ˆ( )N
i
i
RSS Y Y
(1.20)
TSS RSS SSR (1.21)
2 RSSR
TSS (1.22)
2 1SSR
RTSS
(1.23)