By: Kaleem Formula Sheet Econometrics Percentage Change %change Yt Yt 1 100 Yt 1 %change [ln(Yt ) ln(Yt 1
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By: Kaleem
Formula Sheet Econometrics Percentage Change %change
Yt Yt 1 100 Yt 1
%change [ln(Yt ) ln(Yt 1 )] 100
(1.1) (1.2)
Mean
Y
N
Y
i 1 i
(1.3)
N
Standard Deviation s
(Yi Y ) 2 N 1
(1.4)
s2
(Yi Y )2 N 1
(1.5)
Variance
Mean of the probability distribution for X, expected value, mathematical expectation of X
E ( X ) Xp( X )
(1.6)
2 E ( X ) 2 ( X ) 2 p( X )
(1.7)
Variance of probability distribution
Standard Deviation
E( X )
( X )
2
p( X )
(1.8)
Covariance
COV (Y , X )
N i 1
(Yi Y )( X i X ) N 1
(1.9)
Correlation r
COR(Y , X ) sY s X
(1.10)
By: Kaleem
For M variable possibe correlations
M ( M 1) 2
(1.11)
Regression Model
Yi X i i
(1.12)
i Yi X i
(1.13)
Yˆi ˆ ˆ X i
(1.14)
ˆi Yi ˆ ˆ X i
(1.15)
Error term
Fitted Regression Line
Regression Residuals
Sum of Squared Residuals N
SSR ˆi2
(1.16)
i 1
N
SSR (Yi ˆ ˆ X i )2
(1.17)
i 1
N
SSR (Yi Yˆi )2
(1.18)
i 1
R2 N
TSS (Yi Y )2
(1.19)
i 1 N
RSS (Yˆi Y )2
(1.20)
TSS RSS SSR
(1.21)
i 1
R2
RSS TSS
R2 1
SSR TSS
(1.22)
(1.23)