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)