Formula Sheet Econometrics.pdf

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)