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)

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)