Econometrics Formula Sheet
Based on Stock & Watson, 4th Edition
1. Basic Statistics (Ch. 2-3)
•Sample Mean: ¯
Y=1
nPn
i=1 Yi
•Sample Variance: s2
Y=1
n−1Pn
i=1(Yi−¯
Y)2
•Sample Covariance: sXY =1
n−1Pn
i=1(Xi−¯
X)(Yi−¯
Y)
•Correlation: rXY =sXY
sXsY
•Difference of Means t-stat: t=¯
Y1−¯
Y0
√s2
1/n1+s2
0/n0
2. Simple Linear Regression (Ch. 4-5)
Model: Yi=β0+β1Xi+ui
•OLS Slope: ˆ
β1=sXY
s2
X
=P(Xi−¯
X)(Yi−¯
Y)
P(Xi−¯
X)2
•OLS Intercept: ˆ
β0=¯
Y−ˆ
β1¯
X
•R2:1−SSR
T SS where SSR =Pˆu2
i
•SER: qSSR
n−2
•t-statistic (H0:β1= 0): t=ˆ
β1
SE(ˆ
β1)
•95% CI: ˆ
β1±1.96 ×SE (ˆ
β1)
3. Multiple Regression (Ch. 6-7)
Model: Yi=β0+β1X1i+· · · +βkXki +ui
•Adjusted R2:¯
R2= 1 −n−1
n−k−1
SSR
T SS
•F-statistic (Homoskedastic): F=(R2
unr−R2
restr)/q
(1−R2
unr)/(n−kunr −1)
4. Nonlinear Functions (Ch. 8)
•Quadratic: Y=β0+β1X+β2X2+u=⇒∆Y
∆X≈β1+ 2β2X
•Logarithms:
–Linear-Log (Y∼ln X): 1%∆X→0.01β1∆Y
–Log-Linear (ln Y∼X): 1 unit ∆X→100β1%∆Y
–Log-Log (ln Y∼ln X): 1%∆X→β1%∆Y(Elasticity)
•Interaction: Y=β0+β1X1+β2X2+β3(X1×X2)
Effect of X1=β1+β3X2
1
