Basic Econometrics - Lecture Notes 3m4px

Basic Econometrics PGDMB15(2014-16) Lecture 5 Notes

Consider the following simple linear regression equation: Yi = β1 + β2 Xi + ui Gauss-Markov Assumptions are the following: 1. The regression equation is linear in parameters (β 0 s). 2. X is non-random/non-stochastic (fixed in repeated samples) 3. Error term has zero mean: E(ui ) = 0 4. Error term is homoscedastic: E(u2i ) = σ 2 5. Zero autocorrelation between errors: Cov(ui , uj ) = E(ui uj ) = 0 where i 6= j 6. Zero covariance between u and X: Cov(u, X) = 0 7. No. of observations is greater than no of parameters to be estimated: n > k where k is the number of regressors including the intercept 8. Not all values of X are the same: V ar(X) > 0 Gauss-Markov theorem: Given the above assumptions OLS estimators are Best Linear Unbiased Estimators(BLUE).

R2 is a measure of goodness of fit (Also known as coefficient of determination) the following: • R2 lies between 0 and 1. • R2 = r2 Y,Yb • R2 is generally high in time-series data. • R2 is generally low in cross-sectional data. • R2 is most meaningful in OLS estimation with an intercept.(can lie outside [0, 1] interval if estimated without an intercept) • R2 from two different regression equations with different dependent variables cannot be compared. Excel output

(Yi − Y )2 [Total sum of sq with df = n − 1] P • ESS = (Ybi − Y )2 [Regression sum of sq with df = k − 1] ⇒ M S = • T SS =

P

1

ESS k−1

• RSS = • R2 =

P

ubi 2 =

P (Yi − Ybi )2 [Residual sum of sq with df = n − k] ⇒ M S =

ESS T SS

• Multiple R =

√ R2

• R2 = 1 − (1 − R2 )

n−1 n−k



• Standard error (SE)= σ b

2

RSS n−k

=σ b2