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Introduction to Econometrics
Chapter 4
The linear regression model
The linear regression model (LRM)
LRM with an exogenous explanatory variable
The OLS estimator
Symbols in the LRM
LRM, averages
Unconditional expectation of the error term
Understanding the LRM
LRM: Interpretation of the OLS estimator
Fitted values and residuals in the LRM
LRM, simulation
The difference between the error term and the residual
The statistical formula for b2
The properties of the OLS estimator
When are the OLS estimators unbiased and consistent?
Homoscedasticity, heteroscedasticity and the Gauss-Markov assumptions
The variance of the OLS estimators
Estimating σ2
Estimating the variance of the OLS estimators
The Gauss-Markov theorem
Unbiasedness and consistency in the LRM
Proving that the slope OLS estimator is unbiased
Proving that the intercept OLS estimator is unbiased
Heteroscedasticity
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Chapter 4
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The difference between the error term and the residual
Problem
Show that
\[ε_i-e_i=b_1-β_1+x_i\left( b_2-β_2 \right)\]
Show solution
Solution
