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Lecture 12 2010 - III SimpleRegression A Introduction B C D...

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1 III. Simple Regression. A. Introduction B. Population Regression Equation C. Sample Regression Equation D. Ordinary Least Squares E. Classical Regression Model. F. Properties of OLS Estimators ( BLUE ) G. Estimator for σ 2 H. Inference (we’ve done this before!) F. Properties of OLS Estimators What properties do we want for our estimators? What are we trying to describe? U d l d i Unbiased and Min. Variance Sampling Distribution Use expected values to determine Center: Variance: 1 1 ˆ [ ] E β β = 2 1 1 1 ˆ ˆ ( ) [ ( ) ] Var E β β β = CRMA # 6 : We assume that the disturbances are normally distributed. Linear combinations of normally distributed variables are also normally distributed. Y is a linear combination of u. OLS estimators linear combinations of Y. OLS estimators are normally distributed.
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