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Lecture5_Part2 - Ordinary Least Squares SUNY at Albany...

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SUNY at Albany - Department of Economics Eco 320 Economic Statistics • Regression Ordinary Least Squares
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SUNY at Albany - Department of Economics Eco 320 Economic Statistics • Regression A. The purpose of regression analysis is to take a purely theoretical population equation like: B. and use a set of sample data to obtain an estimated equation like: C. where each “hat” indicates a sample estimate of true population value and “ Y - hat” is the sample estimate of E ( Y | X s) . K K X X Y ... 1 1 0 K K X X Y ˆ ... ˆ ˆ ˆ 1 1 0
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SUNY at Albany - Department of Economics Eco 320 Economic Statistics • Regression 1. What does OLS attempt to do? A. Ordinary Least Squares ( OLS ) is an estimation technique used to obtain numerical values for the coefficients of an otherwise completely theoretical regression equation. Thus, OLS is an estimator, and a produced by OLS is an estimate of the population coefficient. ˆ
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SUNY at Albany - Department of Economics Eco 320 Economic Statistics • Regression 2. How does OLS work? A. OLS selects the so as to minimize the sum of the squared residuals: s ˆ N i iK K i i i N i i i N i i X X X Y Y Y e 1 2 2 2 1 1 0 1 2 1 2 ) ˆ ... ˆ ˆ ˆ ( ) ˆ (
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SUNY at Albany - Department of Economics Eco 320 Economic Statistics • Regression 2. How does OLS work? (continued) B. OLS estimators for simple regression : N i i N i i i X X Y Y X X 1 2 1 1 ) ( ) ( ) ( ˆ ) ( 1 1 0 X Y
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SUNY at Albany - Department of Economics Eco 320 Economic Statistics • Regression 2. How does OLS work? (continued) B. OLS estimators for simple regression : 2 1 2 1 1 ) , cov( ) ( ) ( ) ( ˆ x N i i N i i i S Y X sample X X Y Y X X ) ( 1 1 0 X Y
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SUNY at Albany - Department of Economics Eco 320 Economic Statistics • Regression 2. How does OLS work? (continued) B. OLS estimators for simple regression : X Y S Y X sample X X Y Y X X x N i i N i i i 1 0 2 1 2 1 1 ˆ ˆ ) , cov( ) ( ) ( ) ( ˆ ) ( 1 1 0 X Y
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SUNY at Albany - Department of Economics Eco 320 Economic Statistics • Regression 2. How does OLS work? (continued) C.
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