Lecture5_Part2

Lecture5_Part2 - SUNY at Albany - Department of Economics...

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Unformatted text preview: SUNY at Albany - Department of Economics Eco 320 Economic Statistics Regression Ordinary Least Squares 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 K K X X Y ... 1 1 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. 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 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 1 2 1 2 ) ... ( ) ( 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 ) ( ) ( ) ( ) ( 1 1 X Y 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( ) ( ) ( ) ( x N i i N i i i S Y X sample X X Y Y X X ) ( 1 1 X Y 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 2 1 2 1 1 ) , cov( ) ( ) ( ) ( ) ( 1 1 X Y SUNY at Albany - Department of Economics...
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Lecture5_Part2 - SUNY at Albany - Department of Economics...

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