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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 Yhat 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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 Spring '11
 Chan
 Economics

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