Normal Equations Proof

Normal Equations Proof - AGEC 317 Dr. Capps Fall 2008...

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Unformatted text preview: AGEC 317 Dr. Capps Fall 2008 Derivation of Ordinary Least Squares Estimators u x y i i i + + = 1 where y i is a dependent variable, x i is an independent right-hand side (RHS) variable, i u is the error term (unobservable), 1 and are coefficients. The ordinary least squares procedure minimizes the error sum of squares (SSE). The minimization problem is given as follows: b)- (1 ) ( 2 a)- (1 ) 1 ( 2 . . . ) , ( 1 ^ 1 ^ ^ 1 1 ^ 1 ^ ^ 2 1 ^ 1 ^ 1 2 ^ 1 ^ =- -- = =- -- = -- = = = = = = i n i i i n i i i n i i i n i i x x y SSE x y SSE C O F x y u SSE Minimize Step 1: Derive the OLS estimate of ) ( 1 ^ 1 ^ = -- = n i i i x y divide equation (1-a) by -2 1 1 ^ 1 1 ^ =-- = = = n i i n i n i i x y re-arrange = = =-- n i i n i i x n y 1 1 ^ 1 ^ divide both sides by n ....
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This note was uploaded on 12/02/2009 for the course STA 4210 taught by Professor Staff during the Spring '08 term at University of Florida.

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Normal Equations Proof - AGEC 317 Dr. Capps Fall 2008...

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