PPT OLS - Derivation of Ordinary Linear Square Estimators i...

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Unformatted text preview: Derivation of Ordinary Linear Square Estimators i i i y x = + + (the subscript could denote time; A factor model for then it is a time series) : i y are the regressors (factors), and and are the regression coefficients that need to be estimated. are random noise, or regarded as a residual error. The hats are used to denote estimates. Minimi i i x ( ) 2 2 1 1 ze the sum of squares of the "residual" or "error": n n i i i i i SSR y x = = = =-- ( ) ( ) 2 2 1 1 1 1 1 1 1 2 ( 1) So 1 1 Let and be the sample means. Then n n i i i i i n i i i n n i i i i n n i i i i Minimize SSR y x SSR y x y n x y y x x n n y x = = = = = = = = =-- =--- = -- = = = =- ( ) 1 2 1 1 1 1 1 2 1 1 1 1 1 2 ( ) So Previously we have: 1 1 1 Multiply by : Subtract to g n i i i i n n n i i i i i i i n n i i i i n n n n n i i i i i i i i i i SSR y x x x y x x y n x x x y x x n n n = = = = = = = = = = = =--- = -- = = + = + 1 1 1 2 2 1 1 et rid of : ( , ) var( )...
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This note was uploaded on 03/23/2012 for the course AMATH 541 taught by Professor Kk.t during the Winter '11 term at University of Washington.

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PPT OLS - Derivation of Ordinary Linear Square Estimators i...

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