Wk3 Regression Theory

# Wk3 Regression Theory - t est t he over al l si gni f i...

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I nt r oduct i on t o Economet r i cs Spr i ng 2010 Wk3. Theor y and Pr act i ce of Li near Regr essi on

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Goodness- of - f i t , R 2
TSS = ESS + RSS or R 2 = ESS / TSS = 1 – RSS / TSS wher e ESS i s expl ai ned sum of squar es, TSS i s t ot al sum of squar es and RSS i s ( unexpl ai ned) r esi dual sum of squar es. The R 2 can be i nt er pr et ed as t he f r act i on of sampl e var i at i on i n Y t hat i s expl ai ned by X Al so, not e t hat

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Mor e i n R- squar ed The adj ust ed R- squar ed i s To t est t he over al l si gni f i cance of

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Unformatted text preview: t est t he over al l si gni f i cance of t he r egr essi on i s equi val ent t o t est i ng whet her R 2 = To per f or m t hi s, f i nd F 1) TSS/( ) RSS/( 1 2---= n k n R wher e k i s t he number of coef f i ci ent s i ncl udi ng t he const ant Assumpt i ons of OLS The Gauss- Mar kov Theor em • Gi ven our assumpt i ons, i t can be shown t hat OLS i s “ BLUE” • Best • Li near • Unbi ased • Est i mat or • Thus, i f t he assumpt i ons hol d, OLS i s cool ^^...
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