05slides.pdf - Multiple Linear Regression Tyler Ransom Univ...

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MultipleLinearRegression TylerRansom UnivofOklahoma Jantwo.osfnine.osf,two.osfzero.osfone.osfnine.osf one.osf/two.osffour.osf
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Today’splan one.osf. Reviewreadingtopics one.osf.one.osf MultipleRegressionModel one.osf.two.osf FormulasforOLSEstimates one.osf.three.osf Interpretation two.osf. In-classactivity:Practicerunningmultiplelinearregressions two.osf/two.osffour.osf
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TheMultipleRegressionModel three.osf/two.osffour.osf
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MultipleRegression:What&Why - multipleregressionmodel = simpleregressionmodel,butwiththree.osfplus.osfvariables - Reasonsforhavingmorethantwoindependentvariables: one.osf. Betterchanceofuncoveringcausaleffects two.osf. Canbuildbettermodelsforpredicting y three.osf. Canincorporatemoreflexiblefunctionalformrelationships four.osf/two.osffour.osf
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MotivationforMultipleRegression - Consideranextensionofthe log ( wage ) equationweusedforsimple regression: log ( wage )= β zero.osf + β one.osf educ + β two.osf IQ + u where IQ isIQscore(inthepopulation,ithasameanofone.osfzero.osfzero.osfandsdequal.osfone.osffive.osf) - Primarilyinterestedin β one.osf ,but β two.osf isofsomeinterest,too. - IQ includedintheequation nolongerinerrorterm - If IQ proxiesintelligence,getsusclosertocausaleffectofschooling five.osf/two.osffour.osf
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Themodelwithtwo x ’s - Generally,wecanwriteamodelwithtwoindependentvariablesas y = β zero.osf + β one.osf x one.osf + β two.osf x two.osf + u , where: - β zero.osf istheintercept - β one.osf measuresthechangein y withrespectto x one.osf , holdingotherfactorsfixed - β two.osf measuresthechangein y withrespectto x two.osf , holdingotherfactorsfixed six.osf/two.osffour.osf
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Thekeyassumption - Asbefore,thekeyassumptionabouthow u isrelatedtothe x ’sis E ( u | x one.osf , x two.osf )= zero.osf - Foranyvaluesof x one.osf and x two.osf inthepopulation,theaverageunobservable = zero.osf - Inthewageequation,theassumptionis E ( u | educ , IQ )= zero.osf - Now u nolongercontainsintelligence(wehope),andsothisconditionhas abetterchanceofbeingtrue.
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