n　多元回归估计与假设检验

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1、1第4章　多元回归分析:估计与假设检验MultipleRegressionAnalysisy=b0+b1x1+b2x2+...bkxk+uEstimationandInference2ParallelswithSimpleRegressionYi=b0+b1Xi1+b2Xi2+...bkXik+uib0isstilltheinterceptb1tobkallcalledslopeparameters,alsocalledpartialregressioncoefficientsandanycoefficientbjdenotethechangeofYwiththecha

2、ngesofXjasalltheotherindependentvariablesfixed.uisstilltheerrorterm(ordisturbance)Stillminimizingthesumofsquaredresiduals,sohavek+1firstorderconditions3ObtainingOLSEstimates4ObtainingOLSEstimates,cont.TheaboveestimatedequationiscalledtheOLSregressionlineorthesampleregressionfunction(SRF)

3、theaboveequationistheestimatedequation,isnotthereallyequation.Thereallyequationispopulationregressionlinewhichwedon’tknow.Weonlyestimateit.So,usingadifferentsample,wecangetanotherdifferentestimatedequationline.Thepopulationregressionlineis5InterpretingMultipleRegression6AnExample(Wooldri

4、dge,p76)Thedeterminationofwage(dollarsperhour),wage:Yearsofeducation,educYearsoflabormarketexperience,experYearswiththecurrentemployer,tenureTherelationshipbtw.wageandeduc,exper,tenure:wage=b0+b1educ+b2exper+b3tenure+uTheestimatedequationasbelow:wage=-2.873+0.599educ+0.022exper+0.169tenu

5、re7A“PartiallingOut”Interpretation8A“PartiallingOut”Interpretation9“PartiallingOut”continuedPreviousequationimpliesthatregressingYonX1andX2givessameeffectofX1asregressingYonresidualsfromaregressionofX1onX2ThismeansonlythepartofXi1thatisuncorrelatedwithXi2arebeingrelatedtoYi,sowe’reestima

6、tingtheeffectofX1onYafterX2hasbeen“partialledout”10ThewagedeterminationsTheestimatedequationasbelow:wage=-2.873+0.599educ+0.022exper+0.169tenureNow,wefirstregresseduconexperandtenuretopatialouttheexperandtenure’seffects.Thenweregresswageontheresidualsofeduconexperandtenure.Whetherwegetth

7、esameresult.?educ=13.575-0.0738exper+0.048tenuredenoteresidualsresidwage=5.896+0.599residWecanseethatthecoefficientofresidisthesameofthecoefficienofthevariableeducinthefirstestimatedequation.Soisinthesecondequation.11Goodness-of-Fit:R212Goodness-of-Fit13Goodness-of-Fit(co