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1、第二章 多元回归分析:估计y=b0+b1x1+b2x2+...bkxk+u1MultipleRegressionAnalysisy=b0+b1x1+b2x2+...bkxk+u1.Estimation2ParallelswithSimpleRegressiony=b0+b1x1+b2x2+...bkxk+ub0isstilltheinterceptb1tobkallcalledslopeparametersuisstilltheerrorterm(ordisturbance)Stillneedtomakeazeroconditionalmeanassu
2、mption,sonowassumethatE(u
3、x1,x2,…,xk)=0Stillminimizingthesumofsquaredresiduals,sohavek+1firstorderconditions3ObtainingOLSEstimates4ObtainingOLSEstimates,cont.TheaboveestimatedequationiscalledtheOLSregressionlineorthesampleregressionfunction(SRF)theaboveequationistheestimatedequa
4、tion,isnotthereallyequation.Thereallyequationispopulationregressionlinewhichwedon’tknow.Weonlyestimateit.So,usingadifferentsample,wecangetanotherdifferentestimatedequationline.ThepopulationregressionlineisOLSinterceptestimateOLSslopeestimates5InterpretingMultipleRegression6AnExa
5、mple(Wooldridge,p76)Thedeterminationofwage(dollarsperhour),wage:Yearsofeducation,educYearsoflabormarketexperience,experYearswiththecurrentemployer,tenureTherelationshipbtw.wageandeduc,exper,tenure:wage=b0+b1educ+b2exper+b3tenure+ulog(wage)=b0+b1educ+b2exper+b3tenure+uTheestimate
6、dequationasbelow:wage=-2.873+0.599educ+0.022exper+0.169tenurelog(wage)=0.284+0.092educ+0.0041exper+0.022tenureTheSTATAcommandUse[path]wage1.dta(insheetusing[path]wage1.raw/wage1.txt)RegwageeducexpertenureReglwageeducexpertenure7A“PartiallingOut”Interpretation8“PartiallingOut”con
7、tinuedPreviousequationimpliesthatregressingyonx1andx2givessameeffectofx1asregressingyonresidualsfromaregressionofx1onx2Thismeansonlythepartofxi1thatisuncorrelatedwithxi2arebeingrelatedtoyisowe’reestimatingtheeffectofx1onyafterx2hasbeen“partialledout”9ThewagedeterminationsTheesti
8、matedequationasbelow:wage=-2.873+0.599educ+0.022exper+0.169tenurelog(wage)=0.284+0.092educ+0.0041exper+0.022tenureNow,wefirstregresseduconexperandtenuretopatialouttheexperandtenure’seffects.Thenweregresswageontheresidualsofeduconexperandtenure.Whetherwegetthesameresult.?educ=13.
9、575-0.0738exper+0.048tenurewage=5.896+0.599resi
