拟合值与残差课件.ppt

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1、AnalysisofCrossSectionandPanelDataYanZhangSchoolofEconomics,FudanUniversityCCER,FudanUniversityIntroductoryEconometricsAModernApproachYanZhangSchoolofEconomics,FudanUniversityCCER,FudanUniversityAnalysisofCrossSectionandPanelDataPart1.RegressionAnalysisonCrossSectionalDataChap

2、2.TheSimpleRegressionModel——PracticeforlearningmultipleRegressionBivariatelinearregressionmodel:theslopeparameterintherelationshipbetweenyandxholdingtheotherfactorsinufixed;itisofprimaryinterestinappliedeconomics.:theinterceptparameter,alsohasitsuses,althoughitisrarelycentralto

3、ananalysis.MoreDiscussion:Aone-unitchangeinxhasthesameeffectony,regardlessoftheinitialvalueofx.Increasingreturns:wage-education(f.form)Canwedrawceterisparibusconclusionsabouthowxaffectsyfromarandomsampleofdata,whenweareignoringalltheotherfactors?Onlyifwemakeanassumptionrestrict

4、inghowtheunobservablerandomvariableuisrelatedtotheexplanatoryvariablexClassicalRegressionAssumptionsFeasibleassumptioniftheintercepttermisincludedLinearlyuncorrelatedzeroconditionalexpectationMeaning=内生性PRF(PopulationRegressionFunction):sth.fixedbutunknownOLSMinimizeuusamplereg

5、ressionfunction(SRF)ThepointisalwaysontheOLSregressionline.拟合值与残差PRF:OLSCoefficientofdeterminationthefractionofthesamplevariationinythatisexplainedbyx.thesquareofthesamplecorrelationcoefficientbetweenandLowR-squaredsUnitsofMeasurementIfoneofthedependentvariablesismultipliedbyth

6、econstantc—whichmeanseachvalueinthesampleismultipliedbyc—thentheOLSinterceptandslopeestimatesarealsomultipliedbyc.Ifoneoftheindependentvariablesisdividedormultipliedbysomenonzeroconstant,c,thenitsOLSslopecoefficientisalsomultipliedordividedbycrespectively.Thegoodness-of-fitofth

7、emodel,R-squareds,shouldnotdependontheunitsofmeasurementofourvariables.FunctionFormLinearNonlinearLogarithmicdependentvariableAPercentagechangeiny,semi-elasticityanincreasingreturntoedu.Othernonlinearity:diplomaeffectBi-LogarithmicAaConstantelasticityChangeofunitsofmeasurementP

8、45,error:b0*＝b0+log(c1)-b1·log(c2)Bi-LogarithmicAaCons