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1、Part1RegressionAnalysiswithCross-SectionalData2021/8/61DepartmentofStatistics-ZhaoliqinCh2TheSimpleRegressionModely=b0+b1x+u2021/8/62DepartmentofStatistics-Zhaoliqin2021/8/6DepartmentofStatistics-Zhaoliqin31MotivationforthelinearregressionmodelEconomicTheorysuggestsinter
2、estingrelationsbetweenvariables.Example1:ReturnstoeducationAmodelofhumancapitalinvestmentpredictsthatgettingmoreeducationshouldleadtohigherwages:Wages=f(Education).However,letuslookatadataset:USnationalsurveyofpeopleinthelabourforcethatalreadycompletedtheireducation,526p
3、eople.2021/8/6DepartmentofStatistics-Zhaoliqin42021/8/6DepartmentofStatistics-Zhaoliqin5Graphaboveshow:Peoplewiththesameyearsofeducationhavedifferenthourlywages.HowcanwestudyiftheevidenceofthedatasupportsEconomicTheory?2021/8/6DepartmentofStatistics-Zhaoliqin6Apossibilit
4、yistolookatmeansofwagesconditionalontheyearsofEducation.2021/8/6DepartmentofStatistics-Zhaoliqin72021/8/6DepartmentofStatistics-Zhaoliqin8Hence,weareinterestedinstudyingisthemeanofwagesgiventheyearsofEducationthatwillbedenotedasE[Wages
5、Education]Followingeconomictheory,w
6、eassumeaspecificmodelforE[Wages
7、Education]2021/8/6DepartmentofStatistics-Zhaoliqin9ApossiblemodelforE[Wages
8、Education]isalinearoneE[Wages
9、Education]=β0+β1Education,whereβ0andβ1areunknownparametersthatwewouldliketoestimate.β1isthechangeofthemean(expectedvalue)ofWagesforone
10、additionalyearofEducation.2021/8/6DepartmentofStatistics-Zhaoliqin10ThemodelcanbewritteninthemorefamiliareconometrictermsWages=β0+β1Education+u,ThismodelisknownasTheSimpleRegressionModel.Itislinearintheparametersβ0andβ1(andintheexplanatoryvariables).2021/8/6DepartmentofS
11、tatistics-Zhaoliqin11whereE[u
12、Education]=0.whyE[u
13、Education]?Meanthattheaveragelevelofabilityisthesameregardlessofyearsofeducation.Becausewewanttolearningeneralabouttheceterisparibuseffectofxony(causality).Soweshouldmakeanassumptionrestrictinghowtheunobservedvariableuisr
14、elatedtox.2021/8/6DepartmentofStatistics-Zhaoliqin122ASimpleAssumptionTheaveragevalueofu,theerrorterm,i
