Bruderl Applied Regression Analysis Using Stata 2005.pdf

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1、AppliedRegressionAnalysisUsingSTATAJosefBrüderlRegressionanalysisisthestatisticalmethodmostoftenusedinsocialresearch.Thereasonisthatmostsocialresearchersareinterestedinidentifying”causal”effectsfromnon-experimentaldata.Regressionisthemethodfordoingthis.Theterm,,Regression“:1889Si

2、rFrancisGaltoninvestigatedtherelationshipbetweenbodysizeoffathersandsons.Therebyhe”invented”regressionanalysis.HeestimatedSs85.70.56SF.Thismeansthatthesizeofthesonregressestowardsthemean.Therefore,henamedhismethodregression.Thus,thetermregressionstemsfromthefirstapplicationofth

3、ismethod!Inmostlaterapplications,however,thereisnoregressiontowardsthemean.1a)TheIdeaofaRegressionWeconsidertwovariables(Y,X).Dataarerealizationsofthesevariablesy1,x1,…,yn,xnresp.yi,xi,fori1,…,n.Yisthedependentvariable,Xistheindependentvariable(regressionofYonX).Thegeneral

4、ideaofaregressionistoconsidertheconditionaldistributionfYy

5、Xx.Thisishardtointerpret.Themajorfunctionofstatisticalmethods,namelytoreducetheinformationofthedatatoafewnumbers,isnotfulfilled.Thereforeonecharacterizestheconditionaldistributionbysomeofitsaspects:AppliedRegressionAn

6、alysis,JosefBrüderl2•Ymetric:conditionalarithmeticmean•Ymetric,ordinal:conditionalquantile•Ynominal:conditionalfrequencies(crosstabulation!)Thus,wecanformulatearegressionmodelforeverylevelofmeasurementofY.RegressionwithdiscreteXInthiscasewecomputeforeveryX-valueanindexnumberofthe

7、conditionaldistribution.Example:IncomeandEducation(ALLBUS1994)Yisthemonthlynetincome.Xishighesteducationallevel.Yismetric,sowecomputeconditionalmeansEY

8、x.Comparingthesemeanstellsussomethingabouttheeffectofeducationonincome(varianceanalysis).Thefollowinggraphisthescattergramofth

9、edata.Sinceeducationhasonlyfourvalues,incomevalueswouldconcealeachother.Therefore,valuesare”jittered”forthisgraph.Theconditionalmeansareconnectedbyalinetoemphasizethepatternofrelationship.NurVollzeit,unter10.000DM(N=1459)10000800060004000EinkommeninDM20000HauptRealAbiturUniBildun

10、gAppliedRegressionAnalysis,JosefBrüderl3