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1、CHPTER2ExploringMultivariateDataGraphically1.1IntroductionAccordingtoChambersetal.《GraphicalMethodsforDataAnalysis》,1983,“thereisnostatisticaltoolthatisaspowerfulasawell-chosengraph”.Certainlygraphicalpresentationhasanumberofadvantagesovertabulardisplaysofnu
2、mericalresults,notleastincreatinginterestandattractingtheattentionoftheviewer.Andgraphicalanalysisoftenprovidesthevehiclefordiscoveringtheunexpected.Duringthelasttwodecadesawidevarietyofnewmethodsfordisplayingdatagraphicallyhasbeendeveloped;thesewillhuntfors
3、pecialeffectsindata,indicateoutliers,identifypatterns,diagnosismodelsandgenerallysearchfornovelandperhapsunexpectedphenomena.Largenumbersofgraphsmayberequiredandcomputerswillgenerallybeneededtodrawthemforthesamereasonstheyareneededfornumericalanalysis,namely
4、thattheyarefastandtheyareaccurate.So,becausethemachineisdoingtheworkthequestionisnolonger“shallweplot?”butrather“whatshallweplot?”Therearemanyexcitingpossibilitiesincluding,ofcourse,dynamicgraphics(seeCleveland,W.S.andMcGill,M.E.,1987,《DynamicGraphicsforStat
5、istics》).Butexplorationmightbegin,atleast,withsomesimpler,well-knownmethods.Univariatemarginalviewsofmultivariatedatamight,forexample,beobtainedusingsimplehistograms,stem-and-leafplotsorbox-and-whiskerplots.Butvariable-by-variableexaminationofmultivariatedat
6、acannotrevealanyrelationshipsamongvariables.Consequently,abetterplacetobeginourdiscussionofgraphicalmethodsforsuchdataisthesimplescatterplot.1.1TheScatterplotThesimplexyscatterplothasbeeninusesinceatleastthe18thcenturyandhasmanyvirtues–indeed,accordingtoTuft
7、e,E.R.(《TheVisualDisplayofQuantitativeInformation》,1983)Therelationalgraphic–initsbarestformthescatterplotanditsvariants–isthegreatestofallgraphicaldesigns.Itlinksatleasttwovariables,encouragingandevenimploringtheviewertoassessthepossiblecasualrelationshipsb
8、etweentheplottedvariables.Itconfrontscasualtheoriesthatxcausesywithempiricalevidenceastotheactualrelationshipbetweenxandy.Table2.1Heights(mm)andages(years)ofbothpartnersinasampleof169marriedcoup
