商务统计全套配套课件[美]AmirD.AczelJayavelSounderpandian著谭英平等译Chap017.ppt

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1、COMPLETEBUSINESSSTATISTICSbyAMIRD.ACZEL&JAYAVELSOUNDERPANDIAN6thedition.Chapter17MultivariateAnalysisTheMultivariateNormalDistributionDiscriminantAnalysisPrincipalComponentsandFactorAnalysisUsingtheComputerMultivariateAnalysis17DescribeamultivariatenormaldistributionExplainwhenadiscriminantan

2、alysiscouldbeconductedInterprettheresultsofadiscriminantanalysisExplainwhenafactoranalysiscouldbeconductedDifferentiatebetweenprincipalcomponentsandfactorsInterpretfactoranalysisresultsLEARNINGOUTCOMES17Afterstudyingthischapter,youshouldbeableto:Ak-dimensional(vector)randomvariableX:X=(X1,X2,X3

3、...,Xk)Arealizationofak-dimensionalrandomvariableX:x=(x1,x2,x3...,xk)Ajointcumulativeprobabilitydistributionfunctionofak-dimensionalrandomvariableX:F(x1,x2,x3...,xk)=P(X1x1,X2x2,...,Xkxk)17-2TheMultivariateNormalDistributionTheMultivariateNormalDistributionf(x1,x2)x1x2PicturingtheBivariateNo

4、rmalDistributionInadiscriminantanalysis,observationsareclassifiedintotwoormoregroups,dependingonthevalueofamultivariatediscriminantfunction.X2X1Group1Group212LineLAsthefigureillustrates,itmaybeeasiertoclassifyobservationsbylookingatthemfromanotherdirection.Thegroupsappearmoreseparatedwhenview

5、edfromapointperpendiculartoLineL,ratherthanfromapointperpendiculartotheX1orX2axis.Thediscriminantfunctiongivesthedirectionthatmaximizestheseparationbetweenthegroups.17-3DiscriminantAnalysisGroup1Group2CCuttingScoreTheformoftheestimatedpredictedequation:D=b0+b1X1+b2X2+...+bkXkwherethebiarethedis

6、criminantweights.b0isaconstant.Theintersectionofthenormalmarginaldistributionsoftwogroupsgivesthecuttingscore,whichisusedtoassignobservationstogroups.ObservationswithscoreslessthanCareassignedtogroup1,andobservationswithscoresgreaterthanCareassignedtogroup2.Sincethedistributionsmayoverlap,someo

7、bservationsmaybemisclassified.Themodelmaybeevaluatedintermsofthepercentagesofobservationsassignedcorrectlyandincorrectly.TheDiscriminantFunctionDiscriminant'Repay''Assets''Debt''Famsize'.Group01Count1418SummaryofClassificationPuti