相关系数计算公式

相关系数计算公式相关系数计算公式StatisticalcorrelationcoefficientDuetothestatisticalcorrelationcoefficientusedmorefrequently,sohereistheuseofafewarticlesintroducethesecoefficients.Thecorrelationcoefficient:astudyoftwothings(inthedatawecallthedegreeofcorrelationbetweenthevariables).Iftherearetwovariables:X,Y,correlationcoefficientobtainedbythemeaningcanbeunderstoodasfollows:(1),whenthecorrelationcoefficientis0,XandYtwovariablerelationship.(2),whenthevalueofXincreases(decreases),Yvalueincreases(decreases),thetwovariablesarepositivecorrelation,correlationcoefficient(3),whenthevalueofXincreases(decreases),thevalueofYdecreases(increases),twovariablesarenegativelycorrelated,thecorrelationcoefficientbetween-1.00and0.Theabsolutevalueofthecorrelationcoefficientisbigger,strongercorrelations,thecorrelationcoefficientiscloseto1or-1,thehigherdegreeofcorrelation,thecorrelationcoefficientiscloseto0andthecorrelationisweak.Therelatedstrengthnormallythroughthefollowingrangeofjudgmentvariables:Thecorrelationcoefficient0.8-1.0strongcorrelation0.6-0.8strongcorrelation0.4-0.6mediumdegree.0.2-0.4weakcorrelation0.0-0.2veryweaklycorrelatedornotcorrelatedPearson(Pearson)correlationcoefficientPearsonisalsoknownasthecorrelation(orcorrelation)isakindofcalculationmethodofthelinearcorrelationofBritishstatisticianPearsonintwentiethCentury.SupposetherearetwovariablesX,Y,thenthePearsoncorrelationcoefficientbetweenthetwovariablescanbecalculatedbythefollowingformula:Aformula:Formulatwo:Formulathree:Formulafour:Fourequivalentformulaslistedabove,whereEisthemathematicalexpectation,covsaidthecovariance,Nrepresentsthenumberofvariables.2,scopeofapplicationWhenthetwovariablesofthestandarddeviationisnotzero,thecorrelationcoefficientisdefined,thecorrelationcoefficientforPearson:(1),isthelinearrelationshipbetweenthetwovariables,arecontinuousdata.(2)overall,twovariablesarenormallydistributed,ornearnormalunimodaldistribution.(3)andtheobservationvaluesoftwovariablesisinpairs,eachpairofobservationsareindependentofeachother.PearsoncorrelationcoefficientMatlab(accordingtotheformulafour):[cpp]viewplaincopyFunctioncoeff=myPearson(X,Y)%ofthefunctionoftherealizationofthePearsoncorrelationcoefficientcalculatingoperation%%X:numericalsequenceinput%Y:numericalsequenceinput%%output:%coeff:twoinputnumericalsequenceX,thecorrelationcoefficientofY%Error(two'numericalsequencedimensionisnotequalto');Coeff=fenzi/fenmu;End%myPearsonendfunctionCalculatethePearsoncorrelationcoefficientfunctioncanalsobeusedin[cpp]viewplaincopy4,referencecontentSpearmanRank(Spielmanrankcorrelationcoefficient)Instatistics,SpielmancorrelationcoefficientisnamedforCharlesSpearman,andoftenusetheGreeksymbol(rho)saiditsvalue.SpielmanrankcorrelationcoefficientisusedtoestimatethecorrelationbetweenthetwovariablesXandY,thecorrelationbetweenvariablescanbeusedtodescribethemonotonefunction.Ifthetwosetsoftwovariabledoesnothavethesametwoelements,so,whenoneofthevariablescanbeexpressedasamonotonefunctionwellwhenanothervariable(i.e.changesintwovariablesofthesametrend),betweenthetwovariablescanreach+1or-1.SupposethattworandomvariableswereX,Y(alsocanbeseenasasetoftwo),thenumberoftheirelementsareN,twoI(1<=i<=N)randomvariablestakevaluesrespectivelywithXi,Yisaid.SortofX,Y(atthesametimeasascendingordescending),tworankingelementssetX,y,Xi,YielementswhichareXiinXandYirankingintheYranking.ThecollectionofX,yelementsinthecorrespondingsubtractiontogetalistofdifferencesetD,di=xi-yi,1<=i<=N.SpielmanrankcorrelationcoefficientbetweenrandomvariablesXandYcanbeobtainedbyX,yorDcalculation,thecalculationmethodsareasfollows:ByrankingdifferencecalculatedfromDdiversity(formulaone):FromthetopsetX,calculatedfromY(SpielmanrankcorrelationcoefficientwerealsoconsideredafterrankingtworandomvariablesPearsoncorrelationcoefficient,thefollowingistheactualPearsoncalculatedthecorrelationcoefficientX,y)(formulatwo):Thefollowingisasetofelementsinthelistofexamplesofcalculation(calculatedonlyforSpielmanrankcorrelationcoefficient)Note:whenthetwovariablesofthesame,theirrankingisobtainedbytheaverageoftheirpositions.2,scopeofapplicationSpielmanrankcorrelationcoefficientofthedataconditionswithoutPearsoncorrelationcoefficientisstrict,aslongastheobservedvaluesoftwovariablesortransformedbycontinuousvariabledataleveldata,regardlessoftheoveralldistributionofthetwovariablesoftheform,thesizeofthesample,wecanuseSpielmancorrelationthecoefficientof.Asourceprogram:SpielmanrankcorrelationcoefficientMatlab(basedonrankingdifferencediversityDcalculatedusingtheaboveformula)[cpp]viewplaincopyFunctioncoeff=mySpearman(X,Y)%ofthefunctionusedtoachievecomputingSpielmanrankcorrelationcoefficient%%X:numericalsequenceinput%Y:numericalsequenceinput%%output:%coeff:twoinputnumericalsequenceX,thecorrela