cfa l2 correlation and regression讲义

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1、Reading11CorrelationandRegression32.CORRELATIONANALYSISScatterplotandcorrelationanalysisareusedtoCorrelationcoefficientmeasuresthedirectionandexaminehowtwosetsofdataarerelated.strengthoflinearassociationbetweentwovariables.Thecorrelationcoefficientbetweentwo

2、assetsXandY2.1ScatterPlotscanbecalculatedusingthefollowingformula:201=Ascatterplotgraphicallyshowstherelationship 
betweentwovaraibles.Ifthepointsonthescatterplot 
 clustertogetherinastraightline,

3、thetwovariables

haveastronglinearrelation.Observationsinthe=(
)()scatterplotarerepresentedbyapoint,andthepointsarenotconnected.or
(,)2.2&CorrelationAnalysis&Calculatingand=()()2.3InterpretingtheCorrelationCoefficientThesamplecovarianceisc

4、alculatedas:NOTE:∑−−

=UnlikeCovariance,Correlationhasnounitof−1measurement;itisasimplenumber.where,Example:n=samplesize=47.78=40=250Xi=ithobservationonvariableX=meanofthevariableXobservations47.78Yi=ithobservationonvariableY==

5、0.478=meanofthevariableYobservations40250·Thecovarianceofarandomvariablewithitselfis·Thecorrelationcoefficientcanrangefrom-1tosimplythevarianceofrandomvariable.+1.·Covariancecanrangefrom–to+.·Twovariablesareperfectlypositivelycorrelated·Thecovariancenu

6、mberdoesn’ttelltheinvestorififcorrelationcoefficientis+1.therelationshipbetweentwovariablese.g.returns·Ifcorrelationcoefficientis-1,thatmeanstheoftwoassets(XandY)isstrongorweak.Itonlytellsassetreturnshaveaperfectinverse(negative)thedirectionofthisrelationshi

7、p.Forexample,linearrelationshiptoeachother.oPositivenumberofcovarianceshowsthatrates·Whencorrelationcoefficientequals0,thereisofreturnoftwoassetsaremovinginthesamenolinearrelationshipbetweenthereturnsondirection:whentherateofreturnofassetXisthetwoassets.nega

8、tivethereturnsofotherassettendtobe·Thecloserthecorrelationcoefficientisto1,thenegativeaswellandviceversa.strongertherelationshipbetweenthereturnsofoNegativenumberofcovarianceshowsthatratestwoass