Correlation and Regression_111893

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1、Measureofassociation:CorrelationMeasuresofassociationaredescriptivestatisticsthatquantifythestrengthoftheassociationorrelationshipbetweenanindependentvariableandadependentvariable.However,thereisnocleardistinctionbetweentheindependentanddependentvariables.We

2、simplystatethattwovariablesarecorrelatedwitheachother.Examples:smokingandlungcancer;incomeandeducation;studyhoursandgradesMeasureofassociation:correlationCorrelationanswersthreequestionsabouttherelationshipbetweentwovariables:Whetherornotarelationshipexists

3、HowstrongistherelationshipWhatisthedirectionorpatternoftherelationshipMostmeasuresofassociationcanhaveavaluebetween–1and0and0and+1.PearsonrcorrelationcoefficientThePearsonrcorrelationcoefficientisameasureofassociationfortwointervallevelvariables.Itassumestha

4、tbothvariablesarenormallydistributedandlinearlyrelated.TheexistenceofarelationshipAvalueofzeroindicatedthatthereisnorelationshipbetweenthevariables.Conversely,ifthereisarelationshipbetweenthevariable,themeasurewillhaveavaluelessthanzeroorgreaterthanzero.Thest

5、rengthofarelationshipHigherpositivevalues(uptoamaximumof+1)andlowernegativevalues(uptoaminimumof–1)indicatestrongerrelationships.Thefollowingtableprovidesaframeworkfordescribingthestrengthofthemeasureofassociation:MeasureofAssociationDescriptiveAdjective>0.00

6、to0.20;<-0.00to–0.20Veryweakorverylow>0.20to0.40;<-0.20to–0.40Weakorlow>0.40to0.60;<-0.40to–0.60Moderate>0.60to0.80;<-0.60to–0.80Strongorhigh>0.80to1.0;<-0.80to–1.0VeryhighorverystrongThedirectionofarelationshipIfthemeasureofassociationisapositivenumber,therei

7、sadirectorpositiverelationshipbetweenthedatavaluesofthevariables.Ifthemeasureofassociationisanegativenumber,thereisaninverseornegativerelationshipbetweenthedatavaluesofthevariables.ScatterplotsandcorrelationTestingthesignificanceofacorrelationcoefficientH0:r=

8、0Ha:r≠0;r<0orr>0CorrelationmatrixexampleInthediagonalline,perfectcorrelations(r=1)betweenthetwosamevariablesarepresented.Thep-valueofthecoefficientsareoftennotedthiswayusin