chapter 6 linear regression and correlation：6章线性回归与相关

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1、Chapter6:LinearRegressionandCorrelationCHAPTER6LINEARREGRESSIONANDCORRELATIONPageContents6.1Introduction1006.2CurveFitting1006.3FittingaSimpleLinearRegressionLine1016.4LinearCorrelationAnalysis1056.5Spearman’sRankCorrelation109Exercise112Objectives:Inbusinessandeconomicapplications,frequentl

2、yinterestisinrelationshipsbetweentwoormorerandomvariables,andtheassociationbetweenvariablesisoftenapproximatedbypostulatingalinearfunctionalformfortheirrelationship.Afterworkingthroughthischapter,youshouldbeableto:(i)understandthebasicconceptsofregressionandcorrelationanalyses;(ii)determineb

3、oththenatureandthestrengthofthelinearrelationshipbetweentwovariables.113Chapter6:LinearRegressionandCorrelation6.1IntroductionThischapterpresentssomestatisticaltechniquestoanalyzetheassociationbetweentwovariablesanddeveloptherelationshipforprediction.6.2CurveFittingVeryofteninpracticearelati

4、onisfoundtoexistbetweentwo(ormore)variables.Itisfrequentlydesirabletoexpressthisrelationshipinmathematicalformbydetermininganequationconnectingthevariables.Toaidindetermininganequationconnectingvariables,afirststepisthecollectionofdatashowingcorrespondingvaluesofthevariablesunderconsideratio

5、n.linearnon-linearFigure1.Scatterdiagram113Chapter6:LinearRegressionandCorrelation6.3FittingaSimpleLinearRegressionLineTodeterminefromasetofdata,alineofbestfittoinfertherelationshipbetweentwovariables.6.3.1TheMethodofLeastSquaresFigure2.SampleobservationsandthesampleregressionlineDetermining

6、thelineof“bestfit”:byminimizing.Tominimize,weapplycalculusandfindthefollowing“normalequations”:Solve(1)and(2)simultaneously,wehave:Notes:113Chapter6:LinearRegressionandCorrelation1.Theformulaforcalculatingtheslopebiscommonlywrittenaswhichthenumeratoranddenominatorthenreducetoformulasandrespe

7、ctively;andisthey-interceptoftheregressionline.2.Whentheequationiscalculatedfromasampleofobservationsratherthanfromapopulation,itisreferredasasampleregressionline.Example1Supposeanappliancestoreconductsa5-monthexperimenttodeterminetheeffectofadvert