STAT1_004 Chapter 4.ppt

Chapter4 RegressionDiagnostics Section4 1 ExaminingResiduals 3 Objectives Reviewtheassumptionsoflinearregression Examinetheassumptionswithscatterplotsandresidualplots 4 AssumptionsforRegression 5 ScatterPlotofCorrectModel Y 3 0 0 5XR2 0 67 6 ScatterPlotofCurvilinearModel Y 3 0 0 5XR2 0 67 7 ScatterPlotofOutlierModel Y 3 0 0 5XR2 0 67 8 ScatterPlotofInfluentialModel Y 3 0 0 5XR2 0 67 9 VerifyingAssumptions 10 ExaminingResidualPlots 11 DetectingOutliers 12 StudentizedResidual Studentizedresiduals SR areobtainedbydividingtheresidualsbytheirstandarderrors Suggestedcutoffsareasfollows SR 2fordatasetswitharelativelysmallnumberofobservations SR 3fordatasetswitharelativelylargenumberofobservations 13 ThisdemonstrationillustratesproducingresidualplotsintheREGprocedure ResidualPlots Section4 2 InfluentialObservations 15 Objectives Usestatisticstoidentifypotentialinfluentialobservations 16 InfluentialObservations 17 DiagnosticStatistics FourstatisticsthathelpidentifyinfluentialobservationsareSTUDENTresidualCook sDRSTUDENTresidualDFFITS 18 Cook sDStatistic Cook sDstatisticisameasureofthesimultaneouschangeintheparameterestimateswhenanobservationisdeletedfromtheanalysis Asuggestedcutoffis wherenisthesamplesize Iftheaboveconditionistrue thentheobservationmighthaveanadverseeffectontheanalysis 19 RSTUDENT 20 DFFITS DFFITSimeasurestheimpactthattheithobservationhasonthepredictedvalue istheithpredictedvalue istheithpredictedvaluewhentheithobservationisdeleted isthestandarderroroftheithpredictedvalue 21 Thisdemonstrationillustratesobtainingparameterestimates testingforstatisticalsignificanceofthemodel andexaminingtheinfluenceofindividualobservations LookingforInfluentialObservations 22 HowtoHandleInfluentialObservations Recheckthedatatoensurethatnotranscriptionordataentryerrorshaveoccurred Ifthedataisvalid onepossibleexplanationisthatthemodelisnotadequate Amodelwithhigherorderterms suchaspolynomialsandinteractionsbetweenthevariables mightbenecessarytofitthedatawell Section4 3 Collinearity 24 Objectives Determineifcollinearityexistsinamodel Generateoutputtoevaluatethestrengthofthecollinearityandwhatvariablesareinvolvedinthecollinearity Determinemethodstominimizecollinearityinamodel 25 AModelwithNoCollinearity ModelR2 0 37X1 p value 0 0001X2 p value 0 0001 Error Collinearity 26 CollinearPredictorsinMultipleRegression ModelR2 7492Performance p value 4272Runtime p value 5622rPerformance Runtime 0 98841 Error Collinearity Oxygen Consumption 55 37940 0 85780 Performance 1 40429 Runtime 27 Thisdemonstrationillustratestheadverseeffectsofcollinearity ExampleofCollinearity 28 CollinearityDiagnostics PROCREGoffersthesetoolsthathelpquantifythemagnitudeofthecollinearityproblemsandidentifythesubsetofXsthatiscollinear VIFCOLLINCOLLINOINT 29 VarianceInflationFactor VIF TheVIFisarelativemeasureoftheincreaseinthevariancebecauseofcollinearity Itcanbethoughtofastheratio AVIFi 10indicatesthatcollinearityisaproblem 30 COLLINandCOLLINOINTOptions Bothoptionsgenerateconditionindicesandvarianceproportionstatistics TheCOLLINoptionincludestheintercept TheCOLLINOINTisadjustedfortheintercept 31 COLLINGuidelines Conditionindexvaluesbetween10and30suggestweakdependenciesbetween30and100indicatemoderatedependenciesgreaterthan100indicatestrongcollinearity 32 VarianceProportions Thosepredictorswithvarianceproportionsgreaterthan0 50associatedwithalargeconditionindexidentifysubsetsofcollinearpredictors 33 COLLINOINTGuidelines TherearenopublishedguidelinesfortheCOLLINOINToptionstatistics However usingtheCOLLINguidelinesinconjunctionwiththeCOLLINOINTstatisticsenablesyoutoevaluatetheseverityofthecollinearityadjustingouttheintercept 34 Thisdemonstrationillustratesapplyingcollinearitydiagnosticstoassessthemagnitudeoftheproblemandidentifythetermsinvolvedintheproblem CollinearityDiagnostics 35 GuidelinesforEliminatingTerms DeterminethesetofXsinvolvedincollinearityusingthevariancepro