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CHAPTER17

ModelBuildingtoaccompanyIntroductiontoBusinessStatisticsfourthedition,byRonaldM.WeiersPresentationbyPriscillaChaffe-Stengel

DonaldN.Stengel ?2002TheWadsworthGroupChapter17-LearningObjectivesBuildpolynomialregressionmodelstodescribecurvilinearrelationshipsApplyqualitativevariablesrepresentingtwoorthreecategories.Uselogarithmictransformsinconstructingexponentialandmultiplicativemodels.IdentifyandcompensateformulticollinearityApplystepwiseregressionSelectthemostsuitableamongcompetingmodels?2002TheWadsworthGroupPolynomialModelswithOneQuantitativePredictorVariableSimplelinearregressionequation:Equationforsecond-orderpolynomialmodel:Equationforthird-orderpolynomialmodel:Equationforgeneralpolynomialmodel:?2002TheWadsworthGroupPolynomialModelswithTwoQuantitativePredictorVariablesFirst-ordermodelwithnointeraction:First-ordermodelwithinteraction:Second-ordermodelwithnointeraction:Second-ordermodelwithinteraction:?2002TheWadsworthGroupModelswithQualitativeVariablesEquationforamodelwithacategoricalindependentvariablewithtwopossiblestates:wherestate1isshownx=1wherestate2isshownx=0Equationforamodelwithacategoricalindependentvariablewiththreepossiblestates:wherestate1isshownx1

=1,x2=0wherestate2isshownx1

=0,x2=1Wherestate3isshownx1

=0,x2=0?2002TheWadsworthGroupModelswithDataTransformationsExponentialModel:Generalequationforanexponentialmodel:Correspondinglinearregressionequationforanexponentialmodel:MultiplicativeModel:Generalequationforamultiplicativemodel:Correspondinglinearregressionequationforamultiplicativemodel:?2002TheWadsworthGroupExample,Problem17.8InternationalDataCorporationhasreportedthefollowingcostspergigabyteofharddrivestoragespaceforyears1995through2000.Usingx=1through6torepresentyears1995through2000,fitasecond-orderpolynomialmodeltothedataandestimatethecostpergigabytefortheyear2008. Theregressionequation willhavetheform:Yearx=Yry=Cost19951$261.8419962137.941997369.681998429.301999513.09200066.46?2002TheWadsworthGroupExample,Problem17.8,cont. MicrosoftExcelOutput?2002TheWadsworthGroupSUMMARYOUTPUTRegressionStatisticsMultipleR0.99655892RSquare0.99312968AdjRSquare0.98854948StandardError10.5650522Observations6Example,Problem17.8,cont. MicrosoftExcelOutput

Theregressionequationis:?2002TheWadsworthGroupCoefficientsStandardErrortStatP-valueIntercept387.99318.899339920.5294470.0002527x-147.6567512.3644646-11.942030.0012629x^214.18839291.729112558.20559240.0037879Example,Problem17.8,cont.Toestimatethecostpergigabytefortheyear2008,evaluatewhenx=14.

Sothecostpergigabytein2008isestimatedtobe$1101.99.Doesthismakesense?Ofcoursenot.Explanation:Althoughthepolynomialequationprovidesagoodfitforthedataduringtheperiod1995-2000,thisformisnotappropriatetoextrapolatethedataoutto2008.?2002TheWadsworthGroupExample,Problem17.32AnexponentialmodelwillprobablybemoreappropriatetothedatausedinProblem17.8.?2002TheWadsworthGroupyLogyx$261.842.4180361137.942.13969269.681.843108329.301.466868413.091.1169456.460.8102336Example,Problem17.32,cont. MicrosoftExcelOutput?2002TheWadsworthGroupSUMMARYOUTPUTRegressionStatisticsMultipleR0.998899423RSquare0.997800057AdjRSquare0.997250071StandardError0.03222401Observations6Example,Problem17.32,cont. MicrosoftExcelOutput

Theregressionequationis:?2002TheWadsworthGroupCoefficientsStandardErrortStatP-valueIntercept2.7808299850.0299989292.697678.12E-08x-0.328100280.00770301-42.59381.82E-06Example,Problem17.32,cont.Forx=14,Basedontheexponentialmodel,thecostpergigabytein2008willbe$0.0154,orjustunder2cents.?2002TheWadsworthGroupExample,Problem17.27Anefficiencyexperthasstudied12employeeswhoperformsimilarassemblytasks,recordingproductivity(unitsperhour),numberofyearsofexperience,andwhichoneofthreepopularassemblymethodstheindividualhaschosentouseinperformingthetask.Giventhedata,shownonthenextslide,determinethelinearregressionequationforestimatingproductivitybasedontheothervariables.Foranyqualitativevariablesthatareused,besuretospecifythecodingstrategyeachwillemploy.?2002TheWadsworthGroupExample,Problem17.27,cont.

?2002TheWadsworthGroupWorkerProd.Yrs.ExpMethodWorkerProd.Yrs.ExpMethod1757A79712B28810C88510C3914B910212C4935B109313A59511C1111212B6773A128614AExample,Problem17.27,cont.Theequationforamodelwithonequantitativevariableandacategoricalindependentvariablewiththreepossiblestatesis:wherex1representstheyearsofexperiencewherestate1isshownx2

=1ifmethodAisused,

0ifotherwisewherestate2isshownx3

=1ifmethodBisused,

0ifotherwisewherestate3isshownx2

=0andx3=0ifmethodCisused.?2002TheWadsworthGroupExample,Problem17.27,cont.Sothedatatobeanalyzedare:?2002TheWadsworthGroupWorkeryx1x2x317571028810003914014935015951100677310Example,Problem17.27,cont.

?2002TheWadsworthGroupWorkeryx1x2x379712018851000910212001093131011112120112861410Example,Problem17.27,cont. MicrosoftExcelOutput?2002TheWadsworthGroupSUMMARYOUTPUTRegressionStatisticsMultipleR0.86075031RSquare0.74089109AdjRSquare0.64372525StandardError6.0861957Observations

12Example,Problem17

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