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Chapter14:MorePowerfulStatisticalMethods
MultipleChoice
Ifyouarestudyingtheimpactoftrainingonsalespersonperformanceasindicatedonanexamtakenbysalespersonsattheendoftraining,salespersonsaleswouldbethe____________variable,andthesalespersonexamscorewouldbethe_____________variable.
a. criterion,predictor
b. covariate,independent
c. independent,predictor
d. dependent,independent
e. covariate,dependent
Answer:d
Whichofthefollowingtechniquesrequiresthatbothvariablesareratioorintervaldata?
a. bivariateregression
b. ANOVA
c. ttest
d. Pearson’sproduct-momentcorrelation
e. Allareappropriate.
Answer:a
Thepercentageoftotalvariationinthedependentvariablethatisdescribedbytheindependentvariableisexpressedby_________.
a. coefficientofdetermination
b. correlationcoefficient
c. coefficientofcovariation
d. regressioncoefficient
e. noneofthese
Answer:a
Inaregressionequation,saleswouldtypicallybethe______________variable.
a. independent
b. coefficient
c. dependent
d. noneofthese
Answer:c
____________isthemathematicaltechniqueforfittingalinethatbestdescribestherelationshipbetweentwovariables.
a. Pearson’sproduct-momentcorrelation
b. Leastsquaresprocedure
c. Chi-squaretest
d. Significancetest
e. noneofthese
Answer:b
Aregressionequationthatestimatesthenumberofhoursofstudythatimpactatestscorewouldmostlikelyproducewhattypeofrelationship?
a. positive
b. negative
c. curvilinear
d. noneofthese
Answer:a
Researchonfearappealinadvertisingsuggeststhatamoderateamountoffearismosteffectiveatachievingpersuasion.Thatis,usingnotenoughfearortoomuchfearinadvertisingwillnotbeeffective.Thisisanexampleofwhattypeofrelationshipthatregressionmightfind?
a. positivelinear
b. negativelinear
c. curvilinear
d. norelationship
e. noneofthese
Answer:c
Whichofthefollowingistheappropriatetechniqueforcorrelationanalysis,whichinvolvesmetric(intervalorratio)data?
a. Spearman’srank-ordercorrelation
b. Jensen’sanalysisofcovariance
c. Kendall’scoefficientofconcordance
d. Pearson’sproduct-momentcorrelation
e. Edward’smetricanalysis
Answer:d
Whatarethepossiblevaluesincorrelationanalysis?
a. 0to1
b. -1to+1
c. -1to0
d. -.99to+.99
e. -∞to+∞
Answer:b
Whentwovariablesarenotcorrelatedatall,thecorrelationcoefficientwouldbe_______.
a. -1
b. 0
c. 1
d. -∞
e. +∞
Answer:b
Whentwovariablesareperfectlypositivelycorrelated,thecorrelationcoefficientwouldbe_______.
a. -1
b. 0
c. 1
d. -∞
e. +∞
Answer:c
Theexplainedvariationbytheregressionisreferredtoasthe:
a. totalvariation.
b. bivariate.
c. sumofsquaresduetoregression.
d. noneofthese
Answer:c
IfamarketerwantstocorrelateanordinalrankingofTVsetswiththenominalscalevariablegender,themarketerwouldhavetouse_____________.
a. ANOVA
b. Pearson’sproduct-momentcorrelation
c. z-test
d. chi-squaretest
e. noneofthese
Answer:e
Whichteststatisticisusedtotestthesignificanceoftheresultsofaregressionanalysis?
a. F
b. t
c. Z
d. chi-square
e. leastsquare
Answer:a
Inregression,thehigherthe_________value,themorelikelytherelationshipbetweenvariablesissignificant.
a. F
b. p
c. Z
d. t
e. noneofthese
Answer:a
Bivariateregressioncannotdemonstrate:
a. whenthetwovariablesarelinear.
b. whenthetwovariablesarestronglyinverselyrelated.
c. whenthetwovariablesarestronglypositivelyrelated.
d. whenthetwovariablesarecausallyrelated.
Answer:d
Correlationcannotdemonstrate:
a. whenthetwovariablesarelinear.
b. whenthetwovariablesarestronglyinverselyrelated.
c. whenthetwovariablesarestronglypositivelyrelated.
d. whenthetwovariablesarecausallyrelated.
Answer:d
AcorrelationanalysisbetweensalesandsalestrainingscoresresultsinR=+.98.Whichofthefollowingbestinterpretstherelationshipbetweensalesandsalestraining?
a. Exactly98%ofthesalespeopletakingthetesthavehighersales.
b. Thecorrelationbetweensalesandsalestrainingisveryweakandinsignificant.
c. Thecorrelationbetweensalesandsalestrainingisstrongandpositive,indicatingthathighersalestrainingscoresarecloselyassociatedwithhighersalesandvice-versa.
d. Exactly98%ofthevariationinsalesisexplainedbyvariationsinsalestrainingscores.
e. noneofthese
Answer:c
Whenthevalueofonevariableincreasesatexactlythesamerateasanothervariabledecreases,thisissaidtobea___________________relationship.
a. strongpositivelinear
b. positivelinear
c. perfectnegativelinear
d. parabolic
e. strongcurvilinearassociation
Answer:c
Inaregressionoutput,R2represents:
a. theindependentvariable.
b. thedependentvariable.
c. theestimatedslopeoftheregressionline.
d. thecoefficientofdetermination.
Answer:d
AnR2of.05wouldindicate:
a. asignificantrelationshipbetweenXandY.
b. anegativerelationshipbetweenXandY.
c. averyweakrelationshipbetweenXandY.
d. noneofthese
Answer:c
Inaregressionequation,whichsymbolrepresentsthedependentvariable?
a. Y
b. X
c. e
d. r
e. p
Answer:a
Whichofthefollowingisnotincludedintheequationforthecoefficientofdetermination?
a. explainedvariation
b. totalvariation
c. estimatedvariation
d. unexplainedvariation
Answer:c
___________arestatisticalmethodsofanalyzingtherelationshipbetweentwovariables.
a. Bivariatetechniques
b. Univariatetechniques
c. Multivariatetechniques
d. Noneofthese
Answer:a
Thedependentvariableisalsocalledthe__________________.
a. measure
b. criterion
c. principle
d. standard
e. predictor
Answer:b
_______________referstoanalysisisoneofstrengthofthelinearrelationshipbetweentwovariableswhenoneisconsideredtheindependentvariableandtheotherthedependentvariable
a. Multivariateregression
b. Univariateregression
c. Bivariateregression
d. Trivariateregression
e. Noneofthese
Answer:c
Whatisthevariationnotexplainedbytheregression?
a. Sumofsquaresduetoregression
b. Errorsumofsquares
c. NeithersumofsquaresduetoregressionorErrorsumofsquares
d. BothSumofsquaresduetoregressionandErrorsumofsquares
Answer:b
Thedegreetowhichchangesinonevariable(thedependentvariable)areassociatedwithchangesinanotheriswhichofthefollowing?
a. correlation
b. consideration
c. regression
d. association
e. noneofthese
Answer:a
Whatismultivariateanalysis?
a. aprocedureformanaginglargedatabasesystems.
b. synonymouswithdecisionsupportanalysis.
c. agroupofstatisticalproceduresusedtoanalyzesimultaneouslymultiplemeasurementsoftheindividualorobjectbeingmeasured.
d. themeasurementprocedureformonitoringhowseveralmarketingvariablesfunctioninmultiplemarketsituations.
Answer:c
Whichofthefollowingisaprocedurethatisusefulforanalyzingtherelationshipamongtwoormorepredictor/independentvariablesandonemetriccriterion/dependentvariable?
a. multiplediscriminantanalysis
b. multipleregressionanalysis
c. conjointanalysis
d. clusteranalysis
Answer:b
Whichofthefollowingwouldnotbeanapplicationbestsuitedformultipleregressionanalysis?
a. estimatingtherelationshipbetweenvariousdemographicandlifestylevariablesandtheattitudetowardaparticularproduct
b. determiningwhichvariablesbestpredictthesalesofaparticularproductorservice
c. estimatingtheeffectofseveralmarketingmixvariablesonproductsales
d. reducingalargenumberofpotentialpredictorvariablestoasmallersetofcompositevariables
Answer:d
Thecoefficientofdeterminationisnormallyassociatedwithwhichofthefollowingmultivariateprocedures?
a. multipleregressionanalysis
b. factoranalysis
c. conjointanalysis
d. clusteranalysis
Answer:a
Whichofthefollowingmultivariateproceduresdoesnotincludeadependentvariableinitsanalysis?
a. multipleregressionanalysis
b. clusteranalysis
c. multiplediscriminantanalysis
d. Alloftheseproceduresincludeadependentvariable.
Answer:b
Whichofthefollowingtechniquesmightbemostusefulinhelpingarestaurantdeterminehowtopositionitselfinthemarketplace?
a. factoranalysis
b. multipleregressionanalysis
c. conjointanalysis
d. perceptualmapping
Answer:d
Adependentvariableiscoded1=respondentdidpurchaseand0=respondentdidnotpurchase.Independentvariablesincludevariousdemographicandlifestylecharacteristicsoftherespondents.Thegoaloftheanalysisistodeterminehowrespondentswhodidpurchasearedifferentfromrespondentswhodidnotpurchase.Whichofthefollowingproceduresgoeswiththeprecedingdescription?
a. multiplediscriminantanalysis
b. multipleregressionanalysis
c. clusteranalysis
d. perceptualmapping
Answer:a
Acompanythatistryingtodeterminewhichthreedistincttargetmarketstofocusitsmarketingeffortsonmightusewhichstatisticaltool?
a. ANOVA
b. multipleregressionanalysis
c. clusteranalysis
d. bivariateregression
Answer:c
Clusteranalysisisparticularlyvaluableforwhattypeofmarketingstrategy?
a. productdifferentiation
b. positioning
c. segmentation
d. costleadership
Answer:c
Supposeananalystwantedtodeterminewhetherornotdollarsspentonadvertising,numberofsalespeople,numberofnewproductsintroduced,anddollarsspentonresearchanddevelopmentwerecontributingtothegrowthincompanymarketshare.Whichofthefollowingprocedureswouldbemostappropriate?
a. conjointanalysis
b. clusteranalysis
c. multipleregressionanalysis
d. perceptualmapping
Answer:c
Whichofthefollowingisnotastepinconjointanalysis?
a. collectingtrade-offdata
b. estimatingfactorloadings
c. estimatingpreferencestructures
d. predictingconsumers’choice
Answer:b
AninsurancecompanywantstoknowwhetherthesubscriberstoitsHMO,PPO,ortraditionalsingleindemnityplanexhibitbetterhealthcharacteristics.Theyhavethefollowingdataforeachoftheirsubscribers:%ofbodyweightoveroptimumweight;bloodpressure;cholesterolandhoursperweekofexercise.Theanalysiswillgroupsubscribersaseitherhealthy,somewhathealthyornothealthy.Whichofthefollowingwouldbethebestprocedureformakingsuchadetermination?
a. factoranalysis
b. multiplediscriminantanalysis
c. multipleregressionanalysis
d. clusteranalysis
Answer:d
Summarizinganumberofsurveyquestionsintoasingleconceptcouldbeachievedwithwhichtypeofanalysis?
a. factoranalysis
b. multiplediscriminantanalysis
c. multipleregressionanalysis
d. clusteranalysis
Answer:a
Whichofthefollowingtechniquesisoftenusedforconcepttestingofnewproducts?
a. conjointanalysis
b. multipleregressionanalysis
c. perceptualmapping
d. clusteranalysis
Answer:a
______________isameasureofthepercentageofthevariationinthedependentvariablethatisexplainedbythevariationintheindependentvariables.
a. Discriminantweights
b. Factorloadings
c. Coefficientofdetermination
d. Coefficientofcorrelation
Answer:c
Dummyvariablescreatedtoincludenominallyscaledvariablesinananalysisarecommonlyusedin:
a. multiplediscriminantanalysis.
b. factoranalysis.
c. conjointanalysis.
d. multipleregressionanalysis.
Answer:d
Independentvariablesareimportantcomponentsinmultipleregressionanalysisand________________.
a. multiplediscriminantanalysis
b. factoranalysis
c. conjointanalysis
d. clusteranalysis
Answer:a
Whichofthefollowingismultiplediscriminantanalysismostsimilarto?
a. multipleregressionanalysis
b. factoranalysis
c. conjointanalysis
d. clusteranalysis
Answer:a
Clusteranalysisproducesmutuallyexclusiveandexhaustivegroupssuchthattheindividualsorobjectsgroupedare______________withinand______________betweengroups.
a. homogeneous;heterogeneous
b. homogeneous;homogeneous
c. heterogeneous;homogeneous
d. heterogeneous;heterogeneous
Answer:a
Ifthegoalistoclassifybusinesstravelersintodistinctgroupsbasedontheirresponsesto20questionsonpreferencestomodeoftransportation,hotelaccommodation,andethnicfood,whichofthefollowingtechniqueswouldbemostappropriate?
a. multipleregressionanalysis
b. conjointanalysis
c. clusteranalysis
d. factoranalysis
Answer:c
Thepurposeoffactoranalysiscanbebestdescribedas:
a. datasimplificationbysummarizingtheinformationcontainedinalargenumberofvariablesintosummarymeasures.
b. presentingtherelationshipbetweenmultiplecategoricalmeasuresinalow-dimensionaldiagram.
c. assessingthesignificanceofgroupdifferencesacrossmanymetricdependentvariablessimultaneously.
d. assessingthedegreeofcorrelationofagroupofcategoricalmeasures.
Answer:a
Thisanalyticaltechniquehelpsdeterminewhatfeaturesanewproductorserviceshouldhaveandhowitshouldbepriced.
a. factoranalysis
b. perceptualmapping
c. multiplediscriminantanalysis
d. conjointanalysis
Answer:d
Infactoranalysis,thecorrelationbetweenfactorscoresandtheoriginalvariablesisknownasthefactor________.
a. loading
b. mapping
c. attributerating
d. conjoint
Answer:a
Allofthefollowingaretechniquesformultivariateanalysisprocedureexcept_____.
a. Clusteranalysis
b. Factoranalysis
c. Conjointanalysis
d. BivariateRegressionanalysis
Answer:d
Inthemultipleregressionformula,whichofthefollowingrepresentsthedependentvariable?
a. Y
b. a
c. b1
d. X1
Answer:a
Inthecaseofmultipleregressionanalysis,thedependentvariablemustbe___________;inmultiplediscriminantanalysis,thedependentvariableis__________innature.
a. metric;nonmetric
b. metric;nominal
c. nominal;categorical
d. categorical;nonmetric
Answer:b
AnadjustedR2correctsthecoefficientofdeterminationbasedontherelationshipbetweenthenumberofpredictorvariablesandwhichofthefollowing?
a. overallsamplesize
b. coefficientofcorrelation
c. regressionresults
d. population
Answer:a
Whichofthefollowingisnotanexampleofaclustertechnique?
a. K-means
b. Nearestneighbor
c. Decisiontrees
d. BIRCH
e. Alloftheseareexamples
Answer:e
Hadoop,anopen-sourceplatform,ismostcloselyrelatedtowhichofthefollowing?
a. FactorAnalysis
b. ClusterAnalysis
c. MultipleDiscriminantAnalysis
d. ConjointAnalysis
e. BigData
Answer:e
Whichofthefollowingisnotapartofusingpredictiveanalysis?
a. AcquiringaDataSet
b. Pre-processing
c. Modeling
d. ValidatingResults
e. Alloftheseareapart
Answer:e
True/False
Dependentvariablesarealsoknownaspredictorvariables.
Answer:False
Bivariatestatisticaltechniquesareoftenusedtoestablishcauseandeffectrelationshipsbetweentwoormorevariables.
Answer:False
Incorrelationanalysis,thecloserthevalueofRisto–1or+1,thestrongerthecorrelationbetweenthetwovariablesinquestion.
Answer:True
32. Aperfectcorrelationindicatesthattwovariablesarecausallyrelated.
Answer:False
AnR=-.95isalwaysweakerthan+.95,becausepositiverelationshipsaremoresignificantthannegativerelationships.
Answer:False
Inbivariateregression,boththeindependentanddependentvariablesaremeasuredintheformofnominaland/orordinaldata.
Answer:False
ThevariationexplainedbytheregressionequationiscalledSSRorsumofsquaresduetotheregression.
Answer:True
Theleastsquaresestimationprocedureoftenresultsinaperfectlystraightline.
Answer:False
TheR2statisticrangesfrom-1to1.
Answer:False
Thecoefficientofdeterminationisusedincorrelationanalysis.
Answer:False
Ascatterplotcomparesactualdatatoapredictedrelationshipbetweentwovariables.
Answer:True
AnR2of0indicatesnorelationshipbetweenvariables.
Answer:True
Onewaytostudytherelationshipbetweenthedependentandindependentvariableistoplotthedatainascatterdiagram.
Answer:True
Onewaytostudytherelationshipbetweenthedependentandindependentvariableistoplotthedatainabarchart.
Answer:False
Intheequationforregressionanalysis,theletterXrepresentstheindependentvariable.
Answer:True
ThecorrectformulafortheanalysisofvarianceusedtotestthesignificanceofresultsisF=MSR/MSE.
Answer:True
Inregression,theunexplainedvariationisreferredtoaserrorsumofsquares(SSE).
Answer:True
ThecoefficientofcorrelationdescribesthedegreeofassociationbetweenXandY.
Answer:True
Multivariatetechniquesanalyzerelationshipsbetweenmorethantwovariables.
Answer:True
Inmultipleregressionanalysisthedependentvariableisnominalorcategorical.
Answer:False
Ifthegoalofananalysisistogrouprespondentsintomutuallyexclusiveandcollectivelyexhaustivesubgroups,thepreferredprocedurewouldbeclusteranalysis.
Answer:True
Multipleregressionanalysiscangrouprespondentsintosubgroupswhenthereareatleast4classificationvariables.
Answer:False
Theindependentvariablesinmultipleregressionshouldnotbecorrelatedwitheachother.
Answer:True
Thereisnodependentvariableinafactoranalysis.
Answer:True
Multipleregressionenablestheresearchertoshowthattwovariablesarecausallyrelated.
Answer:False
Inordertomakevalidcomparisonsofregressioncoefficients,thecoefficientsmustbescaledinthesameunits,orbestandardized.
Answer:True
AnanalystwillalwayspreferthattheR2beclosetozero.
Answer:False
Thegoaloffactoranalysisistoidentifyasmanyfactorsaspossible.
Answer:False
Collinearityisasituationinwhichindependentvariablesareheavilycorrelatedwitheachother.
Answer:True
Multiplediscriminantanalysisisusefulwhenthedependentvariableismetric.
Answer:False
Clusteranalysisisusefulforclusteringgroupsofquestionstogetherintofactors.
Answer:False
Ifacompanywasinterestedintheimpactthatadvertisingandsalespricehadonsales,clusteranalysiswouldbeanappropriatetooltouse.
Answer:False
Inmultipleregression,thevalueofR2isinfluencedbythenumberofpredictorvariablesrelativetosamplesize.
Answer:True
Infactoranalysis,namingfactorsisasomewhatsubjectivestep,combiningintuitionandknowledgeofthevariableswithaninspectionofthevariablesthathavehighloadingsoneachfactor.
Answer:True
Thetypeofconjointapproachusedimpactshowtheexerciseispresentedandwhatstatisticalproceduresaremostappropriateforanalyzingtheresults.
Answer:True
Oneofthemostcommonapproachestoconductingconjointanalysisistheuseofadiscretechoice.
Answer:True
Ifkeyattributesorpopularoptionswithinkeyattributesareexcludedfromthestudy,demandestimatescouldbeseverelyimpactedinconjointanalysis.
Answer:True
Predictiveanalyticsdonotapplytobigdata.
Answer:False
EssayQuestions
Someoftheresultsofaregressionanalysisareasfollows:
SSE=52,500 SST=485,200
ComputetheCoefficientofDetermination(R2)andinterpret.
Answer:R2=(SST--SSE)/SST
R2=.8918whichmeansthatover89%ofthevariationinthedependentvariablecanbeexplainedbytheindependentvariable.
Interpretthecorrelationcoefficientforthefollowingdata:
Sales
SalesTraining
Score
45,000
98
34,500
74
23,750
57
51,450
99
41,000
85
Theresultingcorrelationcoefficientis+.98andtheprobabilityofinsignificanceis1%.
Answer:Thereisastrongpositivecorrelationbetweensalesandsalestrainingscores.Hence,highersalesareassociatedwithhighersalestrainingscoresandvice-versa.
DrawagraphdepictingastrongbutinversecorrelationbetweenX(Sales)andnumberoftimesthesalesforcedidnotreachitsquota.Interprettherelationship.
Answer:Theinterpretationoftherelationshipwouldbethatasthenumberoftimesthesalesforcedidnotreachitsquotaincreases,salesdecrease.Theresultinggraphwillbelinearanddownslopingtotheright(negativeslope).
Giventhecorrelationmatrixbelow,answerthefollowingthreequestions.
AGE
INCOME
EDUCATION
AGE
1.00
.000
400
-.65
.000
400
-.10
.221
400
INCOME
-.65
.000
400
1.00
.000
400
.62
.000
400
EDUCATION
-.10
.221
400
.62
.000
400
1.00
.000
400
Assumethatrespondentsansweredthequestionswithratioscaleresponses.
Whichoftherelationshipsinthematrixisthestrongest?
Answer:ThestrongestrelationshipisbetweenAGEandINCOME,anditindicatesthatinthesampleresultsthatyoungerpersonsconsistentlyhadhigherincomesthanolderpeople,andthatwecanbe100%confidentthatthistrendwillalsooccurinthepopulationfromwhichthesamplewasdrawn.
HowwouldyouinterprettherelationshipbetweenEducationandAge?
Answer:TherelationshipbetweenEDUCATIONandAGEisinsignificant,astheresultsinthematrixindicatea21%chancethatthetrendinthesampledatawouldnotnecessarilyoccurinthepopulationfromwhichwasdrawn.
Howmanypairsofresponseswereinthiscorrelationanalysis?
Answer:Theresultsinthematrixindicatethattherewere400pairsofresultsforeachofthecorrelatedresults.
Explainthemeaningofthecoefficientofdetermination.Whatdoesthiscoefficienttelltheresearcheraboutthenatureoftherelationshipbetweenthedependentandindependentvariables?
Answer:Thecoefficientofdeterminationtellsthemarketingresearcherhowmuchvariationinthedependentvariablecanbeexplainedbyvariationintheindependentvariable.Itisameasureofthestrengthoftherelationship.Ifthecoefficientofdeterminationislow,theindependentvariabledoesnothavesignificantexplanatorypowerinpredictingchangesinthedependentvariable.
Ananalystistryingtogrouptogetherpersonswhoattendtheatreperformancesandwhopreferadinnertoaccompanythetheatreperformance.Hence,thetwopiecesofinformationare1)frequencyofattendingtheatreperformancesand2)preferenceforadinner-theatreformat.Whattypeofanalysisshouldbeundertakentodetermineifthosepersonspreferringthedinner-theatreformatarethosewhoattendtheatreperformancesmorefrequently?
Answer:Thisproblemwouldbebestsolvedusingclusteranalysis,whichwouldsimultaneouslygrouppersonspreferringthedinner-theatreformatwithhowfrequentlytheyattendtheatreperformances.
Anadvertisingagencyhasbeendoingworkforaclientsellingwidgets.Thethree-monthcampaignhasproducedalowcorrelationbetweenadvertisingexpendituresandsalesforitsclient.Hence,theclientisconsideringfiringtheadagency.Theadagencycountersthatconsumersalesarenotafairassessmentoftheeffectivenessoftheadcampaignafteronlythreemonths.Theycounterwithananalysisofadvertisingexpendituresinrelationtonumberofrequestsforinformationaboutthewidgets;numberofdistributorsstockingwidgets;andnumberofretailersrequestingshipmentsofwidgets.Theadagencyhasadatabasewithsuchinformation.Whatkindofanalysiswouldbestassisttheadagencyinmakingt
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