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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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