Solutions Manual for Business
Analytics 1st Edition by Abdey
ISBN: 9781529774108
Solutionstoend-of-chapterexercises
Chapter1
Decision-makingunderuncertainty
1.1Exercises
1.1.1Testyourunderstanding
1. Whatismeantby‘uncertainty’?
Solution:
Uncertaintyreferstoalackofknowledge,informationorpredictabilityaboutaparticularsituation, eventoroutcome.Itsignifiesastateofdoubtorambiguitywherethefutureorthetruenatureof somethingisuncertain.Uncertaintycanarisefromvariousfactors,suchasincompletedata, conflictingevidence,complexity,orthepresenceofunpredictablevariables.Itoftenposeschallenges indecision-making,planning,andriskassessmentasithampersourabilitytoaccuratelyforeseeor quantifypotentialoutcomes.Managinguncertaintyinvolvesacknowledgingitspresence,assessing probabilities,consideringalternativescenarios,andadoptingflexibleapproachestoadaptto changingcircumstances.
2. Whatisthedifferencebetween‘dependent’and‘independent’variables?
Solution:
Adependentvariableisthevariablebeingmeasuredorobservedinanexperimentorstudy.Itisthe outcomeorresultinwhichweareinterestedinunderstanding,explainingorpredicting.Examples ofdependentvariablesinbusinessanalyticsinclude:
• behaviouralresponses,suchascustomerawareness,brandperception,knowledge,intentionto purchaseandpreference.
• performancemetrics,suchassalesrevenues,productioncosts,profits,marketshare,cash-flow andshareprice.
Independentvariablesarethosethatimpactthedependentvariable–thinkofitintermsof‘cause andeffect’.Examplesofindependentvariablesinbusinessanalyticsinclude:
• marketingmixvariables,suchasproduct,price,placementandpromotion(the4Ps),which arecontrollable,i.e.areunderthecontrolofthedecision-maker.
• situationalfactors,suchasdemand,competition,economicclimate,politicalclimate,exchange rates,supplychain,regulationsandtechnology,whichareuncontrollable,i.e.arenotunderthe controlofthedecision-maker.
Therelationshipbetweenthedependentandindependentvariablesisoftenexploredthrough statisticalanalysistodeterminewhetherchangesintheindependentvariablecausechangesinthe dependentvariable.Thishelpsestablishcause-and-effectrelationshipsandprovidesinsightsintothe phenomenonunderinvestigation.Understandingthedistinctionbetweendependentand
independentvariablesisfundamentalfordesigningexperiments,conductingresearch,anddrawing meaningfulconclusionsfromdata.
3. Identifyexamplesofreal-worlddependentvariablesforanybusinessproblemofyourchoice.
Solution:
Considerahotel.Managementmaybeinterestedinthefollowingdependentvariables.
• Customersatisfactionscore–thiscouldbemeasuredusingsurveysorfeedbackformswhere customersratetheiroverallsatisfactionwiththehotel,itsservices,staff,amenities,cleanliness, etc.Thesatisfactionscorecanbeanumericalratingoracategoricalmeasure(forexample, rangingfrom‘verysatisfied’to‘verydissatisfied’).
• Revenuepercustomer–thisvariablerepresentstheaverageamountofmoneyacustomer spendsduringtheirstay.Higherrevenuepercustomercanindicatecustomersatisfaction,as satisfiedguestsaremorelikelytouseadditionalservices,suchasroomupgrades,spa treatments,ordiningoptions.
• Customerretentionrate–thismetricindicatesthepercentageofcustomerswhocontinueto stayatthehoteloveraspecificperiodoftime.Itreflectscustomersatisfactionandloyalty,as satisfiedcustomersaremorelikelytoreturninthefuture!
4. ForeachdependentvariableidentifiedinQuestion3,whatarethelikelyindependentvariables? Brieflyjustifyyourchoice.
Solution:
Customersatisfactionscorewouldlikelydependonthefollowing:
• Servicequality.
• Price/valueformoney.
• Foodandbeveragequality.
• Roomcleanliness.
• Location.
• Facilities.
Revenuepercustomerwouldlikelydependonthefollowing:
• Roomtypebooked.
• Lengthofstay.
• Seasonofthebooking(peakvs.off-peak).
• Ancillaryservicesused.
• In-roomdining.
• Purposeofvisit(businessvs.leisure).
Customerretentionratewouldlikelydependonthefollowing:
• Servicequality(notealsoforcustomersatisfactionscore!).
• Price/valueformoney(notealsoforcustomersatisfactionscore!).
• Loyaltyprograms(accruepointsforfreenights,perhaps).
• Specialpackages(thinkconferences,weddingsetc.).
• Brandimage.
• Partnershipwithotherhotelbrands. Notetheabovearenotnecessarilycollectivelyexhaustivelists!
5. Whatismeantbythe‘fourPs’?
Solution:
The‘fourPs’areknownasthemarketingmixvariables:
• Product–whatthebusinessisselling(whichcouldbeatangiblegood,orintangibleservice).
• Price–whatpricetosellatandwhethertoofferadiscount.
• Placement–theprovisionofcustomeraccessandconvenience.
• Promotion–thechoiceofmarketingcommunications.
6. ExplaintheDIKWpyramid.
Solution:
Thepyramidmodelstheconversionof(i)data,into(ii)information,fromwhichwegain(iii) knowledge,leadingtoourenlightenmentwith(iv)wisdom.Thepyramidillustratestheseas hierarchicalrelationships.
7. Whatisamodel?
Solution:
Amodelisadeliberatesimplificationofreality.
Agoodmodelretainsthemostimportantfeaturesofrealityandignoreslessimportantdetails. Immediatelyweseethatwefaceatrade-off.Thebenefitofamodelisthatwesimplifythecomplex realworld.Thecostofamodelisthatbysimplifyingrealityweengineeradeparturefromreality. Broadlyspeaking,wewouldbehappyifthebenefitexceededthecost,i.e.ifthesimplicitymadeit easierforustounderstandandanalysetherealworldwhileincurringonlyaminimaldeparture fromreality.
8. ForacityotherthanLondonwithametrosystem,lookattheofficialmapofthenetwork.Critique themap,notinganypossibleimprovementsyouwouldrecommendaremade.
Solution:
Possibleimprovementsmayrelateto:
• geographicaccuracy
• clarityofpresentation
• easeofnavigation.
9. AfriendofyoursisacontestantontheMontyHallgameshow.Yourfriendtellsyou‘Nomatter what,Iwillnotswitchdoor’.Wouldyousupportyourfriend’sdecision(tomaintainyour friendship!)orwouldyouadviseotherwise?
Solution:
Attheriskofjeopardisingyourfriendship,youshould(politely)pointoutthatprobabilisticallyitis optimaltoswitchdoor.Ofcourse,youneedtobalancethiswiththepossibilitythattheoriginal doorchosenisthecorrectdoor,inwhichcaseyoumayneverbeforgivenifyourfriendfollowedyour advice!
10. SupposetheproducersoftheMontyHallshowchangedtheformatofthegame.Insteadofthere beingthreedoors,therearenow n> 3doors.Thecontestantchoosesadoor.Monty(whocontinues toknowwherethecaris)opens n 2doors,leavingthecontestant’soriginaldoorandoneother doorunopened.
(a) Intermsof‘toswitch,ornottoswitch?’whatwouldyourecommendistheoptimalstrategy andwhy?
(b) Doyousupporttheproducersinincreasingthenumberofdoorsto n> 3?Justifyyourview.
Solution:
(a) With n> 3doors,theprobabilitythatthecorrectdoorischosenatthestartbythecontestant is1/n.Hencetheprobabilitythatthecorrectdoorisoneoftheother n 1doorsis(n 1)/n, andclearly:
1 n < n 1 n
OnceMontyopens n 2doors(excludingthecontestant’soriginalchoice,ofcourse),the probabilityofwinningbyswitchingis(n 1)/n sincethisamountofprobabilityis‘inherited’ bytheonedoorMontychoosesnottoopen.Decision-makingunderuncertaintyrequiresusto ‘playtotheprobabilities’,henceitisoptimaltoswitch. Chapter4solvestheMontyHallproblemmoreformallyusingBayes’theorem.
(b) Ifcontestantsaresavvyenoughtounderstandtheprobabilisticargumentforswitchingdoor eachtime,thenwewouldexpectallsuchcontestantstoswitch.Thiswouldmeanthat(in percentageterms)thewinrateofcontestants(andhencethelossrateoftheshow’sproducers) inthelongrunwouldbe: n 1 n × 100%
As n increases,thisworsensthesituationfortheshow’sproducers(moreprizesarewon,which costsmoney!)soincreasingthenumberofdoorswouldseemtobeabadidea.Also,television showsaremeanttobeforentertainment,sowith n =3doorsthismaximisestheextentof unpredictabilityaboutwhetherthecontestantwouldwin,whichinturnwouldlikelybe optimalforaudienceviewingfigures.Suspenseismoreexciting!
1.1.2Casestudycorner
Foracompanyorindustryofyourchoice,formulateapossiblequantitativebusinessproblemwhich couldbeanalysed.Inparticular,thinkaboutthefollowing.
Whatisthespecificbusinessquestiontobeaddressed?
Whatarethebusinessobjectivesoftheanalysis?
Whatarethedependentandindependentvariables?
Arethereanychallengesincollectingrelevantdatatoanalysetheproblem?
Arethereanyuncertaintiesinvolvedwiththebusinessproblem?Ifso,whatarethey?
Solution:
Formulatingaproblemsuitableforquantitativeanalysisbeginswithposingaquestion.Supposethe company’squestionis:‘Whatpriceshouldwesetforournewproduct?’
Whilewemayhavepreviouslyreliedongutinstinctdecisions,wenowaimtoapproachthisquestion usingamorequantitativeapproach.Toanswerit,wemustidentifythefactorswhichmayinfluencethe pricingdecision.Thechallengeliesinthelackofknowledgeregardingconsumers’willingnesstopay. However,wewouldlikelyhavedataonmanufacturingcostsandmarketingexpensesforourproduct(or atleastreasonableestimates).
Marketresearchcouldbeconductedtoexaminethecurrentmarketlandscapeandthepricingstrategies adoptedbycompetitorsforsimilarproducts.Suchresearchencompassesvariousapproaches,eachwith itsownsetofassumptionsanduncertainties.Byanalysingthismarketresearch,wecouldestimatewhat consumersmightbewillingtopayforasimilarproductanddevelopapricingstructureaccordingly. However,thereareadditionaluncertaintiesthatneedtobeconsidered.Forinstance:
Willtherestillbedemandforourproductwhenitislaunched?
Willconsumershavethefinancialmeanstopurchaseitatthattime?(Iftherewasarecession, consumersmayreducetheirdiscretionaryspending.)
Evenifwepriceourproductlowerthanourcompetitor(s),willconsumersremainloyaltotheir familiarbrandandrefrainfrompurchasingourproduct?
Toaddresstheseuncertainties,wecouldconductsurveystocollectdataonbrandloyalty,make predictionsregardingconsumers’futurewillingnesstopay,andassumethatdemandforourproductwill bestrongatlaunch.Bygatheringrelevantdatarelatedtotheseuncertaintiesandincorporatinglogical assumptions,wecancreatedata-drivenmodelstopredicttheoutcomesofourproposedpricing structures.