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1、BusinessStatisticsBEO1106WEEK10SIMPLELINEARREGRESSION(cont.)TIME-SERIESANALYSISReference:Selvanathanetal.(2004),Chapters11,13EVALUATINGSIMPLELINEARREGRESSIONThereisjustoneindependentvariableinthemodel.TherelationshipbetweenXandYcanbedepictedwithastraightline.Ex1:
2、(Selvanathan2004ed.-p.494,ex.11.72(2000ed.-p.419,ex.11.61))ThemanagerofColonialFurniturehasbeenreviewingweeklyadvertisingexpenditures.Duringthepastsixmonthsalladvertisementsforthestorehavebeenappearedinthelocalnewspaper.Thenumberofadsperweekhasvariedfromonetoseve
3、n.Thestore’ssalesstaffhasbeentrackingthenumberofcustomerswhoenterthestoreeachweek.Thenumberofadsandthenumberofcustomersperweekforthepast26weekshavebeenstoredinthefileXr11-72.Numberofadsperweekistheindependentvariable(X),andthenumberofcustomersperweekisthedependen
4、tvariable(Y).Thepurposeofadvertisinginthelocalnewspaperistoboostsales,soweexpectapositiverelationshipbetweenXandY.2BEO1106-Week10GraphthepairedobservationsofXandY.Thisscatterdiagramshowsthat,atleastinthesample,thereissomeratherweakpositivelinearrelationshipbetwee
5、nthenumbersofadsandcustomers.Determinethesampleregressionline.WearegoingtorelyonExcel.However,athome,trytoreproducetheresultsmanuallyusingthesumofsquares:SSx=86.654,SSy=463802andSSxy=1850.6.3BEO1106-Week10UsingExcel:Interpretthecoefficients.ThismeansthatwhenX,=0,
6、i.e.noadvertisementisplacedinthelocalnewspaper,theexpectednumberofcustomersperweekis296.92.suggestingthatonagivenweekforeachadditionaladvertisementinthelocalnewspaperthenumberofcustomersisexpectedtoincreaseby21.356.4BEO1106-Week10Findandinterpretthecoefficientofd
7、etermination.Thissuggeststhatonly8.5%ofthetotalvariationinthenumberofcustomerscanbeexplained,orisdueto,thevariationinthenumberofadvertisements.Theremaining91.5%isunexplained,i.e.isduetosomeotherfactorsthanads.Thismodelhasaratherpooroverallfit.Similartothemeanofas
8、inglepopulation,sayµx,theunknownparametersofapopulationregressionmodel,β0andβ1,canbeestimatedwithpointestimatorsandwithintervalestimators,andwecanalsousehypoth
