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1、BusinessStatisticsBEO1106WEEK10SIMPLELINEARREGRESSION(cont.)TIME-SERIESANALYSISReference:Selvanathanetal.(2004),Chapters11,13EVALUATINGSIMPLELINEARREGRESSIONThereisjustoneindependentvariableinthemodel.TherelationshipbetweenXandYcanbedepictedwithastraightline.Ex1:(Selvanathan2004ed.-p.494,ex.11.7
2、2(2000ed.-p.419,ex.11.61))ThemanagerofColonialFurniturehasbeenreviewingweeklyadvertisingexpenditures.Duringthepastsixmonthsalladvertisementsforthestorehavebeenappearedinthelocalnewspaper.Thenumberofadsperweekhasvariedfromonetoseven.Thestore’ssalesstaffhasbeentrackingthenumberofcustomerswhoentert
3、hestoreeachweek.Thenumberofadsandthenumberofcustomersperweekforthepast26weekshavebeenstoredinthefileXr11-72.Numberofadsperweekistheindependentvariable(X),andthenumberofcustomersperweekisthedependentvariable(Y).Thepurposeofadvertisinginthelocalnewspaperistoboostsales,soweexpectapositiverelationsh
4、ipbetweenXandY.2BEO1106-Week10GraphthepairedobservationsofXandY.Thisscatterdiagramshowsthat,atleastinthesample,thereissomeratherweakpositivelinearrelationshipbetweenthenumbersofadsandcustomers.Determinethesampleregressionline.WearegoingtorelyonExcel.However,athome,trytoreproducetheresultsmanuall
5、yusingthesumofsquares:SSx=86.654,SSy=463802andSSxy=1850.6.3BEO1106-Week10UsingExcel:Interpretthecoefficients.ThismeansthatwhenX,=0,i.e.noadvertisementisplacedinthelocalnewspaper,theexpectednumberofcustomersperweekis296.92.suggestingthatonagivenweekforeachadditionaladvertisementinthelocalnewspape
6、rthenumberofcustomersisexpectedtoincreaseby21.356.4BEO1106-Week10Findandinterpretthecoefficientofdetermination.Thissuggeststhatonly8.5%ofthetotalvariationinthenumberofcustomerscanbeexplained,orisdueto,thevariationinthenumberofadvertisements.Theremaining91.5%isunexplained,i.e.isduetosomeotherfact
7、orsthanads.Thismodelhasaratherpooroverallfit.Similartothemeanofasinglepopulation,sayµx,theunknownparametersofapopulationregressionmodel,β0andβ1,canbeestimatedwithpointestimatorsandwithintervalestimators,andwecanalsousehypoth
