商務(wù)與經(jīng)濟(jì)統(tǒng)計習(xí)題答案（第8版中文版）SBE8

本文格式為Word版，下載可任意編輯——商務(wù)與經(jīng)濟(jì)統(tǒng)計習(xí)題答案（第8版中文版）SBE8Chapter15MultipleRegressionLearningObjectives1.Understandhowmultipleregressionanalysiscanbeusedtodeveloprelationshipsinvolvingonedependentvariableandseveralindependentvariables.2.Beabletointerpretthecoefficientsinamultipleregressionanalysis.3.Knowtheassumptionsnecessarytoconductstatisticaltestsinvolvingthehypothesizedregressionmodel.4.Understandtheroleofcomputerpackagesinperformingmultipleregressionanalysis.5.Beabletointerpretandusecomputeroutputtodeveloptheestimatedregressionequation.6.Beabletodeterminehowgoodafitisprovidedbytheestimatedregressionequation.7.Beabletotestforthesignificanceoftheregressionequation.8.Understandhowmulticollinearityaffectsmultipleregressionanalysis.9.Knowhowresidualanalysiscanbeusedtomakeajudgementastotheappropriatenessofthemodel,identifyoutliers,anddeterminewhichobservationsareinfluential.Solutions:1.a.b1=.5906isanestimateofthechangeinycorrespondingtoa1unitchangeinx1whenx2isheldconstant.b2=.4980isanestimateofthechangeinycorrespondingtoa1unitchangeinx2whenx1isheldconstant.2.a.Theestimatedregressionequationis=45.06+1.94x1Anestimateofywhenx1=45is=45.06+1.94(45)=132.36b.Theestimatedregressionequationis=85.22+4.32x2Anestimateofywhenx2=15is=85.22+4.32(15)=150.02c.Theestimatedregressionequationis=-18.37+2.01x1+4.74x2Anestimateofywhenx1=45andx2=15is=-18.37+2.01(45)+4.74(15)=143.183.a.b1=3.8isanestimateofthechangeinycorrespondingtoa1unitchangeinx1whenx2,x3,andx4areheldconstant.b2=-2.3isanestimateofthechangeinycorrespondingtoa1unitchangeinx2whenx1,x3,andx4areheldconstant.b3=7.6isanestimateofthechangeinycorrespondingtoa1unitchangeinx3whenx1,x2,andx4areheldconstant.b4=2.7isanestimateofthechangeinycorrespondingtoa1unitchangeinx4whenx1,x2,andx3areheldconstant.4.a.=235+10(15)+8(10)=255;salesestimate:$255,000b.Salescanbeexpectedtoincreaseby$10foreverydollarincreaseininventoryinvestmentwhenadvertisingexpenditureisheldconstant.Salescanbeexpectedtoincreaseby$8foreverydollarincreaseinadvertisingexpenditurewheninventoryinvestmentisheldconstant.5.a.TheMinitaboutputisshownbelow:TheregressionequationisRevenue=88.6+1.60TVAdvPredictorCoefSECoefTPConstant88.6381.58256.020.000TVAdv1.60390.47783.360.015S=1.215R-Sq=65.3%R-Sq(adj)=59.5%AnalysisofVarianceSourceDFSSMSFPRegression116.64016.64011.270.015ResidualError68.8601.477Total725.500b.TheMinitaboutputisshownbelow:TheregressionequationisRevenue=83.2+2.29TVAdv+1.30NewsAdvPredictorCoefSECoefTPConstant83.2301.57452.880.000TVAdv2.29020.30417.530.001NewsAdv1.30100.32074.060.010S=0.6426R-Sq=91.9%R-Sq(adj)=88.7%AnalysisofVarianceSourceDFSSMSFPRegression223.43511.71828.380.002ResidualError52.0650.413Total725.500SourceDFSeqSSTVAdv116.640NewsAdv16.795c.No,itis1.60inpart2(a)and2.99above.Inthisexerciseitrepresentsthemarginalchangeinrevenueduetoanincreaseintelevisionadvertisingwithnewspaperadvertisingheldconstant.d.Revenue=83.2+2.29(3.5)+1.30(1.8)=$93.56or$93,5606.a.TheMinitaboutputisshownbelow:TheregressionequationisSpeed=49.8+0.0151WeightPredictorCoefSECoefTPConstant49.7819.112.610.021Weight0.0151040.0060052.520.025S=7.000R-Sq=31.1%R-Sq(adj)=26.2%AnalysisofVarianceSourceDFSSMSFPRegression1309.95309.956.330.025Error14686.0049.00Total15995.95b.TheMinitaboutputisshownbelow:TheregressionequationisSpeed=80.5-0.00312Weight+0.105HorsepwrPredictorCoefSECoefTPConstant80.4879.1398.810.000Weight-0.0031220.003481-0.900.386Horsepwr0.104710.013317.860.000S=3.027R-Sq=88.0%R-Sq(adj)=86.2%AnalysisofVarianceSourceDFSSMSFPRegression2876.80438.4047.830.000ResidualError13119.159.17Total15995.957.a.TheMinitaboutputisshownbelow:TheregressionequationisSales=66.5+0.414Compet$-0.270Heller$PredictorCoefSECoefTPConstant66.5241.881.590.156Compet$0.41390.26041.590.156Heller$-0.269780.08091-3.330.013S=18.74R-Sq=65.3%R-Sq(adj)=55.4%AnalysisofVarianceSourceDFSSMSFPRegression24618.82309.46.580.025ResidualError72457.3351.0Total97076.1b.b1=.414isanestimateofthechangeinthequantitysold(1000s)oftheHellermowerwithrespecttoa$1changeinpriceincompetitor’smowerwiththepriceoftheHellermowerheldconstant.b2=-.270isanestimateofthechangeinthequantitysold(1000s)oftheHellermowerwithrespecttoa$1changeinitspricewiththepriceofthecompetitor’smowerheldconstant.c.=66.5+0.414(170)-0.270(160)=93.68or93,680units8.a.TheMinitaboutputisshownbelow:TheregressionequationisReturn=247-32.8Safety+34.6ExpRatioPredictorCoefSECoefTPConstant247.439Safety-32.8413.95-2.350.031ExpRatio34.5914.132.450.026S=16.98R-Sq=58.2%R-Sq(adj)=53.3%AnalysisofVarianceSourceDFSSMSFPRegression26823.23411.611.840.001ResidualError174899.7288.2Total1911723.0b.9.a.TheMinitaboutputisshownbelow:Theregressionequationis%College=26.7-1.43Size+0.0757SatScorePredictorCoefSECoefTPConstant26.7151.670.520.613Size-1.42980.9931-1.440.170SatScore0.075740.039061.940.072S=12.42R-Sq=38.2%R-Sq(adj)=30.0%AnalysisofVarianceSourceDFSSMSFPRegression21430.4715.24.640.027ResidualError152312.7154.2Total173743.1b.=26.7-1.43(20)+0.0757(1000)=73.8Estimateis73.8%10.a.TheMinitaboutputisshownbelow:TheregressionequationisRevenue=33.3+7.98CarsPredictorCoefSECoefTPConstant33.3483.080.400.695Cars7.98400.632312.630.000S=226.7R-Sq=92.5%R-Sq(adj)=91.9%AnalysisofVarianceSourceDFSSMSFPRegression181920678192067159.440.000Error1366793651380Total148860003b.Anincreaseof1000carsinservicewillresultinanincreaseinrevenueof$7.98million.c.TheMinitaboutputisshownbelow:TheregressionequationisRevenue=106+8.94Cars-0.191LocationPredictorCoefSECoefTPConstant105.9785.521.240.239Cars8.94270.774611.550.000Location-0.19140.1026-1.870.087S=207.7R-Sq=94.2%R-Sq(adj)=93.2%AnalysisofVarianceSourceDFSSMSFPRegression28342186417109396.660.000Error1251781743151Totaa.SSE=SST-SSR=6,724.125-6,216.375=507.75b.c.d.Theestimatedregressionequationprovidedanexcellentfit.12.a.b.c.Yes;afteradjustingforthenumberofindependentvariablesinthemodel,weseethat90.5%ofthevariabilityinyhasbeenaccountedfor.13.a.b.c.Theestimatedregressionequationprovidedanexcellentfit.14.a.b.c.Theadjustedcoefficientofdeterminationshowsthat68%ofthevariabilityhasbeenexplainedbythetwoindependentvariables;thus,weconcludethatthemodeldoesnotexplainalargeamountofvariability.15.a.b.MultipleregressionanalysisispreferredsincebothR2andshowanincreasedpercentageofthevariabilityofyexplainedwhenbothindependentvariablesareused.16.Note:theMinitaboutputisshownwiththesolutiontoExercise6.a.No;R-Sq=31.1%b.MultipleregressionanalysisispreferredsincebothR-SqandR-Sq(adj)showanincreasedpercentageofthevariabilityofyexplainedwhenbothindependentvariablesareused.17.a.b.Thefitisnotverygood18.Note:TheMinitaboutputisshownwiththesolutiontoExercise10.a.R-Sq=94.2%R-Sq(adj)=93.2%b.Thefitisverygood.19.a.MSR=SSR/p=6,216.375/2=3,108.188b.F=MSR/MSE=3,108.188/72.536=42.85F.05=4.74(2degreesoffreedomnumeratorand7denominator)SinceF=42.85F.05=4.74theoverallmodelissignificant.c.t=.5906/.0813=7.26t.025=2.365(7degreesoffreedom)Sincet=2.365t.025=2.365,b1issignificant.d.t=.4980/.0567=8.78Sincet=8.78t.025=2.365,b2issignificant.20.AportionoftheMinitaboutputisshownbelow.TheregressionequationisY=-18.4+2.01X1+4.74X2PredictorCoefSECoefTPConstant-18.3717.97-1.020.341X12.01020.24718.130.000X24.73780.94845.000.002S=12.71R-Sq=92.6%R-Sq(adj)=90.4%AnalysisofVarianceSourceDFSSMSFPRegression214052.27026.143.500.000ResidualError71130.7161.5Total915182.9a.Sincethep-valuecorrespondingtoF=43.50is.000a=.05,werejectH0:b1=b2=0;thereisasignificantrelationship.b.Sincethep-valuecorrespondingtot=8.13is.000a=.05,werejectH0:b1=0;b1issignificant.c.Sincethep-valuecorrespondingtot=5.00is.002a=.05,werejectH0:b2=0;b2issignificant.21.a.Inthetwoindependentvariablecasethecoefficientofx1representstheexpectedchangeinycorrespondingtoaoneunitincreaseinx1whenx2isheldconstant.Inthesingleindependentvariablecasethecoefficientofx1representstheexpectedchangeinycorrespondingtoaoneunitincreaseinx1.b.Yes.Ifx1andx2arecorrelatedonewouldexpectachangeinx1tobeaccompaniedbyachangeinx2.22.a.SSE=SST-SSR=16000-12000=4000b.F=MSR/MSE=6000/571.43=10.50F.05=4.74(2degreesoffreedomnumeratorand7denominator)SinceF=10.50F.05=4.74,werejectH0.Thereisasignificantrelationshipamongthevariables.23.a.F=28.38F.01=13.27(2degreesoffreedom,numeratorand1denominator)SinceFF.01=13.27,rejectH0.Alternatively,thep-valueof.002leadstothesameconclusion.b.t=7.53t.025=2.571Sincett.025=2.571,b1issignificantandx1shouldnotbedroppedfromthemodel.c.t=4.06t.025=2.571Sincett.025=2.571,b2issignificantandx2shouldnotbedroppedfromthemodel.24.Note:TheMinitaboutputisshowninpart(b)ofExercise6a.F=47.83F.05=3.81(2degreesoffreedomnumeratorand13denominator)SinceF=47.83F.05=3.81,werejectH0:b1=b2=0.Alternatively,sincethep-value=.000a=.05wecanrejectH0.b.ForWeight:H0:b1=0Ha:b110Sincethep-value=0.386a=0.05,wecannotrejectH0ForHorsepower:H0:b2=0Ha:b210Sincethep-value=0.000a=0.05,wecanrejectH025.a.TheMinitaboutputisshownbelow:TheregressionequationisP/E=6.04+0.692Profit%+0.265Sales%PredictorCoefSECoefTPConstant6.0384.5891.320.211Profit%0.69160.21333.240.006Sales%0.26480.18711.420.180S=5.456R-Sq=47.2%R-Sq(adj)=39.0%AnalysisofVarianceSourceDFSSMSFPRegression2345.28172.645.800.016ResidualError13387.0029.77Total15732.28b.Sincethep-value=0.016a=0.05,thereisasignificantrelationshipamongthevariables.c.ForProfit%:Sincethep-value=0.006a=0.05,Profit%issignificant.ForSales%:Sincethep-value=0.180a=0.05,Sales%isnotsignificant.26.Note:TheMinitaboutputisshownwiththesolutiontoExercise10.a.Sincethep-valuecorrespondingtoF=96.66is0.000a=.05,thereisasignificantrelationshipamongthevariables.b.ForCars:Sincethep-value=0.000a=0.05,Carsissignificantc.ForLocation:Sincethep-value=0.087a=0.05,Locationisnotsignificant27.a.=29.1270+.5906(180)+.4980(310)=289.8150b.Thepointestimateforanindividualvalueis=289.8150,thesameasthepointestimateofthemeanvalue.28.a.UsingMinitab,the95%confidenceintervalis132.16to154.16.b.UsingMinitab,the95%predictionintervalis111.13to175.18.29.a.=83.2+2.29(3.5)+1.30(1.8)=93.555or$93,555Note:InExercise5b,theMinitaboutputalsoshowsthatb0=83.230,b1=2.2902,andb2=1.3010;hence,=83.230+2.2902x1+1.3010x2.Usingthisestimatedregressionequation,weobtain=83.230+2.2902(3.5)+1.3010(1.8)=93.588or$93,588Thedifference($93,588-$93,555=$33)issimplyduetothefactthatadditionalsignificantdigitsareusedinthecomputations.Fromapracticalpointofview,however,thedifferenceisnotenoughtobeconcernedabout.Inpractice,acomputersoftwarepackageisalwaysusedtoperformthecomputationsandthiswillnotbeanissue.TheMinitaboutputisshownbelow:FitStdev.Fit95%C.I.95%P.I.93.5880.291(92.840,94.335)(91.774,95.401)NotethatthevalueofFIT()is93.588.b.Confidenceintervalestimate:92.840to94.335or$92,840to$94,335c.Predictionintervalestimate:91.774to95.401or$91,774to$95,40130.a.Sinceweightisnotstatisticallysignificant(seeExercise24),wewilluseanestimatedregressionequationwhichusesonlyHorsepowertopredictthespeedat1/4mile.TheMinitaboutputisshownbelow:TheregressionequationisSpeed=72.6+0.0968HorsepwrPredictorCoefSECoefTPConstant72.6502.65527.360.000Horsepwr0.0967560.0098659.810.000S=3.006R-Sq=87.3%R-Sq(adj)=86.4%AnalysisofVarianceSourceDFSSMSFPRegression1869.43869.4396.210.000ResidualError14126.529.04Total15995.95UnusualObservationsObsHorsepwrSpeedFitSEFitResidualStResid2290108.000100.7090.8147.2912.52R6450116.200116.1902.0360.0100.00XRdenotesanobservationwithalargestandardizedresidualXdenotesanobservationwhoseXvaluegivesitlargeinfluence.Theoutputshowsthatthepointestimateisaspeedof101.290milesperhour.b.The95%confidenceintervalis99.490to103.089milesperhour.c.The95%predictionintervalis94.596to107.984milesperhour.31.a.UsingMinitabthe95%confidenceintervalis58.37%to75.03%.b.UsingMinitabthe95%predictionintervalis35.24%to90.59%.32.a.E(y)=b0+b1x1+b2x2wherex2=0iflevel1and1iflevel2b.E(y)=b0+b1x1+b2(0)=b0+b1x1c.E(y)=b0+b1x1+b2(1)=b0+b1x1+b2d.b2=E(y|level2)-E(y|level1)b1isthechangeinE(y)fora1unitchangeinx1holdingx2constant.33.a.twob.E(y)=b0+b1x1+b2x2+b3x3wherex2x3Level001102013c.E(y|level1)=b0+b1x1+b2(0)+b3(0)=b0+b1x1E(y|level2)=b0+b1x1+b2(1)+b3(0)=b0+b1x1+b2E(y|level3)=b0+b1x1+b2(0)+b3(0)=b0+b1x1+b3b2=E(y|level2)-E(y|level1)b3=E(y|level3)-E(y|level1)b1isthechangeinE(y)fora1unitchangeinx1holdingx2andx3constant.34.a.$15,300b.Estimateofsales=10.1-4.2(2)+6.8(8)+15.3(0)=56.1or$56,100c.Estimateofsales=10.1-4.2(1)+6.8(3)+15.3(1)=41.6or$41,60035.a.LetType=0ifamechanicalrepairType=1ifanelectricalrepairTheMinitaboutputisshownbelow:TheregressionequationisTime=3.45+0.617TypePredictorCoefSECoefTPConstant3.45000.54676.310.000Type0.61670.70580.870.408S=1.093R-Sq=8.7%R-Sq(adj)=0.0%AnalysisofVarianceSourceDFSSMSFPRegression10.9130.9130.760.408ResidualError89.5631.195Total910.476b.Theestimatedregressionequationdidnotprovideagoodfit.Infact,thep-valueof.408showsthattherelationshipisnotsignificantforanyreasonablevalueofa.c.Person=0ifBobJonesperformedtheserviceandPerson=1ifDaveNewtonperformedtheservice.TheMinitaboutputisshownbelow:TheregressionequationisTime=4.62-1.60PersonPredictorCoefSECoefTPConstant4.62000.319214.470.000Person-1.60000.4514-3.540.008S=0.7138R-Sq=61.1%R-Sq(adj)=56.2%AnalysisofVarianceSourceDFSSMSFPRegression16.40006.400012.560.008ResidualError84.07600.5095Total910.4760d.Weseethat61.1%ofthevariabilityinrepairtimehasbeenexplainedbytherepairpersonthatperformedtheservice;anacceptable,butnotgood,fit.36.a.TheMinitaboutputisshownbelow:TheregressionequationisTime=1.86+0.291Months+1.10Type-0.609PersonPredictorCoefSECoefTPConstant1.86020.72862.550.043Months0.291440.083603.490.013Type1.10240.30333.630.011Person-0.60910.3879-1.570.167S=0.4174R-Sq=90.0%R-Sq(adj)=85.0%AnalysisofVarianceSourceDFSSMSFPRegression39.43053.143518.040.002ResidualError61.04550.1743Total910.4760b.Sincethep-valuecorrespondingtoF=18.04is.002a=.05,theoverallmodelisstatisticallysignificant.c.Thep-valuecorrespondingtot=-1.57is.167a=.05;thus,theadditionofPersonisnotstatisticallysignificant.PersonishighlycorrelatedwithMonths(thesamplecorrelationcoefficientis-.691);thus,oncetheeffectofMonthshasbeenaccountedfor,Personwillnotaddmuchtothemodel.37.a.LetPosition=0ifaguardPosition=1ifanoffensivetackle.b.TheMinitaboutputisshownbelow:TheregressionequationisRating=11.2+0.732Position+0.0222Weight-2.28SpeedPredictorCoefSECoefTPConstant11.2234.5232.480.022Position0.73240.28932.530.019Weight0.022190.010392.140.045Speed-2.27750.9290-2.450.023S=0.6936R-Sq=47.5%R-Sq(adj)=40.1%AnalysisofVarianceSourceDFSSMSFPRegression39.15623.05216.350.003ResidualError2110.10140.4810Total2419.2576c.Sincethep-valuecorrespondingtoF=6.35is.003a=.05,thereisasignificantrelationshipbetweenratingandtheindependentvariables.d.ThevalueofR-Sq(adj)is40.1%;theestimatedregressionequationdidnotprovideaverygoodfit.e.Sincethep-valueforPositionist=2.53a=.05,positionisasignificantfactorintheplayer’srating.f.38.a.TheMinitaboutputisshownbelow:TheregressionequationisRisk=-91.8+1.08Age+0.252Pressure+8.74SmokerPredictorCoefSECoefTPConstant-91.7615.22-6.030.000Age1.07670.16606.490.000Pressure0.251810.045235.570.000Smoker8.7403.0012.910.010S=5.757R-Sq=87.3%R-Sq(adj)=85.0%AnalysisofVarianceSourceDFSSMSFPRegression33660.71220.236.820.000ResidualError16530.233.1Total194190.9b.Sincethep-valuecorrespondingtot=2.91is.010a=.05,smokingisasignificantfactor.c.UsingMinitab,thepointestimateis34.27;the95%predictionintervalis21.35to47.18.Thus,theprobabilityofastroke(.2135to.4718atthe95%confidencelevel)appearstobequitehigh.ThephysicianwouldprobablyrecommendthatArtquitsmokingandbeginsometypeoftreatmentdesignedtoreducehisbloodpressure.39.a.TheMinitaboutputisshownbelow:TheregressionequationisY=0.20+2.60XPredictorCoefSECoefTPConstant0.2002.1320.090.931X2.60000.64294.040.027S=2.033R-Sq=84.5%R-Sq(adj)=79.3%AnalysisofVarianceSourceDFSSMSFPRegression167.60067.60016.350.027ResidualError312.4004.133Total480.000b.UsingMinitabweobtainedthefollowingvalues:xiyiStandardizedResidual132.8.16275.4.94358.0-1.6541110.6.2451413.2.62Thepoint(3,5)doesnotappeartofollowthetrendofremainingdata;however,thevalueofthestandardizedresidualforthispoint,-1.65,isnotlargeenoughforustoconcludethat(3,5)isanoutlier.c.UsingMinitab,weobtainedthefollowingvalues:xiyiStudentizedDeletedResidual13.1327.9135-4.42411.19514.54t.025=4.303(n-p-2=5-1-2=2degreesoffreedom)Sincethestudentizeddeletedresidualfor(3,5)is-4.42-4.303,weconcludethatthe3rdobservationisanoutlier.40.a.TheMinitaboutputisshownbelow:TheregressionequationisY=-53.3+3.11XPredicatorCoefStdevt-ratiopConstant-53.2805.786-9.210.003X3.11000.202215.430.001s=2.851R-sq=98.8%R-sq(adj)=98.3%AnalysisofVarianceSOURCEDFSSMSFpRegression11934.41934.4238.030.001Error324.48.1Total41598.8b.UsingtheMinitabweobtainedthefollowingvalues:xiyiStudentizedDeletedResidual2212-1.942421-.1226311.792835.404070-1.90t.025=4.303(n-p-2=5-1-2=2degreesoffreedom)Sincenoneofthestudentizeddeletedresidualsarelessthan-4.303orgreaterthan4.303,noneoftheobservationscanbeclassifiedasanoutlier.c.UsingMinitabweobtainedthefollowingvalues:xiyihi2212.382421.282631.222835.204070.92ThecriticalvalueisSincenoneofthevaluesexceed1.2,weconcludethattherearenoinfluentialobservationsinthedata.d.UsingMinitabweobtainedthefollowingvalues:xiyiDi2212.602421.002631.262835.03407011.09SinceD5=11.091(ruleofthumbcriticalvalue),weconcludethatthefifthobservationisinfluential.41.a.TheMinitaboutputappearsinthesolutiontopart(b)ofExercise5;theestimatedregressionequationis:Revenue=83.2+2.29TVAdv+1.30NewsAdvb.UsingMinitabweobtainedthefollowingvalues:StandardizedResidual96.63-1.6290.41-1.0894.341.2292.21-.3794.391.1094.24-.4094.42-1.1293.351.08Withtherelativelyfewobservations,itisdifficulttodetermineifanyoftheassumptionsregardingtheerrortermhavebeenviolated.Forinstance,anargumentcouldbemadethattheredoesnotappeartobeanypatternintheplot;alternativelyanargumentcouldbemadethatthereisacurvilinearpatternintheplot.c.Thevaluesofthestandardizedresidualsaregreaterthan-2andlessthan+2;thus,usingtest,therearenooutliers.Asafurthercheckforoutliers,weusedMinitabtocomputethefollowingstudentizeddeletedresiduals:ObservationStudentizedDeletedResidual1-2.112-1.1031.314-.3351.136-.367-1.1681.10t.025=2.776(n-p-2=8-2-2=4degreesoffreedom)Sincenoneofthestudentizeddeletedresidualsislesstan-2.776orgreaterthan2.776,weconcludethattherearenooutliersinthedata.d.UsingMinitabweobtainedthefollowingvalues:ObservationhiDi1.631.522.65.703.04.017.66.818.13.06ThecriticalaveragevalueisSincenoneofthevaluesexceed1.125,weconcludethattherearenoinfluentialobservations.However,usingCook’sdistancemeasure,weseethatD11(ruleofthumbcriticalvalue);thus,weconcludethefirst