商务与经济统计习题答案（第8版，中文版）SBE8-SM16

16-1Chapter16RegressionAnalysis:ModelBuildingLearningObjectives1.Learnhowthegenerallinearmodelcanbeusedtomodelproblemsinvolvingcurvilinearrelationships.2.Understandtheconceptofinteractionandhowitcanbeaccountedforinthegenerallinearmodel.3.UnderstandhowanFtestcanbeusedtodeterminewhentoaddordeleteoneormorevariables.4.Developanappreciationforthecomplexitiesinvolvedinsolvinglargerregressionanalysisproblems.5.Understandhowvariableselectionprocedurescanbeusedtochooseasetofindependentvariablesforanestimatedregressionequation.6.KnowhowtheDurban-Watsontestcanbeusedtotestforautocorrelation.7.Learnhowanalysisofvarianceandexperimentaldesignproblemscanbeanalyzedusingaregressionmodel.Chapter1616-2Solutions:1.a.TheMinitaboutputisshownbelow:TheregressionequationisY=-6.8+1.23XPredictorCoefStdevt-ratiopConstant-6.7714.17-0.480.658X1.22960.46972.620.059s=7.269R-sq=63.1%R-sq(adj)=53.9%AnalysisofVarianceSOURCEDFSSMSFpRegression1362.13362.136.850.059Error4211.3752.84Total5573.50b.Sincethep-valuecorrespondingtoF=6.85is0.59therelationshipisnotsignificant.c.-40+*-Y-**-*-30+----*20+----*10+------+---------+---------+---------+---------+---------+X20.025.030.035.040.045.0Thescatterdiagramsuggeststhatacurvilinearrelationshipmaybeappropriate.d.TheMinitaboutputisshownbelow:TheregressionequationisY=-169+12.2X-0.177XSQPredictorCoefStdevt-ratiopConstant-168.8839.79-4.240.024X12.1872.6634.580.020XSQ-0.177040.04290-4.130.026s=3.248R-sq=94.5%R-sq(adj)=90.8%AnalysisofVarianceRegressionAnalysis:ModelBuilding16-3SOURCEDFSSMSFpRegression2541.85270.9225.680.013Error331.6510.55Total5573.50e.Sincethep-valuecorrespondingtoF=25.68is.013therelationshipissignificant.f.ˆy=-168.88+12.187(25)-0.17704(25)2=25.1452.a.TheMinitaboutputisshownbelow:TheregressionequationisY=9.32+0.424XPredictorCoefStdevt-ratiopConstant9.3154.1962.220.113X0.42420.19442.180.117s=3.531R-sq=61.4%R-sq(adj)=48.5%AnalysisofVarianceSOURCEDFSSMSFpRegression159.3959.394.760.117Error337.4112.47Total496.80Thehighp-value(.117)indicatesaweakrelationship;notethat61.4%ofthevariabilityinyhasbeenexplainedbyx.b.TheMinitaboutputisshownbelow:TheregressionequationisY=-8.10+2.41X-0.0480XSQPredictorCoefStdevt-ratiopConstant-8.1014.104-1.970.187X2.41270.44095.470.032XSQ-0.047970.01050-4.570.045s=1.279R-sq=96.6%R-sq(adj)=93.2%AnalysisofVarianceSOURCEDFSSMSFpRegression293.52946.76528.600.034Error23.2711.635Total496.800Atthe.05levelofsignificance,therelationshipissignificant;thefitisexcellent.c.ˆy=-8.101+2.4127(20)-0.04797(20)2=20.9653.a.Thescatterdiagramshowssomeevidenceofapossiblelinearrelationship.b.TheMinitaboutputisshownbelow:Chapter1616-4TheregressionequationisY=2.32+0.637XPredictorCoefStdevt-ratiopConstant2.3221.8871.230.258X0.63660.30442.090.075s=2.054R-sq=38.5%R-sq(adj)=29.7%AnalysisofVarianceSOURCEDFSSMSFpRegression118.46118.4614.370.075Error729.5394.220Total848.000c.Thefollowingstandardizedresidualplotindicatesthattheconstantvarianceassumptionisnotsatisfied.--*-1.2+*---*-**0.0+--**---1.2+-**--+---------+---------+---------+---------+---------+------YHAT3.04.05.06.07.08.0d.Thelogarithmictransformationdoesnotappeartoeliminatethewedged-shapedpatternintheaboveresidualplot.Thereciprocaltransformationdoes,however,removethewedge-shapedpattern.Neithertransformationprovidesagoodfit.TheMinitaboutputforthereciprocaltransformationandthecorrespondingstandardizedresidualpotareshownbelow.Theregressionequationis1/Y=0.275-0.0152XPredictorCoefStdevt-ratiopConstant0.274980.046015.980.000X-0.0151820.007421-2.050.080s=0.05009R-sq=37.4%R-sq(adj)=28.5%AnalysisofVarianceSOURCEDFSSMSFpRegression10.0105010.0105014.190.080Error70.0175630.002509Total80.028064RegressionAnalysis:ModelBuilding16-5-*---1.0+*-*---*0.0+*---**--1.0+-**---+---------+---------+---------+---------+---------+----YHAT0.1400.1600.1800.2000.2200.2404.a.TheMinitaboutputisshownbelow:TheregressionequationisY=943+8.71XPredictorCoefStdevt-ratiopConstant943.0559.3815.880.000X8.7141.5445.640.005s=32.29R-sq=88.8%R-sq(adj)=86.1%AnalysisofVarianceSOURCEDFSSMSFpRegression1332233322331.860.005Error441721043Total537395b.Thep-valueof.005=.01;rejectH05.TheMinitaboutputisshownbelow:TheregressionequationisY=433+37.4X-0.3831/YPredictorCoefStdevt-ratiopConstant432.6141.23.060.055X37.4297.8074.790.0171/Y-0.38290.1036-3.700.034Chapter1616-6s=15.83R-sq=98.0%R-sq(adj)=96.7%AnalysisofVarianceSOURCEDFSSMSFpRegression2366431832273.150.003Error3751250Total537395b.Sincethelinearrelationshipwassignificant(Exercise4),thisrelationshipmustbesignificant.Notealsothatsincethep-valueof.005=.05,wecanrejectH0.c.Thefittedvalueis1302.01,withastandarddeviationof9.93.The95%confidenceintervalis1270.41to1333.61;the95%predictionintervalis1242.55to1361.47.6.a.Thescatterdiagramisshownbelow:-*1.60+-DISTANCE---1.20+-*---0.80+*--*--**0.40++---------+---------+---------+---------+---------+------NUMBER8.012.016.020.024.028.0b.No;therelationshipappearstobecurvilinear.c.Severalpossiblemodelscanbefittedtothesedata,asshownbelow:ˆy=2.90-0.185x+.00351x22.91aR1ˆ0.046814.4yx2.91aR