商务与经济统计习题答案（第8版，中文版）SBE8-SM15

15-1Chapter15MultipleRegressionLearningObjectives1.Understandhowmultipleregressionanalysiscanbeusedtodeveloprelationshipsinvolvingonedependentvariableandseveralindependentvariables.2.Beabletointerpretthecoefficientsinamultipleregressionanalysis.3.Knowtheassumptionsnecessarytoconductstatisticaltestsinvolvingthehypothesizedregressionmodel.4.Understandtheroleofcomputerpackagesinperformingmultipleregressionanalysis.5.Beabletointerpretandusecomputeroutputtodeveloptheestimatedregressionequation.6.Beabletodeterminehowgoodafitisprovidedbytheestimatedregressionequation.7.Beabletotestforthesignificanceoftheregressionequation.8.Understandhowmulticollinearityaffectsmultipleregressionanalysis.9.Knowhowresidualanalysiscanbeusedtomakeajudgementastotheappropriatenessofthemodel,identifyoutliers,anddeterminewhichobservationsareinfluential.Chapter1515-2Solutions:1.a.b1=.5906isanestimateofthechangeinycorrespondingtoa1unitchangeinx1whenx2isheldconstant.b2=.4980isanestimateofthechangeinycorrespondingtoa1unitchangeinx2whenx1isheldconstant.2.a.Theestimatedregressionequationisˆy=45.06+1.94x1Anestimateofywhenx1=45isˆy=45.06+1.94(45)=132.36b.Theestimatedregressionequationisˆy=85.22+4.32x2Anestimateofywhenx2=15isˆy=85.22+4.32(15)=150.02c.Theestimatedregressionequationisˆy=-18.37+2.01x1+4.74x2Anestimateofywhenx1=45andx2=15isˆy=-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.ˆy=235+10(15)+8(10)=255;salesestimate:$255,000b.Salescanbeexpectedtoincreaseby$10foreverydollarincreaseininventoryinvestmentwhenadvertisingexpenditureisheldconstant.Salescanbeexpectedtoincreaseby$8foreverydollarincreaseinadvertisingexpenditurewheninventoryinvestmentisheldconstant.MultipleRegression15-35.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$93,5606.a.TheMinitaboutputisshownbelow:TheregressionequationisSpeed=49.8+0.0151WeightPredictorCoefSECoefTPConstant49.7819.112.610.021Weight0.0151040.0060052.520.025S=7.000R-Sq=31.1%R-Sq(adj)=26.2%Chapter1515-4AnalysisofVarianceSourceDFSSMSFPRegression1309.95309.956.330.025Error14686.0049.00Total15995.95b.TheMinitaboutputisshownbelow:TheregressionequationisSpeed=80.5-0.00312Weight+0.105HorsepwrPredictorCoefSECoefTPConstant80.4879.1398.810.000Weight-0.0031220.003481-0.900.386Horsepwr0.104710.013317.860.000S=3.027R-Sq=88.0%R-Sq(adj)=86.2%AnalysisofVarianceSourceDFSSMSFPRegression2876.80438.4047.830.000ResidualError13119.159.17Total15995.957.a.TheMinitaboutputisshownbelow:TheregressionequationisSales=66.5+0.414Compet$-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.ˆy=66.5+0.414(170)-0.270(160)=93.68or93,680units8.a.TheMinitaboutputisshownbelow:TheregressionequationisReturn=247-32.8Safety+34.6ExpRatioMultipleRegression15-5PredictorCoefSECoefTPConstant247.4110.42.240.039Safety-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.ˆ24732.8(7.5)34.6(2)70.2y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.ˆy=26.7-1.43(20)+0.0757(1000)=73.8Estimateis73.8