商務(wù)與經(jīng)濟(jì)統(tǒng)計(jì)習(xí)題答案(第8版,中文版)SBE8

商務(wù)與經(jīng)濟(jì)統(tǒng)計(jì)習(xí)題答案（第8版，中文版）SBE8Chapter14SimpleLinearRegressionLearningObjectives1.Understandhowregressionanalysiscanbeusedtodevelopanequationthatestimatesmathematicallyhowtwovariablesarerelated.2.Understandthedifferencesbetweentheregressionmodel,theregressionequation,andtheestimatedregressionequation.3.Knowhowtofitanestimatedregressionequationtoasetofsampledatabasedupontheleast-squaresmethod.4.Beabletodeterminehowgoodafitisprovidedbytheestimatedregressionequationandcomputethesamplecorrelationcoefficientfromtheregressionanalysis output. 5. Understand the assumptions necessary forstatisticalinferenceandbeabletotestforasignificantrelationship.6.Learnhowtousearesidualplottomakeajudgementastothevalidityofthe regression assumptions, recognizeoutliers,andidentifyinfluentialobservations.7.Knowhowtodevelopconfidenceintervalestimatesofygivenaspecificvalueofxinboththecaseofameanvalueofyandanindividualvalueofy.8.Beabletocomputethesamplecorrelationcoefficientfromtheregressionanalysisoutput.9.Know the definition of the following terms: independent anddependent simple linear regression regression modelregression equation and estimated regression equation scatterdiagramcoefficientofdeterminationstandarderroroftheestimateconfidenceintervalpredictionintervalresidualplotstandardizedresidualplotoutlierinfluentialobservationleverageSolutions:1a.b.Thereappearstobealinearrelationshipbetweenxandy.c.Manydifferentstraightlinescanbedrawntoprovidealinearapproximationoftherelationshipbetweenxandy;inpartdwewilldeterminetheequationofastraightlinethat“best”representstherelationshipaccordingtotheleastsquarescriterion.d.Summationsneededtocomputetheslopeandy-interceptare:e.2.a.b.Thereappearstobealinearrelationshipbetweenxandy.c.Manydifferentstraightlinescanbedrawntoprovidealinearapproximationoftherelationshipbetweenxandy;inpartdwewilldeterminetheequationofastraightlinethat“best”representstherelationshipaccordingtotheleastsquarescriterion.d.Summationsneededtocomputetheslopeandy-interceptare:e.3.a.b.Summationsneededtocomputetheslopeandy-interceptare:c.4.a.b.Thereappearstobealinearrelationshipbetweenxandy.c.Manydifferentstraightlinescanbedrawntoprovidealinearapproximationoftherelationshipbetweenxandy;inpartdwewilldeterminetheequationofastraightlinethat“best”representstherelationshipaccordingtotheleastsquarescriterion.d.Summationsneededtocomputetheslopeandy-interceptare:e.pounds5.a.b.Thereappearstobealinearrelationshipbetweenxandy.c.Manydifferentstraightlinescanbedrawntoprovidealinearapproximationoftherelationshipbetweenxandy;inpartdwewilldeterminetheequationofastraightlinethat“best”represents therelationshipaccordingtotheleastsquarescriterion.Summationsneededtocomputetheslopeandy-interceptare:d.Aonemilliondollarincreaseinmediaexpenditureswillincreasecasesalesbyapproximately14.42million.e.6.a.b.Thereappearstobealinearrelationshipbetweenxandy.c.Summationsneededtocomputetheslopeandy-interceptare:d.Aonepercentincreaseinthepercentageofflightsarrivingontimewilldecreasethenumberofcomplaintsper100,000passengersby0.07.e7.a.b.Letx=DJIAandy=SP.Summationsneededtocomputetheslopeandy-interceptare:c.orapproximately15008.a.Summationsneededtocomputetheslopeandy-interceptare:b.Increasingthenumberoftimesanadisairedby one will increase the number of household exposures byapproximately3.07million.c.9.a.b.Summationsneededtocomputetheslopeandy-interceptare:c.10.a.b.Letx=performancescoreandy=overallrating.Summationsneededtocomputetheslopeandy-interceptare:c.orapproximately8411.a.b.Thereappearstobealinearrelationshipbetweenthevariables.c.Thesummationsneededtocomputetheslopeandthey-interceptare:d.12.a.b.Thereappearstobeapositivelinearrelationshipbetweenthenumberofemployeesandtherevenue.c.Letx=numberofemployeesandy=revenue.Summationsneededtocomputetheslopeandy-interceptare:d.13.a.b.Thesummationsneededtocomputetheslopeandthey-interceptare:c.orapproximately$13,080.Therequestforanauditappearstobejustified.14.a.b.Thesummationsneededtocomputetheslopeandthey-interceptare:c.15.a.Theestimatedregressionequationandthemeanforthedependentvariableare:ThesumofsquaresduetoerrorandthetotalsumofsquaresareThus,SSR=SST-SSE=80-12.4=67.6b.r2=SSR/SST=67.6/80=.845Theleastsquareslineprovidedaverygoodfit;84.5%ofthevariabilityinyhasbeenexplainedbytheleastsquaresline.c.16.a.Theestimatedregressionequationandthemeanforthedependentvariableare:ThesumofsquaresduetoerrorandthetotalsumofsquaresareThus,SSR=SST-SSE=114.80-6.33=108.47b.r2=SSR/SST=108.47/114.80=.945Theleastsquareslineprovidedanexcellentfit;94.5%ofthevariabilityinyhasbeenexplainedbytheestimatedregressionequation.c.Note:thesignforrisnegativebecausetheslopeoftheestimatedregressionequationisnegative.(b1=-1.88)17.Theestimatedregressionequationandthemeanforthedependentvariableare:ThesumofsquaresduetoerrorandthetotalsumofsquaresareThus,SSR=SST-SSE=11.2-5.3=5.9r2=SSR/SST=5.9/11.2=.527Weseethat52.7%ofthevariabilityinyhasbeenexplainedbytheleastsquaresline.18.a.Theestimatedregressionequationandthemeanforthedependentvariableare:ThesumofsquaresduetoerrorandthetotalsumofsquaresareThus,SSR=SST-SSE=335,000-85,135.14=249,864.86b.r2=SSR/SST=249,864.86/335,000=.746Weseethat74.6%ofthevariabilityinyhasbeenexplainedbytheleastsquaresline.c.19.a.Theestimatedregressionequationandthemeanforthedependentvariableare:ThesumofsquaresduetoerrorandthetotalsumofsquaresareThus,SSR=SST-SSE=47,582.10-7547.14=40,034.96b.r2=SSR/SST=40,034.96/47,582.10=.84Weseethat84%ofthevariabilityinyhasbeenexplainedbytheleastsquaresline.c.20.a.Letx=incomeandy=homeprice.Summationsneededtocomputetheslopeandy-interceptare:b.ThesumofsquaresduetoerrorandthetotalsumofsquaresareThus,SSR=SST-SSE=11,373.09 –2017.37=9355.72r2=SSR/SST=9355.72/11,373.09=.82Weseethat82%ofthevariabilityinyhasbeenexplainedbytheleastsquaresline.c.orapproximately$173,50021.a.Thesummationsneededinthisproblemare:b.$7.60c.Thesumofsquaresduetoerrorandthetotalsumofsquaresare:Thus,SSR=SST-SSE=5,648,333.33-233,333.33=5,415,000r2=SSR/SST=5,415,000/5,648,333.33=.9587Weseethat95.87%ofthevariabilityinyhasbeenexplainedbytheestimatedregressionequation.d.22.a.Thesummationsneededinthisproblemare:b.Thesumofsquaresduetoerrorandthetotalsumofsquaresare:Thus,SSR=SST-SSE=1998-1272.4495=725.5505r2=SSR/SST=725.5505/1998=0.3631Approximately37%ofthevariabilityinchangeinexecutivecompensationisexplainedbythetwo-yearchangeinthereturnonequity.c.Itreflectsalinearrelationshipthatisbetweenweakandstrong.23.a.s2=MSE=SSE/(n-2)=12.4/3=4.133b.c.d.t.025=3.182(3degreesoffreedom)Sincet=4.04 t.05=3.182werejectH0:b1=0e.MSR=SSR/1=67.6F=MSR/MSE=67.6/4.133=16.36F.05=10.13(1degreeoffreedomnumeratorand3denominator)SinceF=16.36 F.05=10.13werejectH0:b1=0SourceofVariationSumofSquaresDegreesofFreedomMeanSquareFRegression67.6167.616.36Error12.434.133Total80.0424.a.s2=MSE=SSE/(n-2)=6.33/3=2.11b.c.d.t.025=3.182(3degreesoffreedom)Sincet=-7.18 -t.025=-3.182werejectH0:b1=0e.MSR=SSR/1=8.47F=MSR/MSE=108.47/2.11=51.41F.05=10.13(1degreeoffreedomnumeratorand3denominator)SinceF=51.41F.05=10.13werejectH0:b1=0SourceofVariationSumofSquaresDegreesofFreedomMeanSquareFRegression108.471108.4751.41Error6.3332.11Total114.80425.a.s2=MSE=SSE/(n-2)=5.30/3=1.77b.t.025=3.182(3degreesoffreedom)Sincet=1.82t.025=3.182wecannotrejectH0:b1=0;xandydonotappeartoberelated.c.MSR=SSR/1=5.90/1=5.90F=MSR/MSE=5.90/1.77=3.33F.05=10.13(1degreeoffreedomnumeratorand3denominator)SinceF=3.33 F.05=10.13wecannotrejectH0:b1=0;xandydonotappeartoberelated.26.a.s2=MSE=SSE/(n-2)=85,135.14/4=21,283.79t.025=2.776(4degreesoffreedom)Sincet=3.43 t.025=2.776werejectH0:b1=0b.MSR=SSR/1=249,864.86/1=249.864.86F=MSR/MSE=249,864.86/21,283.79=11.74F.05=7.71(1degreeoffreedomnumeratorand4denominator)SinceF=11.74 F.05=7.71werejectH0:b1=0c.SourceofVariationSumofSquaresDegreesofFreedomMeanSquareFRegression*****.861*****.8611.74Error*****.144*****.79Total*****527.Thesumofsquaresduetoerrorandthetotalsumofsquaresare:SSE=SST=2442Thus,SSR=SST-SSE=2442-170=2272MSR=SSR/1=2272SSE=SST-SSR=2442-2272=170MSE=SSE/(n-2)=170/8=21.25F=MSR/MSE=2272/21.25=106.92F.05=5.32(1degreeoffreedomnumeratorand8denominator)SinceF=106.92F.05=5.32werejectH0:b1=0.Yearsofexperienceandsalesarerelated.28.SST=411.73SSE=161.37SSR=250.36MSR=SSR/1=250.36MSE=SSE/(n-2)=161.37/13=12.413F=MSR/MSE=250.36/12.413=20.17F.05=4.67(1degreeoffreedomnumeratorand13denominator)SinceF=20.17 F.05=4.67werejectH0:b1=0.29.SSE=233,333.33SST=5,648,333.33SSR=5,415,000MSE=SSE/(n-2)=233,333.33/(6-2)=58,333.33MSR=SSR/1=5,415,000F=MSR/MSE=5,415,000/58,333.25=92.83SourceofVariationSumofSquaresDegreesofFreedomMeanSquareFRegression5,415,000.0015,415,00092.83Error233,333.33458,333.33Total5,648,333.335F.05=7.71(1degreeoffreedomnumeratorand4denominator)SinceF=92.83 7.71werejectH0:b1=0.Productionvolumeandtotalcostarerelated.30.UsingthecomputationsfromExercise22,SSE=1272.4495SST=1998SSR=725.5505=45,833.9286t.025=2.571Sincet=1.69 2.571,wecannotrejectH0:b1=0Thereisnoevidenceofasignificantrelationshipbetweenxandy.31.SST=11,373.09SSE=2017.37SSR=9355.72MSR=SSR/1=9355.72MSE=SSE/(n-2)=2017.37/16=126.0856F=MSR/MSE=9355.72/126.0856=74.20F.01=8.53(1degreeoffreedomnumeratorand16denominator)SinceF=74.20F.01=8.53werejectH0:b1=0.32.a.s=2.033b.10.6±3.182(1.11)=10.6±3.53or7.07to14.13c.d.10.6±3.182(2.32)=10.6±7.38or3.22to17.9833.a.s=1.453b.24.69±3.182(.68)=24.69±2.16or22.53to26.85c.d.24.69±3.182(1.61)=24.69±5.12or19.57to29.8134.s=1.332.28±3.182(.85)=2.28±2.70or-.40to4.982.28±3.182(1.58)=2.28±5.03or-2.27to7.3135.a.s=145.892,033.78±2.776(68.54)=2,033.78±190.27or$1,843.51to$2,224.05b.2,033.78±2.776(161.19)=2,033.78±447.46or$1,586.32to$2,481.2436.a.b.s=3.523280.859±2.160(1.055)=80.859±2.279or78.58to83.14c.80.859±2.160(3.678)=80.859±7.944or72.92to88.8037.a.s2=1.88s=1.3713.08±2.571(.52)=13.08±1.34or11.74to14.42or$11,740to$14,420b.sind=1.4713.08±2.571(1.47)=13.08±3.78or9.30to16.86or$9,300to$16,860c.Yes,$20,400ismuchlargerthananticipated.d.Anydeductionsexceedingthe$16,860upperlimitcouldsuggestanaudit.38.a.b.s2 =MSE=58,333.33s=241.525046.67±4.604(267.50)=5046.67±1231.57or$3815.10to$6278.24c.Basedononemonth,$6000isnotoutoflinesince$3815.10to$6278.24isthepredictioninterval.However,asequenceoffivetosevenmonthswithconsistentlyhighcostsshouldcauseconcern.39.a.Summationsneededtocomputetheslopeandy-interceptare:b.SST=39,065.14SSE=4145.141SSR=34,920.000r2=SSR/SST=34,920.000/39,065.141=0.894Theestimatedregressionequationexplained89.4%ofthevariabilityiny;averygoodfit.c.s2=MSE=4145.141/8=518.143270.63±2.262(8.86)=270.63±20.04or250.59to290.67d.270.63±2.262(24.42)=270.63±55.24or215.39to325.8740.a.9b.=20.0+7.21xc.1.3626d.SSE=SST-SSR=51,984.1-41,587.3=10,396.8MSE=10,396.8/7=1,485.3F=MSR/MSE=41,587.3/1,485.3=28.00F.05=5.59(1degreeoffreedomnumeratorand7denominator)SinceF=28F.05=5.59werejectH0:B1=0.e.=20.0+7.21(50)=380.5or$380,50041.a.=6.1092+.8951xb.t.025=2.306(1degreeoffreedomnumeratorand8denominator)Sincet=6.01 t.025=2.306werejectH0:B1=0c.=6.1092+.8951(25)=28.49or$28.49permonth42a.=80.0+50.0xb.30c.F=MSR/MSE=6828.6/82.1=83.17F.05=4.20(1degreeoffreedomnumeratorand28denominator)SinceF=83.17 F.05=4.20werejectH0:B1=0.Branchofficesalesarerelatedtothesalespersons.d.=80+50(12)=680or$680,00043.a.TheMinitaboutputisshownbelow:TheregressionequationisPrice=-11.8+2.18IncomePredictorCoefSECoefTPConstant-11.8012.84-0.920.380Income2.18430.27807.860.000S=6.634R-Sq=86.1%R-Sq(adj)=84.7%AnalysisofVarianceSourceDFSSMSFPRegression12717.92717.961.750.000ResidualError10440.144.0Total113158.0PredictedValuesforNewObservationsNewObsFitSEFit95.0%CI95.0%PI175.792.47(70.29,81.28)(60.02,91.56)b.r2=.861.Theleastsquareslineprovidedaverygoodfit.c.The95%confidenceintervalis70.29to81.28or$70,290to$81,280.d.The95%predictionintervalis60.02to91.56or$60,020to$91,560.44.a/b.Thescatterdiagramshowsalinearrelationshipbetweenthetwovariables.c.TheMinitaboutputisshownbelow:TheregressionequationisRental$=37.1-0.779Vacancy%PredictorCoefSECoefTPConstant37.0663.53010.500.000Vacancy%-0.77910.2226-3.500.003S=4.889R-Sq=43.4%R-Sq(adj)=39.8%AnalysisofVarianceSourceDFSSMSFPRegression1292.89292.8912.260.003ResidualError16382.3723.90Total17675.26PredictedValuesforNewObservationsNewObsFitSEFit95.0%CI95.0%PI117.592.51(12.27,22.90)(5.94,29.23)228.261.42(25.26,31.26)(17.47,39.05)ValuesofPredictorsforNewObservationsNewObsVacancy%125.0211.3d.Sincethep-value=0.003islessthana=.05,therelationshipissignificant.e.r2=.434.Theleastsquareslinedoesnotprovideaverygoodfit.f.The95%confidenceintervalis12.27to22.90or$12.27to$22.90.g.The95%predictionintervalis17.47to39.05or$17.47to$39.05.45.a.b.Theresidualsare3.48,-2.47,-4.83,-1.6,and5.22c.Withonly5observationsitisdifficulttodetermineiftheassumptionsaresatisfied.However,theplotdoessuggestcurvatureintheresidualsthatwouldindicatethattheerrortermassumptionsarenotsatisfied.Thescatterdiagramforthesedataalsoindicatesthattheunderlyingrelationshipbetweenxandymaybecurvilinear.d.Thestandardizedresidualsare1.32,-.59,-1.11,-.40,1.49.e.Thestandardizedresidualplothasthesameshapeastheoriginalresidualplot.Thecurvatureobservedindicatesthattheassumptionsregardingtheerrortermmaynotbesatisfied.46.a.b.Theassumptionthatthevarianceisthesameforallvaluesofxisquestionable.Thevarianceappearstoincreaseforlargervaluesofx.47.a.Letx=advertisingexpendituresandy=revenueb.SST=1002SSE=310.28SSR=691.72MSR=SSR/1=691.72MSE=SSE/(n-2)=310.28/5=62.0554F=MSR/MSE=691.72/62.0554=11.15F.05=6.61(1degreeoffreedomnumeratorand5denominator)SinceF=11.15 F.05=6.61weconcludethatthetwovariablesarerelated.c.d.Theresidualplotleadsustoquestiontheassumptionofalinearrelationshipbetweenxandy.Eventhoughtherelationshipissignificantatthe.05levelofsignificance,itwouldbeextremelydangeroustoextrapolatebeyondtherangeofthedata.48.a.b.Theassumptionsconcerningtheerrortermappearreasonable.49.a.Letx=returnoninvestment(ROE)andy=price/earnings(P/E)ratio.b.c.Thereisanunusualtrendintheresiduals.Theassumptionsconcerningtheerrortermappearquestionable.50.a.The*****outputisshownbelow:TheregressionequationisY=66.1+0.402XPredictorCoefStdevt-ratiopConstant66.1032.062.060.094X0.40230.22761.770.137s=12.62R-sq=38.5%R-sq(adj)=26.1%AnalysisofVarianceSOURCEDFSSMSFpRegression1497.2437Error5795.7159.1Total61292.9UnusualObservationsObs.XYFitStdev.FitResidualSt.Resid1135145.00120.424.8724.582.11RRdenotesanobs.withalargest.resid.Thestandardizedresidualsare:2.11,-1.08,.14,-.38,-.78,-.04,-.41Thefirstobservationappearstobeanoutliersinceithasalargestandardizedresidual.b.2.4+-******D---1.2+----*0.0+*--**-*--1.2+*---+---------+---------+---------+---------+---------+ YHAT110.0115.0120.0125.0130.0135.0Thestandardizedresidualplotindicatesthattheobservationx=135,y=145maybeanoutlier;notethatthisobservationhasastandardizedresidualof2.11.c.Thescatterdiagramisshownbelow-Y-*--135+--**--120+** *-105+--*----+---------+---------+---------+---------+---------+--X105120135150165180Thescatterdiagramalsoindicatesthattheobservationx=135,y=145maybeanoutlier;theimplicationisthatforsimplelinearregressionanoutliercanbeidentifiedbylookingatthescatterdiagram.51.a.TheMinitaboutputisshownbelow:TheregressionequationisY=13.0+0.425XPredictorCoefStdevt-ratiopConstant13.0022.3965.430.002X0.42480.21162.010.091s=3.181R-sq=40.2%R-sq(adj)=30.2%AnalysisofVarianceSOURCEDFSSMSFpRegression140.7840.784.030.091Error660.7210.12Total7101.50UnusualObservationsObs.XYFitStdev.FitResidualSt.Resid712.024.0002.00R822.019.0022.352.78-3.35-2.16RXRdenotesanobs.withalargest.resid.Xdenotesanobs.whoseXvaluegivesitlargeinfluence.Thestandardizedresidualsare:-1.00,-.41,.01,-.48,.25,.65,-2.00,-2.16Thelasttwoobservationsinthedatasetappeartobeoutlierssincethestandardizedresidualsfortheseobservationsare2.00and-2.16,respectively.b.Using*****,weobtainedthefollowingleveragevalues:.28,.24,.16,.14,.13,.14,.14,.76*****identifiesanobservationashavinghighleverageifhi 6/n;forthesedata,6/n=6/8=.75.Sincetheleveragefortheobservationx=22,y=19is.76,*****wouldidentifyobservation8asahighleveragepoint.Thus,weconcludethatobservation8isaninfluentialobservation.c.24.0+*-Y---20.0+*-*-*--16.0+*-*--*-12.0+*-+---------+---------+---------+---------+---------+------X0.05.010.015.020.025.0Thescatterdiagramindicatesthattheobservationx=22,y=19isaninfluentialobservation.52.a.TheMinitaboutputisshownbelow:TheregressionequationisAmount=4.09+0.196MediaExpPredictorCoefSECoefTPConstant4.0892.1681.890.096MediaExp0.*****0.036355.380.001S=5.044R-Sq=78.3%R-Sq(adj)=75.6%AnalysisofVarianceSourceDFSSMSFPRegression1735.84735.8428.930.001 Residual Error 8 203.51 25.44 Total 9 939.35 UnusualObservationsObsMediaExpAmountFitSEFitResidualStResid112036.3027.553.308.752.30RRdenotesanobservationwithalargestandardizedresidualb.Minitabidentifiesobservation1ashavingalargestandardizedresidual;thus,wewouldconsiderobservation1tobeanoutlier.53.a.TheMinitaboutputisshownbelow:TheregressionequationisExposure=-8.6+7.71AiredPredictorCoefSECoefTPConstant-8.5521.65-0.390.703Aired7.71490.511915.070.000S=34.88R-Sq=96.6%R-Sq(adj)=96.2%AnalysisofVarianceSourceDFSSMSFPRegression1**********227.170.000ResidualError897351217Total9*****UnusualObservationsObsAiredExposureFitSEFitResidualStResid195.0758.8724.432.034.42.46RXRdenotesanobservation with a large standardized residual X denotes anobservationwhoseXvaluegivesitlargeinfluence.b.Minitabidentifiesobservation1ashavingalargestandardizedresidual;thus,wewouldconsiderobservation1tobeanoutlier.Minitabalsoidentifiesobservation1asaninfluentialobservation.54.a.TheMinitaboutputisshownbelow:TheregressionequationisSalary=707+0.00482MktCapPredictorCoefSECoefTPConstant707.0118.05.990.000MktCap0.***-*****0.***-*****5.960.000S=379.8R-Sq=66.4%R-Sq(adj)=64.5%AnalysisofVarianceSourceDFSSMSFPRegression1***-********-*****35.550.000ResidualError18***-**********Total19***-*****UnusualObservationsObsMktCapSalaryFitSEFitResidualStResid6*****3325.03149.5338.6175.51.02X17*****116.21289.586.4-1173.3-3.17RRdenotesanobservationwithalargestandardizedresidualXdenotesanobservationwhoseXvaluegivesitlargeinfluence.b.Minitabidentifiesobservation6ashavingalargestandardizedresidualandobservation17asanobservationwhosexvaluegivesitlargeinfluence.Astandardizedresidualplotagainstthepredictedvaluesisshownbelow:55.No.Regressionorcorrelationanalysiscanneverprovethattwovariablesarecasuallyrelated.56.Theestimateofameanvalueisanestimateoftheaverageofallyvaluesassociatedwiththesamex.Theestimateofanindividualyvalueisanestimateofonlyoneoftheyvaluesassociatedwithaparticularx.57.Todeterminewhetherornotthereisasignificantrelationshipbetweenxandy.However,ifwerejectB1=0,itdoesnotimplyagoodfit.58.a.TheMinitaboutputisshownbelow:TheregressionequationisPrice=9.26+0.711SharesPredictorCoefSECoefTPConstant9.2651.0998.430.000Shares0.71050.14744.820.001S=1.419R-Sq=74.4%R-Sq(adj)=71.2%AnalysisofVarianceSourceDFSSMSFPRegression146.78446.78423.220.001ResidualError816.1162.015Total962.900b.Sincethep-valuecorrespondingtoF=23.22=.001 a=.05,therelationshipissignificant.c.=.744;agoodfit.Theleastsquareslineexplained74.4%ofthevariabilityinPrice.d.59.a.TheMinitaboutputisshownbelow:TheregressionequationisOptions=-3.83+0.296CommonPredictorCoefSECoefTPConstant-3.8345.903-0.650.529Common0.*****0.0264811.170.000S=11.04R-Sq=91.9%R-Sq(adj)=91.2%AnalysisofVarianceSourceDFSSMSFPRegression1**********124.720.000ResidualError111341122Total12*****b.;approximately40.6millionsharesofoptionsgrantsoutstanding.c.=.919;averygoodfit.Theleastsquareslineexplained91.9%ofthevariabilityinOptions.60.a.TheMinitaboutputisshownbelow:TheregressionequationisIBM=0.275+0.950SP500PredictorCoefStDevTPConstant0.27470.90040.310.768SP5000.94980.35692.660.029S=2.664R-Sq=47.0%R-Sq(adj)=40.3%AnalysisofVarianceSourceDFSSMSFPRegression150.25550.2557.080.029Error856.7817.098Total9107.036b.Sincethep-value=0.029islessthana=.05,therelationshipissignificant.c.r2=.470.Theleastsquareslinedoesnotprovideaverygoodfit.d.Woolworthhashigherriskwithamarketbetaof1.25.61.a.b.Itappearsthatthereisapositivelinearrelationshipbetweenthetwovariables.c.TheMinitaboutputisshownbelow:TheregressionequationisHigh=23.9+0.898LowPredictorCoefSECoefTPConstant23.8996.4813.690.002Low0.89800.11218.010.000S=5.285R-Sq=78.1%R-Sq(adj)=76.9%AnalysisofVarianceSourceDFSSMSFPRegression11792.31792.364.180.000ResidualError18502.727.9Total192294.9d.Sincethep-valuecorrespondingtoF=64.18=.000 a=.05,therelationshipissignificant.e.=.781;agoodfit.Theleastsquareslineexplained78.1%ofthevariabilityinhightemperature.f.62.The*****outputisshownbelow:TheregressionequationisY=10.5+0.953XPredictorCoefStdevt-ratiopConstant10.5283.7452.810.023X0.95340.13826.900.000s=4.250R-sq=85.6%R-sq(adj)=83.8%AnalysisofVarianceSOURCEDFSSMSFpRegression1860.05860.0547.620.000Error8144.4718.06Total91004.53FitStdev.Fit95%C.I.95%P.I.39.131.49(35.69,42.57)(28.74,49.52)a.=10.5+.953xb.Sincethep-valuecorrespondingtoF=47.62=.000 a=.05,werejectH0:b1=0.c.The95%predictionintervalis28.74to49.52or$2874to$4952d.Yes,sincetheexpectedexpenseis$3913.63.a.TheMinitaboutputisshownbelow:TheregressionequationisDefects=22.2-0.148SpeedPredictorCoefSECoefTPConstant22.1741.65313.420.000Speed-0.*****0.04391-3.370.028S=1.489R-Sq=73.9%R-Sq(adj)=67.4%AnalysisofVarianceSourceDFSSMSFPRegression125.13025.13011.330.028ResidualError48.8702.217Total534.000PredictedValuesforNewObservationsNewObsFitSEFit95.0%CI95.0%PI114.7830.896(12.294,17.271)(9.957,19.608)b.Sincethep-valuecorrespondingtoF=11.33=.028 a=.05,therelationshipissignificant.c.=.739;agoodfit.Theleastsquareslineex