商务与经济统计习题答案（第8版，中文版）SBE8-SM14

14-1Chapter14SimpleLinearRegressionLearningObjectives1.Understandhowregressionanalysiscanbeusedtodevelopanequationthatestimatesmathematicallyhowtwovariablesarerelated.2.Understandthedifferencesbetweentheregressionmodel,theregressionequation,andtheestimatedregressionequation.3.Knowhowtofitanestimatedregressionequationtoasetofsampledatabasedupontheleast-squaresmethod.4.Beabletodeterminehowgoodafitisprovidedbytheestimatedregressionequationandcomputethesamplecorrelationcoefficientfromtheregressionanalysisoutput.5.Understandtheassumptionsnecessaryforstatisticalinferenceandbeabletotestforasignificantrelationship.6.Learnhowtousearesidualplottomakeajudgementastothevalidityoftheregressionassumptions,recognizeoutliers,andidentifyinfluentialobservations.7.Knowhowtodevelopconfidenceintervalestimatesofygivenaspecificvalueofxinboththecaseofameanvalueofyandanindividualvalueofy.8.Beabletocomputethesamplecorrelationcoefficientfromtheregressionanalysisoutput.9.Knowthedefinitionofthefollowingterms:independentanddependentvariablesimplelinearregressionregressionmodelregressionequationandestimatedregressionequationscatterdiagramcoefficientofdeterminationstandarderroroftheestimateconfidenceintervalpredictionintervalresidualplotstandardizedresidualplotoutlierinfluentialobservationleverageChapter1414-2Solutions:1a.b.Thereappearstobealinearrelationshipbetweenxandy.c.Manydifferentstraightlinescanbedrawntoprovidealinearapproximationoftherelationshipbetweenxandy;inpartdwewilldeterminetheequationofastraightlinethat“best”representstherelationshipaccordingtotheleastsquarescriterion.d.Summationsneededtocomputetheslopeandy-interceptare:21540()()26()10iiiiixyxxyyxx12()()262.610()iiixxyybxxbybx01826302(.)()...yx0226e...().y0226410602468101214160123456xySimpleLinearRegression14-32.a.b.Thereappearstobealinearrelationshipbetweenxandy.c.Manydifferentstraightlinescanbedrawntoprovidealinearapproximationoftherelationshipbetweenxandy;inpartdwewilldeterminetheequationofastraightlinethat“best”representstherelationshipaccordingtotheleastsquarescriterion.d.Summationsneededtocomputetheslopeandy-interceptare:219116()()57.8()30.8iiiiixyxxyyxx12()()57.81.876630.8()iiixxyybxxbybx012321876638303311.(.)(.)...yx3033188e...().y303318861905051015202530350246810xyChapter1414-43.a.b.Summationsneededtocomputetheslopeandy-interceptare:22617()()11.6()22.8iiiiixyxxyyxx12()()11.60.508822.8()iiixxyybxxbybx013405088207542.(.)(5.)...yx075051c...().y0750514279012345670246810xySimpleLinearRegression14-5100105110115120125130135616263646566676869xy4.a.b.Thereappearstobealinearrelationshipbetweenxandy.c.Manydifferentstraightlinescanbedrawntoprovidealinearapproximationoftherelationshipbetweenxandy;inpartdwewilldeterminetheequationofastraightlinethat“best”representstherelationshipaccordingtotheleastsquarescriterion.d.Summationsneededtocomputetheslopeandy-interceptare:2325585()()110()20iiiiixyxxyyxx12()()1105.520()iiixxyybxxbybx011175652405(5.)()...yx240555e.....()yx24055524055563106poundsChapter1414-65.a.b.Thereappearstobealinearrelationshipbetweenxandy.c.Manydifferentstraightlinescanbedrawntoprovidealinearapproximationoftherelationshipbetweenxandy;inpartdwewilldeterminetheequationofastraightlinethat“best”representstherelationshipaccordingtotheleastsquarescriterion.Summationsneededtocomputetheslopeandy-interceptare:2420.65958.7()()142,040.3443()9847.6486iiiiixyxxyyxx12()()142,040.344314.42389847.6486()iiixxyybxxbybx0185124291442386008571542.(.)(.)...yx15421442d.Aonemilliondollarincreaseinmediaexpenditureswillincreasecasesalesbyapproximately14.42million.e.....().yx15421442154214427099398100300500700900110013001500170019002100020406080100120140xySimpleLinearRegression14-76.a.b.Thereappearstobealinearrelationshipbetweenxandy.c.Summationsneededtocomputetheslopeandy-interceptare:2667.27.18()()9.0623()128.7iiiiixyxxyyxx12()()9.06230.0704128.7()iiixxyybxxbybx010797800704741333602.(.)(.)...yx602007d.Aonepercentincreaseinthepercentageofflightsarrivingontimewilldecreasethenumberofcomplaintsper100,000passengersby0.07.e....(80).yx60200760200704200.20.40.60.811.21.466687072747678808284xyChapter1414-87.a.b.Letx=DJIAandy=S&P.Summationsneededtocomputetheslopeandy-interceptare:2104,85014,233()()268,921()1,806,384iiiiixyxxyyxx12()()268,9210.148871,806,384()iiixxyybxx011423.3(.14887)(10,485)137.629bybxˆ137.630.1489yxc.ˆ137.630.1489(11,000)1500.27yorapproximately15008.a.Summationsneededtocomputetheslopeandy-interceptare:21211120.9()()544.0429()177.4286iiiiixyxxyyxx12()()544.04293.0663177.4286()iiixxyybxxbybx0116012863066317285710713.(.)(.)...yx10713307b.Increasingthenumberoftimesanadisairedbyonewillincreasethenumberofhouseholdexposuresbyapproximately3.07million.c.....().yx1071330710713307151532130013501400145015001550960098001000010