2015 1数统学院试卷应用回归分析

学年第一学期班 学 考试科目应用回归分析 A卷闭卷（上机操作 3—二一、计算求解题（—二Consumptiondata.(22Plottheresidualsagainsttimeand inwhetheryoufindanyevidenceofpositiveautocorrelation.(5Conductaformaltestforpositiveautocorrelationusing 0.05.Statethenullhypothesis,thealternative (0.05,dL1.10,dU1.37)(7Handlingautocorrelationwith tionandobtaintheestimatesofequation.(10

and1.WritetheestimatedFromasetofstreptonigrindose-responsedata,anexperimenterdesirestodeveloparelationshipbetweentheproportionoflymphoblastssampledthatcontainaberrationsandthedosageofstreptonigrin.Fivedosagelevelswereappliedtotherabbitsusedfortheexperiment.Alogisticregressionmodelwaspostulated.(15marks)Writethelogisticregressionmodel.(5Computetheweightedleastsquareslogisticregressionequation.(10-1班 A卷闭卷（上机操作 3Inordertostudythegrowthcharacteristicsofcornrootsinthepresenceofaparticularherbicide,anexperimentwasconductedinwhichtheherbicidewasappliedtoaparticulartypeofsoil(Acredale).Datawerecollectedandpercentofcontrol,meaningthepercentofthegrowthobservedwithouttheherbicide,wasusedastheresponse.(20 1 Fitamodelofthetype yxx2,andcompute s2,C,PRESS, 1 Fitthemodelln(yi)01xii,Computethesameinformationasinpart(a).(8Makeacomparisonbetweenthemodelsinparts(a)and(b).Whichispreferred?(2Machinespeed.Thenumberofdefectiveitemsproducedbyamachine(Y)isknowntobelinearlyrelatedtothespeedsettingofthemachine(X).Thedatabelowwerecollectedfromrecentqualitycontrolrecords.(15marks)Fitalinearregressionfunctionbyordinaryleastsquares,andplottheresidualsagainstX.WhatdoestheresidualplotsuggestabouttherelationbetweenthevarianceoftheerrortermandX?(5marks)Writetheweightfunction.Usingtheestimatedweight,obtaintheweightedleastsquaresestimatesof and1Aretheweightedleastsquaresestimatessimilartotheonesobtainedwithordinaryleastsquaresinpart(a)?(10marks)班 ,02学 考试科目应用回归分析 A卷闭卷（上机操作 共 HospitalData.DataaregiventhatreflectinformationtakenfromseventeenU.s.Navalhospitalsatvarioussitesaroundtheworld.Theregressorsareworkloadvariables,i.e.,itemsthatresultintheneedformanpowerinahospitalinstallation.（20marks）Computethevarianceinflationfactorsforthecoefficientsintheabovemodel.(4Computethevariance positionproportions,anddiscussthemulticollinearity.Whatregressorvariablesareinvolvedindependenciesthataredamagingtotheregressioncoefficients?(6marks)Useprinciplecomponentstoestimatecoefficients.Makeanappropriatechoiceregardingthe