北京理工大学数学专业应用回归分析期末试题(MTH17095)

课程编号：课程编号：07000237北京理工大学2011-2012学年第二学期2009级应用回归分析期末试题A卷l.(35)Considerthefollowingmodel:y=B+Px+Px+Px+£,i011i22i33iiwherey=laborforcepaticipation(%)byfamilyheadsofpoorfamilies,xl=meanfamilyincome($),x2=meanfamilysize,x3=unemploymentrate(%ofcivilianlaborforceunemployed).Twoversionsofthemodelwereestimatedasfollows(thestandarderrorsareinthebrackets).(A)y=—33.46+0.019x+15.52x+0.813xili2i3i(48.78)(0.019)(9.46)(1.911)n=15,SS=5130.13,SS(A)=3716.98TRes(B)y=—26.51+0.018x+15.30xi1i2i(44.37)(0.018)(9.12)SS(B)=3778.11ResInterpretthecoefficientofmeanfamilyincomeinmodel(B);=0.05)=0.05)=0.05)=0.05)inmodel(A);(a=0.05inmodel(A);(a=0.05)Testthesignificanceofmodel(B);Finda95%confidenceintervalforthecoefficientP1ofx1inmodel(B);(7)Interprettheconfidencecoefficient95%in(6).2.(15)Coefficients(a)ModelUnstandardizedCoefficientsStandardizedCoefficientstSig.CollinearityStatisticsBStd.ErrorBetaToleranceVIF1(Constant)462.386218.0762.120.060X1.418.1082.8903.880.003.0002002.085X2-.635.160-2.809-3.962.003.0011815.142X3-.007.002-.077-2.695.022.3392.949X417.9204.922.4413.641.005.01952.873X5.400.062.5326.487.000.04124.273aDependentVariable:y

x1=nationalincome(100millionyuan)x2=volumeofconsumption(100millionyuan)x3=volumeofpassengersonrailway(tenthousandspersons)x4=lengthofairlineofcivilaviation(tenthousandspersons)x5=numberofinboundtouristarrivals(tenthousandspersons)y=volumeofpassengersofcivilaviation(tenthousandspersons)(1)WhatproblemdotheVIFsimply?(2)Whichregressioncoefficientsmayhavethewrongsign?(3)Discussthereasonsfortheproblemin(2).3.(12)Considerthefollowingmodel(n=8):y=0。+片x1=nationalincome(100millionyuan)x2=volumeofconsumption(100millionyuan)x3=volumeofpassengersonrailway(tenthousandspersons)x4=lengthofairlineofcivilaviation(tenthousandspersons)x5=numberofinboundtouristarrivals(tenthousandspersons)y=volumeofpassengersofcivilaviation(tenthousandspersons)(1)WhatproblemdotheVIFsimply?(2)Whichregressioncoefficientsmayhavethewrongsign?(3)Discussthereasonsfortheproblemin(2).3.(12)Considerthefollowingmodel(n=8):y=0。+片x+0》x2+£UnstandardizedCoefficientsStandardizedCoefficientstSig.BStd.ErrorBetax.098.0243.2854.153.009x**2-.001.000-2.620-3.312.021(Constant)39.025.370105.331.000wherey=bodytemperatureofapig(centi)x=timelengthafterthepigisinfected(hours)Coefficients(2)Predictbodytemperatureatx=80;(1)Testthesignificanceofx2;(a=0.05)(3)Iftheobservationsofxliein(8,64),what'syoursuggestionaboutthepredictionin(2);4.(18)y=X0+8,X:nxp,rk(X)=p,E(8)=0,VarG)=O2V,V>0,(l)FindGLSEfor0;(2)Findanunbiasedestimatorfor◎2.5.(20)FullmodelSy=0x+0x+8i11i22iiE(8)=0i,nsubsetmodelScov(8,8ij)=Q2,i=j0,i丰jy=0x+8Ei(8)1=10iii,ncov(8,8i)=JQ2,i=jAssumefullmodelistrue,caculateAttachedlist:t(11)=2.201,t(12)=2.1788,t(5)=2.5706,0.0250.0250.025F(1,11)=4.8443,F(2,12)=3.88530.050.05课程编号：MTH17095北京理工大学2012-2013学年第二学期2010级应用回归分析期末试题A卷Attachedlist：F(1,22)=4.30,F(1,23)=4.28,F(3,22)=3.418,0.050.050.04t(22)=2.074,t(23)=2.06870.0250.025(28)Considerthefollowingmodel:y=+Bx+Bx,n=25,wherey=delivertime(minutes),x1=numberofcasesofproduct,x2=distancewalkedbytheroutedriver(feet).Twoversionsofthemodelwereestimatedasfollows(thestandarderrorsareinthebrackets).y=2.341+1.616x+0.014x12(1.097)(0.171)(0.004)SS=5784.543,SS(A)=233.732TResy=3.321+2.176x1(1.371)(0.124)SS(B)=402.134ResInterpretthecoefficientofnumberofcasesofproductinmodel(A);significanteffectupondeliverCarryoutat-testtotestwhetherformodel(A)numberofcasesofproducthasasignificanteffectupondelivertime;G=0.05)significanteffectupondeliver(a=0.05)CarryoutapartialF-testtotestwhetherdistancehasatime;(a=0.05)Testthesignificanceofmodel(B);Finda95%confidenceintervalfortheparameterB1frommodel(B);Finda90%BonferroniconfidenceintervalfortheparameterBandBfrommodel(B);Explaintheresultin(6).(18)Considerthefollowingmodel:y=B0+Bx+Bx,n=25,wherey=delivertime(minutes),x1=numberofcasesofproduct,x2=distancewalkedbytheroutedriver(feet).(1)Whatarethehorizontalscaleandverticalscaleinthefollowingpartialregressionplot?Whatdoestheplotindicate?Pahu]PkilDependpnT片工也了1DependpnT片工也了1上：yJ0£14Itisreportedthatstudentizedresidualatpoint9r9=3.2138,h99=0.4983,wherehistheithdiagonalelementofhatmatrixH,andCOOK'sdistanceD9=3.418.Interprettheresults.Thecorrelationcoefficientsr12betweenx1andx2isr12=0.824.Whatdoestheresultimply?Whataresourcesoftheproblem?(15)Tostudytherelationshipbetweentheannualpercapitaexpenditureoneducationandtheannualpercapitaconsumptionexpenditure,twomodelsareusedtofitthedata,wherey:Theannualpercapitaexpenditureoneducation,x:Theannualpercapitaconsumptionexpenditure.

PowerModelSummaryRRsquareAdjustedRsquareStd.ErroroftheEstimate.977.954.950.266TheindependentvariableisxANOVASumofSquaredfMeanSquareFSig.Regression16.217116.217229.580.000Residual.77711.071Total16.99412TheindependentvariableisxCoefficientsUnstandardizedCoefficientsStandardizedCoefficientstSig.BStd.ErrorBetaln(x)1.846.122.97715.152.000(Constant)3.58E-005.000.963.356Thedependentvariableisln(y)ExponentialModelSummaryRRsquareAdjustedRsquareStd.ErroroftheEstimate.997.995.994.090TheindependentvariableisxANOVASumofSquaredfMeanSquareFSig.Regression16.905116.9052086.351.000Residual.08911.008Total16.99412TheindependentvariableisxCoefficientsUnstandardizedCoefficientsStandardizedCoefficientstSig.BStd.ErrorBetax.000.000.99745.677.000(Constant)20.9551.22617.090.000Thedependentvariableisln(y)Considertheaboveoutputanddiscusswhichmodelissuperior.(21)Considerthesimplelinearregressionmodel:y=B0+片x^+£,withE(£)=0,Var(£)=◎CaculateOLSEP1forCaculateOLSEP1forP1;(3)CaculateVar(1)ShowE(MS)=6+卩2S;(2)ShowE(MS)=b2.R1xxRes(18)Alinearregressionmodeliswrittenasfollows:y=Px+Px+Px+Px+8,11223344E(£)=0,Var(£)=C2.Thedataisshowninthefollowingtable:yX]x2x3x412420.211118.01-11-19.711-1-11.91-1-11C)1C)1.课程编号：课程编号：MTH17095北京理工大学2013—2014学年第二学期2011级应用回归分析期末试题*卷（年份推断为2011，试卷类型未知）附表：F（5,10）=3.33,t（10）=2.22810.050.025（28分）中国民航客运量回归方程为：（括号里是标准误差）y=450.9+0.354x-0.561x-0.0073x+21.578x+0.435x,12345（178.08）（0.085）（0.125）（0.002）（4.030）（0.052）n=16,SST=13843371.750,SSR=13818876.769其中：y—民航客运量（万人）X]—国民收入（亿元）x2—消费额（亿元）x3—铁路客运量（万人）x4—民航航线里程（万公里）x5—来华旅游入境人数（万人）（1）解释回归方程中民航航线里程的回归系数；（2）检验回归方程的显著性；G=0.05）（3）计算回归方程的决定系数，并作出解释；（4）计算回归的标准误差，解释这一结果；（5）对模型中来华旅游入境人数对民航客运量是否有显著影响进行t-检验；（6）建立x4的回归系数0的置信水平为95%的置信区间。44（15分）中国民航客运量回归方程为：y=450.9+0.354x-0.561x-0.0073x+21.578x+0.435x,12345其中：y—民航客运量（万人）X]—国民收入（亿元）x2—消费额（亿元）x3—铁路客运量（万人）x4—民航航线里程（万公里）x5—来华旅游入境人数（万人）CollinearityDiagnostics3DimensionEigenvalueConditionIndexVarianceProportions(Constant)X1X2X3X4X515.5781.000.00.00.00.00.00.002.3763.842.00.00.00.00.00.0033.745E-0212.205.01.00.00.00.03.1944.203E-0336.431.17.00.01.09.50.0451.939E-0353.643.72.00.0168.080E-05262.76a.DependentVariable：Y（1）写出条件数的定义，解释中国民航客运量模型中的关于条件数的结果；（2）解释中国民航客运量模型中的关于方差比例的结果；（3）结合中国民航客运量模型说明多重共线性对回归模型的影响。3.（16分）研究切割工具类型对切割工具寿命的影响。y是切割工具寿命，x1是每分钟车床的转速，x2是切割工具的类型，x2=0，如果观测值来自工具类型A，x2=1，如果观测值来自工具类型B。ModelA：y=B+Bx+0x+£01122CoefficientsModelUnstandardizedCoefficientstSig.

BStd.ErrorConstant36.986x1-0.0270.005-5.887.000x215.0041.36011.035.000ModelB：y=0+0x+0x+0xx+801122312CoefficientsModelUnstandardizedCoefficientstSig.BStd.ErrorConstant32.775x1-0.0210.0061-3.45.000x223.9716.76903.54.000x1*x2-0.0120.0088-1.35.200写出模型(A)的回归方程；解释模型(A)的回归系数，模型(A)中x2对y有显著性影响吗？G=0.05)⑶讨论模型(A)和模型(B)的区别；(4)模型(B)中的两条回归线的斜率相等吗？G=0.05)C2，i=j上j=12,n。0,i主jy=0+0x,i01i0C2，i=j上j=12,n。0,i主jy=0+0x,i01i00,0是00,01的最小二乘估计,证明：^2=1y证明：^2=1y=X0+8E（8）=0VarG）=o21Jn其中y、x12x22xn2丿n-2EG厂X)2是°2的无偏估计。i=1(20分)设全模型为二元线性回归模型，模型矩阵表示为〈IP）1IB丿选模型为一元线性回归模型：y=0x+8,E(8)=0,cov(£,8)=<i11iiiij试求：(1)全模型下0,0的最小二乘估计0,0；(2)选模型下0的最小二乘估计0；121211(3)证明若全模型正确，则选模型回归系数01的最小二乘估计01是全模型相应参数01的有偏估计；(4)简述自变量选择对回归方程估计和预测的影响。(8分)什么是自相关？举例说明自相关产生的原因。课程编号：课程编号：MTH17095北京理工大学2015—2016学年第二学期2013级应用回归分析期末试题B卷课程编号：课程编号：MTH17095北京理工大学2014—2015学年第二学期2012级应用回归分析期末试题B卷附表：F(1,22)=4.30,F(1,23)=4.28,t(23)=2.06870.050.050.025(30分)考虑如下模型：y=0+0x+0x,n=25,01122其中：『=送货时间(分)X]=产品的箱数，x2=送货的距离(英尺)，有如下两个回归方程(括号里是标准误差)。y=2.341+1.616x+0.014x12(1.097)(0.171)(0.004)SST=5784.543,SSE(A)=233.732y=3.321+2.176x(1.371)(0.124)SSE(B)=402.134解释模型(A)中产品的箱数的回归系数；对送货距离对送货时间是否有显著的线性效应作偏F-检验；G=0.05)计算y与X],x2的复相关系数，并对结果作出解释；(4)计算y与x2的偏相关系数；(5)检验模型(B)的显著性G=0.05)；(6)建立模型(B)中参数片的95%置信区间。(15分)以下三问在第1题中送货模型下考虑。模型(A)中，已知9号点的学生化残差SRE=3.2138，杠杆值h=0.4983，库克距999离D=3.418，解释这个结果；9说明学生化残差，杠杆值和库克距离之间的关系；⑶如果模型(A)正确而误用了模型(B)，对估计和预测会产生什么影响？(18分)某经济学家想调查文化程度对家庭储蓄的影响，在一个中等收入的样本中，随机调查了13户高学历家庭与14户中低学历的家庭，因变量y为上一年家庭储蓄增加额，自变量x1为上一年家庭总收入，自变量x2表示家庭学历，高学历家庭x2=1，低学历家庭x2=0，模型(A)：y=—7976+3826x—3700x，12模型(B)：y=—8763+4057x—776x—787xx，1212解释模型(A)中的回归系数；13户高学历家庭的平均年储蓄增加额为3009.31元，14户低学历家庭的平均年储蓄增加额为5059.36元，这样会认为高学历家庭每年的储蓄额比低学历的家庭平均少5059.36-3009.31=2050.05元，将此结果与模型(A)得到的结果进行比较；⑶讨论模型(B)和模型(A)的区别；⑷模型(B)中x1x2的系数的显著性检验的显著性概率(sig)=0.247，解释这一结果。(10分)在一次关于公共交通的社会调查中，一个调查项目是“是乘坐公交汽车上下班，还是骑自行车上下班。”因变量y=1表示主要乘坐公交汽车上下班，y=0表示主要骑自行车上下班。自变量x1是年龄，作为连续型变量；x2是性别，x2=1表示男性，x2=0表示女性。VariableBS.E.WalddfSigRExp(B)SEX-2.22391.04764.50591.0338-.2546.1082AGE.1023.04584.98561.0256.27781.1077Constant-2.62851.55372.86201.0907(1)写出Logistic回归方程；(2)解释性别的回归系数。(20分)考虑如下的简单线性回(归模型)，y=0+0x+8,8i.idN(0,c2),i=1,2,n，其中0已知。i01iii□…0(1)求片的最小二乘估计；(2)求0]的最小二乘估计的方差；求片的置信水平为1-Q的置信区间。(7分)如何正确理解多元线性回归方程显著性检验中拒绝原假设？附表：F（5,10）=3.33,t（10）=2.2281,ln7.33=1.99,ln11.5=2.44,ln17.99=2.890.050.025（30分）中国民航客运量回归方程为：（括号里是标准误差）y=450.9+0.354x-0.561x-0.0073x+21.578x+0.435x,12345（178.078）（0.085）（0.125）（0.002）（4.030）（0.052）n=16,SST=13843371.750,SSR=138