北京理工大學(xué)數(shù)學(xué)專業(yè)應(yīng)用回歸分析期末試題(MTH17095)

課程編號(hào)：課程編號(hào)：07000237北京理工大學(xué)2011-2012學(xué)年第二學(xué)期2009級(jí)應(yīng)用回歸分析期末試題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豐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課程編號(hào)：MTH17095北京理工大學(xué)2012-2013學(xué)年第二學(xué)期2010級(jí)應(yīng)用回歸分析期末試題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.課程編號(hào)：課程編號(hào)：MTH17095北京理工大學(xué)2013—2014學(xué)年第二學(xué)期2011級(jí)應(yīng)用回歸分析期末試題*卷（年份推斷為2011，試卷類型未知）附表：F（5,10）=3.33,t（10）=2.22810.050.025（28分）中國(guó)民航客運(yùn)量回歸方程為：（括號(hào)里是標(biāo)準(zhǔn)誤差）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—民航客運(yùn)量（萬(wàn)人）X]—國(guó)民收入（億元）x2—消費(fèi)額（億元）x3—鐵路客運(yùn)量（萬(wàn)人）x4—民航航線里程（萬(wàn)公里）x5—來華旅游入境人數(shù)（萬(wàn)人）（1）解釋回歸方程中民航航線里程的回歸系數(shù)；（2）檢驗(yàn)回歸方程的顯著性；G=0.05）（3）計(jì)算回歸方程的決定系數(shù)，并作出解釋；（4）計(jì)算回歸的標(biāo)準(zhǔn)誤差，解釋這一結(jié)果；（5）對(duì)模型中來華旅游入境人數(shù)對(duì)民航客運(yùn)量是否有顯著影響進(jìn)行t-檢驗(yàn)；（6）建立x4的回歸系數(shù)0的置信水平為95%的置信區(qū)間。44（15分）中國(guó)民航客運(yùn)量回歸方程為：y=450.9+0.354x-0.561x-0.0073x+21.578x+0.435x,12345其中：y—民航客運(yùn)量（萬(wàn)人）X]—國(guó)民收入（億元）x2—消費(fèi)額（億元）x3—鐵路客運(yùn)量（萬(wàn)人）x4—民航航線里程（萬(wàn)公里）x5—來華旅游入境人數(shù)（萬(wàn)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）寫出條件數(shù)的定義，解釋中國(guó)民航客運(yùn)量模型中的關(guān)于條件數(shù)的結(jié)果；（2）解釋中國(guó)民航客運(yùn)量模型中的關(guān)于方差比例的結(jié)果；（3）結(jié)合中國(guó)民航客運(yùn)量模型說明多重共線性對(duì)回歸模型的影響。3.（16分）研究切割工具類型對(duì)切割工具壽命的影響。y是切割工具壽命，x1是每分鐘車床的轉(zhuǎn)速，x2是切割工具的類型，x2=0，如果觀測(cè)值來自工具類型A，x2=1，如果觀測(cè)值來自工具類型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寫出模型(A)的回歸方程；解釋模型(A)的回歸系數(shù)，模型(A)中x2對(duì)y有顯著性影響嗎？G=0.05)⑶討論模型(A)和模型(B)的區(qū)別；(4)模型(B)中的兩條回歸線的斜率相等嗎？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的最小二乘估計(jì),證明：^2=1y證明：^2=1y=X0+8E（8）=0VarG）=o21Jn其中y、x12x22xn2丿n-2EG廠X)2是°2的無偏估計(jì)。i=1(20分)設(shè)全模型為二元線性回歸模型，模型矩陣表示為〈IP）1IB丿選模型為一元線性回歸模型：y=0x+8,E(8)=0,cov(￡,8)=<i11iiiij試求：(1)全模型下0,0的最小二乘估計(jì)0,0；(2)選模型下0的最小二乘估計(jì)0；121211(3)證明若全模型正確，則選模型回歸系數(shù)01的最小二乘估計(jì)01是全模型相應(yīng)參數(shù)01的有偏估計(jì)；(4)簡(jiǎn)述自變量選擇對(duì)回歸方程估計(jì)和預(yù)測(cè)的影響。(8分)什么是自相關(guān)？舉例說明自相關(guān)產(chǎn)生的原因。課程編號(hào)：課程編號(hào)：MTH17095北京理工大學(xué)2015—2016學(xué)年第二學(xué)期2013級(jí)應(yīng)用回歸分析期末試題B卷課程編號(hào)：課程編號(hào)：MTH17095北京理工大學(xué)2014—2015學(xué)年第二學(xué)期2012級(jí)應(yīng)用回歸分析期末試題B卷附表：F(1,22)=4.30,F(1,23)=4.28,t(23)=2.06870.050.050.025(30分)考慮如下模型：y=0+0x+0x,n=25,01122其中：『=送貨時(shí)間(分)X]=產(chǎn)品的箱數(shù)，x2=送貨的距離(英尺)，有如下兩個(gè)回歸方程(括號(hào)里是標(biāo)準(zhǔn)誤差)。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解釋模型(A)中產(chǎn)品的箱數(shù)的回歸系數(shù)；對(duì)送貨距離對(duì)送貨時(shí)間是否有顯著的線性效應(yīng)作偏F-檢驗(yàn)；G=0.05)計(jì)算y與X],x2的復(fù)相關(guān)系數(shù)，并對(duì)結(jié)果作出解釋；(4)計(jì)算y與x2的偏相關(guān)系數(shù)；(5)檢驗(yàn)?zāi)Ｐ?B)的顯著性G=0.05)；(6)建立模型(B)中參數(shù)片的95%置信區(qū)間。(15分)以下三問在第1題中送貨模型下考慮。模型(A)中，已知9號(hào)點(diǎn)的學(xué)生化殘差SRE=3.2138，杠桿值h=0.4983，庫(kù)克距999離D=3.418，解釋這個(gè)結(jié)果；9說明學(xué)生化殘差，杠桿值和庫(kù)克距離之間的關(guān)系；⑶如果模型(A)正確而誤用了模型(B)，對(duì)估計(jì)和預(yù)測(cè)會(huì)產(chǎn)生什么影響？(18分)某經(jīng)濟(jì)學(xué)家想調(diào)查文化程度對(duì)家庭儲(chǔ)蓄的影響，在一個(gè)中等收入的樣本中，隨機(jī)調(diào)查了13戶高學(xué)歷家庭與14戶中低學(xué)歷的家庭，因變量y為上一年家庭儲(chǔ)蓄增加額，自變量x1為上一年家庭總收入，自變量x2表示家庭學(xué)歷，高學(xué)歷家庭x2=1，低學(xué)歷家庭x2=0，模型(A)：y=—7976+3826x—3700x，12模型(B)：y=—8763+4057x—776x—787xx，1212解釋模型(A)中的回歸系數(shù)；13戶高學(xué)歷家庭的平均年儲(chǔ)蓄增加額為3009.31元，14戶低學(xué)歷家庭的平均年儲(chǔ)蓄增加額為5059.36元，這樣會(huì)認(rèn)為高學(xué)歷家庭每年的儲(chǔ)蓄額比低學(xué)歷的家庭平均少5059.36-3009.31=2050.05元，將此結(jié)果與模型(A)得到的結(jié)果進(jìn)行比較；⑶討論模型(B)和模型(A)的區(qū)別；⑷模型(B)中x1x2的系數(shù)的顯著性檢驗(yàn)的顯著性概率(sig)=0.247，解釋這一結(jié)果。(10分)在一次關(guān)于公共交通的社會(huì)調(diào)查中，一個(gè)調(diào)查項(xiàng)目是“是乘坐公交汽車上下班，還是騎自行車上下班。”因變量y=1表示主要乘坐公交汽車上下班，y=0表示主要騎自行車上下班。自變量x1是年齡，作為連續(xù)型變量；x2是性別，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)寫出Logistic回歸方程；(2)解釋性別的回歸系數(shù)。(20分)考慮如下的簡(jiǎn)單線性回(歸模型)，y=0+0x+8,8i.idN(0,c2),i=1,2,n，其中0已知。i01iii□…0(1)求片的最小二乘估計(jì)；(2)求0]的最小二乘估計(jì)的方差；求片的置信水平為1-Q的置信區(qū)間。(7分)如何正確理解多元線性回歸方程顯著性檢驗(yàn)中拒絕原假設(shè)？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）中國(guó)民航客運(yùn)量回歸方程為：（括號(hào)里是標(biāo)準(zhǔn)誤差）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