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)：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1.(35)Considerthefollowingmodel:yi

x0 1

x22i

x33i

,iwherey=laborforcepaticipation(%)byfamilyheadsofpoorfamilies,x=meanfamilyincome($),x=meanfamilysize,1 2x=unemploymentrate(%ofcivilianlaborforceunemployed).3Twoversionsofthemodelwereestimatedasfollows(thestandarderrorsareinthebrackets).i

33.460.019x1i

15.52x2i

0.813x3i(48.78) (0.019) (9.46) (1.911)n15,SST

5130.13,SS

Re

A3716.98i

26.510.018x1i

15.30x2i(44.37) (0.018) (9.12)SS B3778.11ResInterpretthecoefficientofmeanfamilyincomeinmodel(B);Carryoutat-testtotestwhetherinmodel(A)meanfamilysizehasasignificanteffectuponlaborforcepaticipation;0.05CarryoutapartialF-testtotestwhetherinunemploymentratehasasignificanteffectuponlaborforcepaticipation;0.05WhatistheadjustedcoefficientofdeterminationR

inmodel(A);Testthesignificanceofmodel(B);

0.05Finda95%confidenceintervalforthecoefficient of x inmodel(B);1 1Interprettheconfidencecoefficient95%in2.(15)Coefficients(a)Model

UnstandardizedCoefficients

Standardized Coefficients

Sig. 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 .3392.949X4 17.9204.922.4413.641.005 .01952.873X5 .400.062.5326.487.000 .04124.273aDependentVariable:yx=nationalincome(100millionyolumeofconsumption(100millionyuan)1 2x=volumeofpassengersonrailway(tenthousandspersons)3x=lengthofairlineofcivilaviation(tenthousandspersons)4x=numberofinboundtouristarrivals(tenthousandspersons)5y=volumeofpassengersofcivilaviation(tenthousandspersons)(1)WhatproblemdotheVIFsimply?(2)Whichregressioncoefficientsmayhavethewrong(3)Discussthereasonsfortheproblemin(2).3.(12)Considerthefollowing

x x20 1 2wherey=bodytemperatureofapiglengthafterthepigisinfected(hours)CoefficientsUnstandardizedB Std.Error BetaCoefficienttsSig.x .098 .024 3.2854.153.009x**2 -.001 .000 -2.620-3.312.021(Constant)39.025 .370105.331.000(1)Testthesignifican2of

0.05 (2)Predictbodytemperatureatx=80;(3)Iftheobservationsofxliein8,gestionaboutthepredictionin(2);X X 0,(1)FindGLSEfor;(2)Findanunbiasedestimator2ory xi 12

x2i i5.(20)FullmodeEi

0 2jcov,i j jyi 1subsetmodelEi

xi0 2jcov,i j jUndersubsetmodelcaculateOLSEfor ;1 1Assumefullmodelistrue,caulateVar .1 1Attachedlist:t0.02511 2.201t0.025122.1788t0.02552.5706,F0.051,110.052,123.8853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

4.30,F

4.28,F

3.418, 0.05

0.05

0.04t 0.025

2.074,t

0.025

232.06871.(28)Considerthefollowingmodel:0

x1

x22

,n=25,wherey=delivertime(minutes),x=numberofcasesofproduct,x=distancewalkedbytheroutedriver(feet).1 2Twoversionsofthemodelwereestimatedasfollows(thestandarderrorsareinthebrackets).(A)2.3411.616x1

0.014x2(1.097) (0.171) (0.004)SS 5784.543,SST

Re

A233.732(B) 3.3212.176x1(1.371) (0.124)SSRe

B402.134Interpretthecoefficientofnumberofcasesofproductinmodel(A); Carryoutat-testtotestwhetherformodel(A)numberofcasesofproducthasasignificanteffectupondelivertime; CarryoutapartialF-testtotestwhetherdistancehasasignificanteffectupondelivertime; Testthesignificanceofmodel(B);0.05Finda95%confidenceintervalfortheparameter1

frommodel(B);Finda90%Bonferroniconfidenceintervalfortheparameter0Explaintheresultin(6).

and 1

frommodel(B);2.(18)Considerthefollowingmodel:0

x1

x22

,n=25,wherey=delivertime(minutes),x=numberofcasesofproduct,x=distancewalkedbytheroutedriver(feet).1 2Whatarethehorizontalscaleandverticalscaleinthefollowingpartialregressionplot?Whatdoestheplotindicate?Itisreportedthatstudentizedresidualatpoint9 r9

3.2138,h99

0.4983,where hii

istheithdiagonalelementofhatmatrixH,anddistance D9

3.418.Interprettheresults.Thecorrelationcoefficientsr12Whataresourcesoftheproblem?

betweenx1

andx2

is r12

0.824.Whatdoestheresultimply?3.(15)Tostudytherelationshipbetweentheannualpercapitaexpenditureoneducationandtheannualpercapitaconsumptionexpenditure,twomodelsareusedtofitthedata,wherey:Theannualpercapitaexpenditureoneducation,x:Theannualpercapitaconsumptionexpenditure.PowerModelSummaryPowerModelSummaryR.977Rsquare AdjustedRsquare.954.950Std.ErroroftheEstimate.266TheindependentvariableisxANOVASumofSquareRegression 16.217Residual .777ANOVASumofSquareRegression 16.217Residual .777Total 16.994df11112MeanSquare16.217.071F229.580Sig..000TheindependentvariableisxCoefficientsUnstandardizedCoefficientsln(x)(Constant)B1.8463.58E-005Std.Error.122.000StandardizedBeta.977tSig.15.152.963.000.356Thedependentvariableisln(y)ExponentialModelSummaryR.997Rsquare AdjustedRsquare.995.994Std.ErroroftheEstimate.090TheindependentvariableisxANOVASumofSquareRegression 16.905Residual .089Total 16.994df11112MeanSquare16.905.008F2086.351Sig..000TheindependentvariableisxCoefficientsUnstandardizedCoefficients StandardizedCoefficients B Std.Error Betax .000 .000 .997 45.677(Constant) 20.955 1.226 17.090Thedependentvariableisln(y)Considertheaboveoutputanddiscusswhichmodelissuperior.

Sig..000.0004.(21)Considerthesimplelinearregressionmodel:y

x

,with E

0,Var

0 112,and uncorrelated.(1)Show EMSR

22S1 xx

; (2)Show E

Re

2.5.(18)Alinearregressionmodeliswrittenasfollows:y

,

11 2

33 44E 0,Var

2.Thedataisshowninthefollowingtable:yx1x2x3x420.211118.01-11-19.711-1-11.91-1-11Constructalinearregressionmodelforthesedata;CaculateOLSE for 1

; (3)CaculateVar .1 1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（年份推斷為201）附表：F0.05

5,10

0.025

102.22811.(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）450.90.354x1

0.561x2

0.0073x3

21.578x4

0.435x,5178.0（0.08）（0.12）（0.00）（4.03）（0.05）n16,SST13843371.750,SSR13818876.769其中：y—民航客運(yùn)量（萬(wàn)人）x—國(guó)民收入（億元）x—消費(fèi)額（億元）1 2x—鐵路客運(yùn)量（萬(wàn)人）x—民航航線里程（萬(wàn)公里）

—來華旅游入境人數(shù)（萬(wàn)人）3 4 5(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；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)行檢驗(yàn)；(6)建立x的回歸系數(shù) 的置信水平為95%的置信區(qū)間。4 42.(15分)中國(guó)民航客運(yùn)量回歸方程為：450.90.354x1

0.561x2

0.0073x3

21.578x4

0.435x,5其中：y—民航客運(yùn)量（萬(wàn)人）x—國(guó)民收入（億元）x—消費(fèi)額（億元）1 2x—鐵路客運(yùn)量（萬(wàn)人）x—民航航線里程（萬(wàn)公里）x—來華旅游入境人數(shù)（萬(wàn)人）3 4 5Dimension Eigenvalue ConditionIndexVarianceProportionsCollinearityDimension Eigenvalue ConditionIndexVarianceProportions(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.Dependent(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)y是每分鐘車床的1=0，如果觀測(cè)值來自工具類型=1，如果觀測(cè)值來自工2 2 2具類型B。ModelA：y0

x1

x22CoefficientsModelModelUnstandardizedCoefficientstSig.BStd.ErrorConstant36.986x1-0.0270.005-5.887.000x215.0041.36011.035.000Modely

xxxx 0 11 22 312ModelUnstandardizedModelUnstandardizedCoefficientstSig.ConstantB32.775Std.Errorx1-0.0210.0061-3.45.000x223.9716.76903.54.000x1*x2-0.0120.0088-1.35.200寫出模型的回歸方程；2解釋模型的回歸系數(shù)，模型中x對(duì)y0.052(4（中的兩條回歸線的斜率相等嗎？0.04.(13分)設(shè)yi

x0 1

,Ei

0,cov,i j

2,ij,i,j1,2,0,0,i

,n。x是i 0 1i 0 1 0 1 n

的最小二乘估計(jì)，

n

i1

yi

2是

2的無偏估計(jì)。

yX5.(20分)設(shè)全模型為二元線性回歸模型，模型矩陣表示為E0y

x

2In 1

12

1y2

x x

1 其中y ,X21

22,

,

2， y x x

2 nn2 nn

x

,E

0,cov,

2,ij,i,j1,2, ,ni 1i

i j 0,ij試求：(1)全模型下的最小二乘估計(jì)；(2)選模型下的最小二乘估計(jì)；1 2 1 2 1 1(3)的最小二乘估計(jì)是全模型相應(yīng)參數(shù)

的有偏1 1 1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。6.(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)：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：F0.05

4.30,F0.05

4.28,t

0.025

232.06871.(30分0

x1

x22

,n=25,y送貨時(shí)間（分x1

=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。(A)2.3411.616x1

0.014x2SST5784.543,SSE A 233.732(B) 3.3212.176x1SSEB 402.134 解釋模型 對(duì)送貨距離對(duì)送貨時(shí)間是否有顯著的線性效應(yīng)作偏檢驗(yàn)；0.05yx，x的復(fù)相關(guān)系數(shù)，并對(duì)結(jié)果作出解釋；(4)計(jì)算y

的偏相關(guān)系數(shù)；21 2 0.05 2(5)檢驗(yàn)?zāi)Ｐ停˙）的顯著性

； (6)建立模型中參數(shù)

的95%置信區(qū)間。12.(15分)以下三問在第1題中送貨模型下考慮。模型中，已知9號(hào)點(diǎn)的學(xué)生化殘差SRE9

3.2138，杠桿值h99

0.4983，庫(kù)克距離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；如果模型）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？3.(18分1314y12x為上一年家庭總收入，自變量x12

表示家庭學(xué)歷，高學(xué)歷家庭x

=1，低學(xué)歷家庭x

=0，模型：?79763826x1

2 23700x，2模型B：?87634057x1

776x2

787xx，12解釋模型中的回歸系數(shù)；133009.31元，145059.36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(3)討論模型和模型的區(qū)別；(4)模型（B）中xx12

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。4.(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，VariableBS.E.WalddfSigRExp(B)SEX-2.22391.04764.50591.0338-.2546.1082AGE.1023.04584.98561.0256VariableBS.E.WalddfSigRExp(B)SEX-2.22391.04764.50591.0338-.2546.1082AGE.1023.04584.98561.0256.27781.1077Constant-2.62851.55372.86201.09071）寫出Logistic（）5.(20分)0y0i

x1

,d. i i

0,

,i1,2, n，其中

已知。(1)求1

求1

的最小二乘估計(jì)的方差；(3)求1

的置信水平為1的置信區(qū)間。6.(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)？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卷附表：F0.05

5,103.33,t

0.025

102.2281,ln7.331.99,ln11.52.44,ln17.992.891.(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）450.90.354x1

0.561x2

0.0073x3

21.578x4

0.435x,5178.07（0.08）0.12）（0.00）4.03）0.05）n16,SST13843371.750,SSR13818876.769其中：y—民航客運(yùn)量（萬(wàn)人）x—國(guó)民收入（億元）x