庞皓计量经济学课后答案第四章

1、 统计学2班第三次作业(pyx)(px2)(pyx)(pxx)存在IP2=(Px2)(Px2)(工)2厂2i3i2i3ipxx当X2和X3之间的相关系数为0时，离差形式的2i3i=0-(工yx)(工x2)工yx人2(px2)(px2)px22i3i2i同理得：P3幕会等于&i和-二者的线性组合。八八八p=YPXPX且d二YdX,12233122二YyX33由可得虫2和P3T3:.d=YdX=YPX，12222Y-yX3八八八则：P=YPXPX=Y1YdiX2存在。TVar（P2）=另G2x2(1r2)2i23X2和X3之间相关系数为0,Var（片）=另G2=Var(d)x2(1r2)厶x222

2、i232i同理可得畑（P3）=Va咐彳）2、逐步向前回归和逐步向后回归的程序都存在不足，逐步向前法不能反映引进新的解释变量后的变化情况，即一旦引入新的变量，就保留在方程中，逐步向后法泽一旦剔除一个解释变量就再没有机会重新进入方程。而解释变量之间及其与被解释变量的相关关系与引入的变量个数及同时引入哪些变量而不同。所以采用逐步回归比较好。吸收了逐步向前和逐步向后的优点。3、Y：商品进口额/亿元GDP:国内生产总值/亿元CPI:居民消费价格指数(1985年为100)%建立模型：InY=B+BInGDP+BInCPI+pt12t3tiDependentVariable:LNYMethod:LeastS

3、quaresDate:-102:-Time:17:09Sample:-19852:07Includedobservations:2.3-VariableQoefTicientStd.Errort-StatisticProbC-3.060141.3-37429-9.0669930.0000LNGDP1.6566740.09220717.96693-0.0000LNCPI-1.0&7D53.2:1-640-4.9245950.0001R.-squared0.9922:13Meandependentwar9.155304AdjustedR.-squared0.99-1-40S.D.dependent

4、var1276499S.E.ofregre-ssion0.1-1S101Akaikeinfocriterion-1.313453Sumsquaredresid0.2T8955Schwarzcriterion-1165345Loglikelihood-IS.-10+71Hannan-Ouinncriter.-1.276204F-statistic-12T5.080urbin-Watsonstat745630Probservations:5:3-VariableCoefficientStdErrort-StatisticProb.C-斗.0906590.384253-1D.64574D.0000L

5、NGDP1.2185720.03-&-19634622120.0000F5.-squared0.9S5:7SSMeandependentT/ar9155304AdjustedR-squared.931963S.D.dependentvar1.2T6499S.E.orregression.171433Akaikeinfocriterion-6065:5.0Sumsquaredresid0.6172-1Schwarzcriterion-05075-1-1l_ci叮likelihood3.971871Hannan-Ouinncriter.-.&S14-17F-statistic1-198.691Du

6、rbin-Watsonstat.3643-7-IProbfF-statistic.000InYt一4.090659+1.2185721nGDPT=(-10.64574)(34.62212)R2二0.982783R2二0.981963F=1198.691InY二B+BInCPIt12+U2iVariableOoefficientS-td.EZrrort-StatisUc：Prob.0LNGFI15I.663-TS91.25-3665：一斗3A12110.22:306-11.6809-1.0030.0000R.-squaredAdjustedR.-squa.redS.E.ofregre-ssion

7、Sumsquaredresidl_oglikelihoodF-sta廿mti匚ProtF-statlstlc0.S666-1S.SB0267.47Z166d-T01A3J-14丘了b02-136.-44-36.oooooMeandependentvarS-.D.aepenaenta.rAkaikeinfocriterionSchwarzcriterionl-lannan-Q.uinnoritur.Durin-Watsnstat9.-1&53O+12T&4991.4-4-1036-1539775-1.465S69.-1S23-1-4-DependentVariable:LMVMethod:Lea

8、stS-qliaresate:10/2.3/14Time:1V:1VSample:19852007Includedobserwa廿口口：23InY二-5.442411+2.663789InCPItT(-4.341211)(11.68091)R2二0.866619R2二0.860267F=136.4436InGDP二C+CInCPI+ut12t3iDependentVariable:LNGDPLIethd:LeastSquaresDate:“烂#!斗Time:1T：-19Sample:-19S52:007Includedobservations:2.3VariableCoefficientStd

9、.Errort-StatisticProb.U-143798斗0.73432:3-1.9&S231.0636LNCPI22453TI0.13357716S1+00.0000R-squaredD930S&5Meandependentwar1D.37007AdjustedR-squared.92Y563-S.D.dependentvar1-80S.E.ofregression0.279496Akaikeinfo匚riterion.371300Sumsquaredrssid1640506Schwarzcriterion4700S9Loglikelihood-2269955Hannan-Quinncr

10、iter.396-133-F-statistic2S2.T-107Durbin-Watsonstat.142981-ProbCF-statistic)D000000In叫-1.437984+2.245971lnCPIT(-1.958231)(16.814)R2二0.930855R2二0.927563F=282.7107GDP和CPI均对Y有影响，由可以知道CPI对Y也为正向影响，但两个因素同时作用时方向发生变化。所以存在严重共线性。单个方程拟合效果都较好，回归系数显著，可决系数较高。所以相关关系需要通过相关系数的分析才可以知道。若仅做预测。可以不考虑多重共线性。5、F=8.133+1.059X

11、+0.452X+0.121X123标准误差：（8.92）（0.17）（0.66）（1.09）R2二0.95F=107.37由题结果可知，数据从1921-1950（略去1942-1944）年。共计27个。所以n=27。在给定显著性水平a=0.05,查得F0.o5（k-1,n-k）=F0.05（3,23）=3.028，计算的F=107.37F0.o5（3,23）=3.O28，可决系数R2二0.95，表明方程是显著的。模型整体拟合程度较高。由题结果已知标准误差：（8.92）（0.17）（0.66）（1.09），由t=計可以计算iSE（卩）i出各回归系数的T统计量:8.1338.92=0.911.05

12、90.17=6.230.4520.66=0.690.1211.09=0.11在给定显著性水平a=0.05，查得T005（25）=2.06.所以除X1（工资收入）外，其余所有因素均不通过检验。说明模型中存在严重的多重共线性。6、Y：能源消费标准煤总量/万吨X1：国民总收入/亿元X2:国内生产总值/亿元x3：工业增加值/亿元x4：建筑增加值/亿元x5：交通运输邮电业增加值/亿元x6：人均生活电力消费/亿元x7：能源加工转换效率/%建立模型如下：Iny=B+PInx+PInx+PInx+PInx+PInx+PInx+PInx011223344556677Dep&ndJentvarlsi.Ele:LI

13、MVMetnod:l_。自asqiUMOGDate:14Time:&7samipie:12:07includ&diotserusticns:23va.naEl&croetricientstd.Errort-stati&tieProE.G曰N了1o.-l18-l_lIXT10.7SO34丘曰0.0001l_lIX2-1o.-aD3g1.7180-US-5.9-071日0.0000l_lIX3.氐Z21B7-O.3D2O-7SS7l_lIX4.179022O.-l4日氐0.2375LKIX&-0.199001.I0292-1-1.93353Z0.0723LKIXS.S929了_2.02830O.3

14、SO9LKIXZ1.143815.4S2i55&2.&26日&日0.023R.-&qLiaredi.99234Meandependent11.7S6-14AdljsteaR-s口Limgcn.9913s.D_deipenciGntvarO.3-HS50&s.E.orregression.31&1SAKaiKemrocrit&nonsLiinnisqua.r&aresid.14已日日sc：MWia.rz-criterion-3.413406Logllk&linoodiSI.79718Hannan-Q.LJlnnenter.-3-.709T21F-stallstlc39.4615ourrin-wa

15、.ts0nsial1.6-17064RroEF-stallstlc.OOO由分析可知：R2=0.994234R2=0.991543F=3694546.所以总体拟合效果好。但是同时可以看出Inx,lnx,lnx,lnx所求得参数t检验所对应的3456p值分别为0.7667,0.2375,0.0723.0.3809.在给定显著性水平a=0.05下均不通过检验。并且Inx,lnx,lnx的参数估计为负值。与实际不符。235会。因为X1：国民总收入/亿元和x2:国内生产总值/亿元代表了经济发展水平。具有密切的相关关系。而x3：工业增加值/亿元X4:建筑增加值/亿元x5:交通运输邮电业增加值/亿元x6：

16、人均生活电力消费/亿元X:能源加工转换效率/%则可能也具有相关关系。tcureiatioinLNX1LN?C2LNX3LNX4LNX5LNXBLNX7LT4X1i.ooaaoo0.9399710.9997250.900897D.993B230.9BT19BD.703411LT4X2a.999971i.aooooa0.9997430.907170.993B930.996829D.709D50LT4X3a.9997250.9997431.000DD00.907837D.9917220.995511D.715D60LT4X40.9953070.907170.997BB7i.uoooaaD.9S948

17、50.9B9932D.703S62LT4X50.9935200.9038930.9917220.969435-1.000DOO0.99407DD.667196LT4X6a.9971030.996823a.99&5110.9E99320.994070l.aDOOUDD.6SS726LT4K70.7034110.7D905QQ.715DBQO.7D0952D.6671960.5B572Bi.ooaooo通过相关关系矩阵。我们也可以看出ln珥和lnx2，lnx3，lnx4，lnx5，ln间互相具有高度相关。其相关系数高于0.9。运用逐步回归法，在a=0.05下得出结果如下。DependentVari

18、able:LNYMethod:StepwiseRegressionDate:10/25/1+Time:2:1:21Samp-le:-19852007Includedobservations:2:3Numberofalwaysincludedregressors:JNumberofsearchregressors:7S-eIectionmethod:StepwiseforwardsSio口pingcriterion:p-valueforwards/backwards=OOSOOSVariableCoefTlcientStd.Errort-SiatisticProb*C10.3805:8.14T3

19、S5T3&2213B00000LNX61.34430713033710314-0600000LNX5-6232T6.37450-7.12752500000R-squared.979004Meandependentvar1-1.786-1+AdjustedR-squared.976904-S.D.dependentvar.342695S.E.ofregression052030Akaikeinfocriterin-5:.950965:Sumsquaredresid054247Schwarzcriterion-5.802354Loglikelihood36.93607Hannan-CLuinncr

20、iter.-51.9-137-14F-statlstic4-66.2829Durbin-Watsonstat1.S725-71Frab(F-statiStic)Q.OaOOQOSelectionSummaryAddedLNX6/ddedLNX5p-valuesandsubsequenttestsdlonotaccountforstepwiseselection.Iny二10.88028+1.344307lnx-0.623276Inx657、匚arreldtJonCSNZGZJZZTPOPCUlJlZF4CG1DOODDO0S19QQ1D9Q36500973A400.7609470.959945

21、Q.DB042QNZD91ASD11DODDDO09729919S2B610.9279760.9BQ9610.226200G1D93365JJD9729B11aDODOD99E&22.9439000.992541CM羽444ZZD.973&4dDsazGGiD99B5221aODDOD0.3641520.9960570.154545TFOF07609470.3273730.3439000.3641521.0DD00Da.BBB94B0.3H7757CUM0.959945.938953D.99&D670.8BB84B1.DDD0DD0.1B5173SZklO.D6O42aD.2262000.129444D.154-6460.3877570.1B5-1731.DD00DD根据相关关系表可以看出解释变量间相关系数高。农业增长值，工业增长值，建筑业增长值,最终消费间的相关系数均大于0.9.有显著相关关系。所以会出现本章开始时所出现的异常结果。尝试采用逐步回归法得最终结果DependentVariable:CS-Methd:StepwiseRegressionDate:-10/281斗Time:22:43Sa