龐皓計量經(jīng)濟學課后答案第四章

1、 統(tǒng)計學2班第三次作業(yè)(pyx)(px2)(pyx)(pxx)存在IP2=(Px2)(Px2)(工)2廠2i3i2i3ipxx當X2和X3之間的相關系數(shù)為0時，離差形式的2i3i=0-(工yx)(工x2)工yx人2(px2)(px2)px22i3i2i同理得：P3幕會等于&i和-二者的線性組合。八八八p=YPXPX且d二YdX,12233122二YyX33由可得蟲2和P3T3:.d=YdX=YPX，12222Y-yX3八八八則：P=YPXPX=Y1YdiX2存在。TVar（P2）=另G2x2(1r2)2i23X2和X3之間相關系數(shù)為0,Var（片）=另G2=Var(d)x2(1r2)厶x222

2、i232i同理可得畑（P3）=Va咐彳）2、逐步向前回歸和逐步向后回歸的程序都存在不足，逐步向前法不能反映引進新的解釋變量后的變化情況，即一旦引入新的變量，就保留在方程中，逐步向后法澤一旦剔除一個解釋變量就再沒有機會重新進入方程。而解釋變量之間及其與被解釋變量的相關關系與引入的變量個數(shù)及同時引入哪些變量而不同。所以采用逐步回歸比較好。吸收了逐步向前和逐步向后的優(yōu)點。3、Y：商品進口額/億元GDP:國內生產(chǎn)總值/億元CPI:居民消費價格指數(shù)(1985年為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:“爛#!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均對Y有影響，由可以知道CPI對Y也為正向影響，但兩個因素同時作用時方向發(fā)生變化。所以存在嚴重共線性。單個方程擬合效果都較好，回歸系數(shù)顯著，可決系數(shù)較高。所以相關關系需要通過相關系數(shù)的分析才可以知道。若僅做預測。可以不考慮多重共線性。5、F=8.133+1.059X

11、+0.452X+0.121X123標準誤差：（8.92）（0.17）（0.66）（1.09）R2二0.95F=107.37由題結果可知，數(shù)據(jù)從1921-1950（略去1942-1944）年。共計27個。所以n=27。在給定顯著性水平a=0.05,查得F0.o5（k-1,n-k）=F0.05（3,23）=3.028，計算的F=107.37F0.o5（3,23）=3.O28，可決系數(shù)R2二0.95，表明方程是顯著的。模型整體擬合程度較高。由題結果已知標準誤差：（8.92）（0.17）（0.66）（1.09），由t=計可以計算iSE（卩）i出各回歸系數(shù)的T統(tǒng)計量:8.1338.92=0.911.05

12、90.17=6.230.4520.66=0.690.1211.09=0.11在給定顯著性水平a=0.05，查得T005（25）=2.06.所以除X1（工資收入）外，其余所有因素均不通過檢驗。說明模型中存在嚴重的多重共線性。6、Y：能源消費標準煤總量/萬噸X1：國民總收入/億元X2:國內生產(chǎn)總值/億元x3：工業(yè)增加值/億元x4：建筑增加值/億元x5：交通運輸郵電業(yè)增加值/億元x6：人均生活電力消費/億元x7：能源加工轉換效率/%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.所以總體擬合效果好。但是同時可以看出Inx,lnx,lnx,lnx所求得參數(shù)t檢驗所對應的3456p值分別為0.7667,0.2375,0.0723.0.3809.在給定顯著性水平a=0.05下均不通過檢驗。并且Inx,lnx,lnx的參數(shù)估計為負值。與實際不符。235會。因為X1：國民總收入/億元和x2:國內生產(chǎn)總值/億元代表了經(jīng)濟發(fā)展水平。具有密切的相關關系。而x3：工業(yè)增加值/億元X4:建筑增加值/億元x5:交通運輸郵電業(yè)增加值/億元x6：

16、人均生活電力消費/億元X:能源加工轉換效率/%則可能也具有相關關系。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通過相關關系矩陣。我們也可以看出ln珥和lnx2，lnx3，lnx4，lnx5，ln間互相具有高度相關。其相關系數(shù)高于0.9。運用逐步回歸法，在a=0.05下得出結果如下。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根據(jù)相關關系表可以看出解釋變量間相關系數(shù)高。農(nóng)業(yè)增長值，工業(yè)增長值，建筑業(yè)增長值,最終消費間的相關系數(shù)均大于0.9.有顯著相關關系。所以會出現(xiàn)本章開始時所出現(xiàn)的異常結果。嘗試采用逐步回歸法得最終結果DependentVariable:CS-Methd:StepwiseRegressionDate:-10/281斗Time:22:43Sa