計(jì)量經(jīng)濟(jì)學(xué)-回歸模型實(shí)驗(yàn)報(bào)告資料

1、回歸模型分析報(bào)告背景意義：教育是立國(guó)之本，強(qiáng)國(guó)之基。隨著改革開(kāi)放的進(jìn)行、經(jīng)濟(jì)的快速發(fā)展和人們生活水平的逐步 提高，“教育”越來(lái)越受到人們的重視。一方面，人均國(guó)內(nèi)生產(chǎn)總值的增加與教育經(jīng)費(fèi)收入的 增加有著某種聯(lián)系，而人口的增長(zhǎng)也必定會(huì)對(duì)教育經(jīng)費(fèi)收入產(chǎn)生影響。本報(bào)告將從這兩個(gè)方面進(jìn)行分析。我國(guó)1991年2013年的教育經(jīng)費(fèi)收入、人均國(guó)內(nèi)生產(chǎn)總值指數(shù)、年末城鎮(zhèn)人口數(shù)的統(tǒng)計(jì)資料如下表所示。試建立教育經(jīng)費(fèi)收入 Y關(guān)于人均國(guó)內(nèi)生產(chǎn)總值指數(shù) Xi和年末城鎮(zhèn)人口數(shù) X2 的回歸模型，并進(jìn)行回歸分析。年份教育經(jīng)費(fèi)收入Y （億元）人均國(guó)內(nèi)生產(chǎn)總值指數(shù)X1（1978 年=100）年末城鎮(zhèn)人口數(shù)X2 （萬(wàn)人）19917

2、31.50282256.67312031992867.04905289.723217519931059.93744326.323317319941488.78126364.913416919951877.95011400.63517419962262.33935435.763730419972531.73257471.133944919982949.05918503.254160819993349.04164536.944374820003849.08058577.644590620014637.66262621.094806420025480.02776672.995021220036208

3、.2653735.845237620047242.59892805.25428320058418.83905891.315621220069815.30865998.7958288200712148.06631134.6760633200814500.737421237.4862403200916502.70651345.0764512201019561.847071480.8766978201123869.293561613.6169079201228655.305191730.1871182201330364.718151853.9773111資料來(lái)源：中經(jīng)網(wǎng)統(tǒng)計(jì)數(shù)據(jù)庫(kù)80,000根據(jù)經(jīng)濟(jì)

4、理論和對(duì)實(shí)際情況的分析可以知道，教育經(jīng)費(fèi)收入Y依賴(lài)于人均國(guó)內(nèi)生產(chǎn)總值指70,000 -50,00001100020,00030,00040,000數(shù)X1和年末城鎮(zhèn)人口數(shù) X2的變化，因此我們?cè)O(shè)定回歸模型為4090060,0005090080,000根據(jù)經(jīng)濟(jì)理論和對(duì)實(shí)際情況的分析可以知道，教育經(jīng)費(fèi)收入Y依賴(lài)于人均國(guó)內(nèi)生產(chǎn)總值指70,000 -50,00001100020,00030,00040,000數(shù)X1和年末城鎮(zhèn)人口數(shù) X2的變化，因此我們?cè)O(shè)定回歸模型為4090060,000509002,000800-400-10 00020,00030,00040,0001,600Variable Coe

5、fficiert Std Error t-Statistic Pmn.應(yīng)用EViews的最小二乘法程序，輸出結(jié)果如下表Depencienl Variable: Y Method: L&astSquares D3te：i2iH6 Time: 09:30Sample: 18912013Included observations: 2318863771 8117010.065688268177415,36356-6.3616390.01430.0000O.OOCOR-squared1,600Variable Coefficiert Std Error t-Statistic Pmn.應(yīng)用EViews

6、的最小二乘法程序，輸出結(jié)果如下表Depencienl Variable: Y Method: L&astSquares D3te：i2iH6 Time: 09:30Sample: 18912013Included observations: 2318863771 8117010.065688268177415,36356-6.3616390.01430.0000O.OOCOR-squaredAdjusted R-squarea S.E of regression Sum squaredesid Log livelihood F-statistic Prob(F-stalistic)099914

7、7 O90SD62 983.9005 19558484 -1S9.6500911.4033 O.OOQOOOMe sr dependentar S.D dependent var Akaike info cntenon Schwarz criterior Hannan-duinn criter Durbin-Watson statgo5gM6 5050.681 16.75217 1fi 90028 15.78942 0,549816(2.68)(15.9)(-6.1)R2=0.992=0.99F=911.45058.83523.74903-0.3931762,0001 ,200 r800 r4

8、00-WOOD20,00030,00040,000異方差的檢驗(yàn)Goldfeld-Quandt 檢驗(yàn)Xi和X2的樣本觀測(cè)值均已按照升序排列，去掉中間Xi和X2各5個(gè)觀測(cè)值,用第一個(gè)子樣本回歸：Dependent /triable: YMethod: Least SquaresDate： l2/2irs Time：09:33Sample: 1991 1999included observations:：9VariableCoeffldentStd. Error t-StatishcPron.C-3510.568673.0425-5.216116O.OQ2Q590954。1 朋 25843.7341

9、030.0097X29.0839200 0350552.3932850 0538R-squared0.993516Mean dependentvar1901.933Adjusted R-squared0.991355S.D. dependentar937,96S9S.E. of regression87 21013Akaike info criterion1203572Sum squared resid45633.64Schwarz criterion12 10146Log likelihood-51 16074Harnan-Quinn criter.11 89385Fatalistic459

10、 7017Durbin-Watson stat1 554407Prob(F-statistic)0.OODOOOSSE 1=45633.64用第二個(gè)子樣本回歸:De pendent Variable: YMethod: Least SquaresDate 12/21/15 Time: 09:34Sample 2005 2013VariableCoefi deniStd Errcr t-StatisbcProb.C17G636 B11006421 6220220 1557X1107 36147.715122 2547590 0550X2-4.7487972.706982-17542770 129

11、9Rsquared0.987065Mean dependentvar1820409Adjusted R-squared0 982753S D dependentvar7937 917S.E. of regression1049.035Akaike ink criterion17.0103+Sum mq日d resid66()289 氏Sctiwari criterion17.0760&Log likelihood-73.54652Hannari-Quinn criter.16.86347F-statistic220.9229Dufbin-Watson slat1.923931Prob (Fat

12、alistic)0.000002SSE 2=6602898Ho=ut具有同方差，Hi=ut具有遞增型異方差構(gòu)造 F 統(tǒng)計(jì)量。 =114.7F 0.05(9,9)=3.18所以拒絕原假設(shè)，計(jì)量模型的隨機(jī)誤差項(xiàng)存在異方差White 檢驗(yàn)因?yàn)槟Ｐ椭泻袃蓚€(gè)解釋變量，輔助回歸式一般形式如下輔助回歸式估計(jì)結(jié)果如下因?yàn)?TR因?yàn)?TR2=10.67(5)=9.236H eterasked a sticitTest: .VhiteF-statistic2.942706Prob. F(5d17)0.0430 bsiR-squared10.&7089Pros ChiSquare(5；0 0583Scaled e

13、xplained SS6726204ProD ChhSquare(S)0241STest Equaiion:De pendent Variable RESIDEMethod: Least SquaresDate: 12/21/15 Time: 09:38Sample 1951 2013Included obsedations. 23VariableCoefficientStd. ErrorsiicProb.C-124S277530348W-0.41032S06S67X1-40476.2272466.12-0.5586810.5937X1A2-199195728 91602-0.6&42Q40.

14、5217XFX213633402 2373120,60936505503X21067.4322249.3100.4744540.6412X2A2-00202350 038467-0.5257700.6053R-squarea0.453951Mean depenaentar8503689Adjusted R-siuared0.305250S.D. de pendent var1122691.SE. olregres-sion935081.3Akaike info Grrtripn30.55411Sum squared resid1M9E73Schwarz criterion30 85033Log

15、 likelihood-34&3723Hanran-Quinn criten30 &2061F-statistic294270&Durnin-Watson stat2.844510ProbF-&tatisticj0.043027該回歸模型中存在異方差克服異方差以1/Xi做加權(quán)最小二乘估計(jì),Dependent Jari a bile: YKlethcd: Least SquaresDate: 12/21/15 Time: 10:08Sample: 1991 2013Includedcbsecvations: 23Weighting series： 1/X1Weight type Inverse

16、variance (average scaling)VariableCoefficientStd. Errort-StatisticProbC397&.2011412.40527456130.0125X127.024571.6fi24216.06653o.oo&oX2-03461540.054423-6,3603970.0000Weighted StatisticsR-squared0 907992Mean dependent war6585.27SAdjLietea R.-sqLiarQCI0.995791S.D. dependent var4901347S E. of regression

17、753.06Akaike info criterion16,20955Sum squared resid11367925Schwarz criterion16,35767Log liKBlihoad-183.4083Hannan-Quinn enter.1624631F-statistic8227495Durbin-Watsofi stat0 472689Pro b(F statistic)0.000000Aeigtited man dep5093.234Unweighted StatisticsR-5qum9(Q98 弘 83Mean dependentvar9059.846Adjusted

18、! R-squared0.987331S O dependentvar9050681S.E. of regression1010.697Sum squar&d resid20754674DurblivWats&n stat0 521574估計(jì)的結(jié)果還原變量，得再用上表對(duì)應(yīng)的殘差做White檢驗(yàn)Hetero skedasti city TeststatisticObssquaredScaled explained SS2 0694223 7023303 985003Prob. F(5.17)Prob. ChiSquare(5)Prob. Chi-Square(5)0.119701215Q.551

19、6Test Equation.Dependert Variable：啊GT_RESID上2Method Least SquaresDate: 12/21/15 Time: 10:12Sample: 19912013Induded observations: 23Collinear test regressors dropped fro t speaficationVariableCoefficientStd Error l-StafisticFrobC1113169.214795970,0516240.9595WGT*23574g8215S105010.2290100.92102.662692

20、17.851240.2051790 3299X1fiX2*WGTft2-01374551.263073-0 10970269139X2A2*WGTA20 D031780.0212580 1494310,S830X2*WGTn2-190.95511171.S36-0 16294008725R-squared0.378362Mean dependentvar494257.6adjusted R-squared0.195527S.D. dependents ar556180.0S.E. of regression+98S511Akaike inf。criteriun2929746Sum 陷呵“ re

21、sid423E+12Schwarz criterion29,59368Log likelihood-330.9208Hannan-Quinn crikr.23,37196F-曲 aflstiu2D69422Durbin-Watson stat2 507731Prob(F-statistic)0119712由上表可知TR2=8.7(5)=9.236,說(shuō)明以及克服了異方差性自相關(guān)的檢驗(yàn)DW檢驗(yàn)Dependent Variable: YMeth cd Least SquaresDat瓦 12Gl門(mén)5 Tme-10:08Samiple: 1991 2013Indudedobsefvations: 23

22、Weighting aetles: 1/K1Weigtil type: Inverse variance (average scaling)VariableCq efficientStl Error t-StatistiGFeb.c3876.20114124052.7458130.0125X127.024571.&82C4216,C&6530.0000X2-0.3451540.0S4423-6.3C0397d.DOOOWeighted StatisticsRSquared0 987992Mean dependentar5535.27SMusted R-squared0.985791S.D. d

23、ependentvar4901.347S.E. of regression753.5206Akaike infc criterion16,20956Sum squared resid11367925Schwarz criterion16.35767Log likelihood-1B34Q99Hannan-Quinn enter.16 24681F-statistic8227495Durbin-Watson stat0 472639Prob(Ftatistic)0.000000.Vsighted mean dep5093.284unwe ighted St 曲 stiesR-squared0.9

24、83483Mean depen dent var9059 646Adjusted Rsquared0.987331S.D. dependentvar9050.6B1S.E. of regression1019.697Sum squared resid20764874Durbln-Wateon at0521574已知DW=0.47 ,若給定 =0.05 ,查表得DW 檢驗(yàn)的臨界值 dL=1.17,d u=1.54。因?yàn)镈W=0.471.17,根據(jù)判別規(guī)則，認(rèn)為誤差項(xiàng)ut存在嚴(yán)重的正自相關(guān)。LM檢驗(yàn)Breusch-Cactfrejj Serial Correlation LM Test:F-sta

25、tisticObsfcR-squared3.4597216 364184Prob所以誤差項(xiàng)存在二階自相關(guān)克服自相關(guān)首先估計(jì)自相關(guān)系數(shù)對(duì)原變量做廣義差分變換。令GDY t=Yt-0.765Y t-iGDX it= Xit-0.765X it-iGDX 2t= X2t-0.765X 2t-i以GDYt, GDX it, GDX 2t (19922013 年)為樣本再次回歸Depend&nt Variable: Y-0 765*Y(*1)Method. Least SquaresDate: 12/21H5 Time: 12:19Sample但咖磯皿 1992 2013mciutied observa

26、tions: 22after adjjslmentsVariable Coefficient Std. Error 1-Statistic Prob.cX1-0,766*X1r-1X2,765*X2G1)241,322027 429705250.1S18563.&465187 5221630.156S39-1 92S4902499 0 0030 D0691R-squared0 954230Mean dependent/ar3248.404Aflju steel R-squamd0.949412S D. dependent war3051.463S.E. of regr

27、ession6S63290Afcaifce mfo criterion16C2672Sum squared residS949904.Schwarz criterion16 1764Log livelihood-1732939Hannan-Quinn enter.16 0&VGFatalistic193.0535Durbin-Watsan stat1.368592Pro btF-stati stic)0.009000得到 GDYt=241.322+27.4297GDX it-0.3024GDX 2tDW=1.4 ,介于dL=1.17,d u=1.54之間，所以不能判別ut是否存在一階自相關(guān)，自

28、相關(guān)性沒(méi)有消除由上一步LM統(tǒng)計(jì)量知誤差項(xiàng)存在二階自相關(guān)，采用直接擬合的估計(jì)結(jié)果是，D&pendent VariaDle: YM&tnod Least SquaresDate: W21/15 rime: 12:38Sample (adjusted): 1993 2013Included otservations: 21 after adjustmentsConvergence achieved after? iterationsVariableCoefficientStd. Enart-StatisticPrcb.C2610.3131920.3641.3536410.1947X124,90830

29、23435811C,528300 oocoX2-0 2398960.073680-3.9345180.0012AR(1)1.3958020.sggsae4.G374980.0 0C3AR-1.1527360465390-2.4769240.0248R-squared0 996549Mean dependent var98463 幅Adjusted R-squared0 99568SS.D. dependent var0 90.249S.E. of regression597.0527Akaike info criterion15 82614Sum squared resid57D3551Sch

30、warz enteri on16 07484Log likellihoodl-1611745Hannan-Quinn 匚15,88012F-statistic1155.034Durbin-atson stat1 751039ProbiF-statistiOo.oocoooInverted. Roots,6S-.S2I.如為aEstimated AR process is nonshtonaryR2=0.969=0.968R2=0.969=0.968DW=1.75 介于du=1.54和4- d u=2.46 ,依據(jù)判別規(guī)則，誤差項(xiàng)已消除自相關(guān)多重共線性的檢驗(yàn)1. Klein判別法Covarian

31、ce .Analysis: OrdinaryDate: 12/23/15 Tima： 12:10ample: 1991 2013induded obseivations: 23CovarianceCorrelationXIX2XI23237421.000000X2&2277B51 77E+099.9717271.000000因?yàn)閨rxi x2|=0.97in-Watson stat0.239431ProbiF-statistic)0.000000Dependent Variable: YMethod Least SquaresDate: 12/23/15 Time 12:20Sample: 1

32、3912013Induced obsen/aticins: 23VariableCoefficientStd. Error t-SlatisticProb.C-21977 092913204-7 5439570.0000X20.5147250,05579811,0170。0.0000R-squared5852502Mean depndentvar9059.646Adjusted R-squared0.&4547BS.D. dependent var9050.601S.E. of regression3557750Akaike into criterion19,27459Sum squared

33、resid266E*O6Schwarz crite ri on10 37333Log likelihood-219.657BHannan-Quinncriter.19,29942Fatalistic121 3744Durbin-Watson stat0 122423Prob(Rstalistic)0.000000R2=0.852=0.845取第一個(gè)方程為基本回歸方程，弓I入X2,對(duì)Y做關(guān)于Xi和X2的最小二乘回歸,Dependent VaflaDle: Metricd: Least Squares Date: 12/23/15 Time: 12:24 Sample: 19S1 2013 Inc

34、luded observations: 23Va riabkCoefficieniStd. Error i-StatisticProb.C505ag351SS& 3772 66177400143X128 749081.81173115.85856OOOOQX24).3981760 065688-5.0616380.0000R-squared0 969147Mean de pendent var9059.646Adj u ste d R-squared0 9680623D. dependent var9050.681S.E. of regression988,9005Akaike info cr

35、iterion的 75217Sum squaredr&sid19550434Schwarz criterion15 90023Log likelihood-169.6&00Hannan-Quinn criter.1&7S942F-statistic911 403SDurbin-Watson stat0 549816Frob(F-statistic)0 000000R2=0.989=0.988可以看出，加入X2后，R2和均有所增加，Xi系數(shù)顯著性不受影響，所以在 模型中保留X2綜上:Dependent Variable: YMetriod Least SquaresDate： W21/15 ri

36、mer 12:383arnple (adjusted): 1993 2013Included observations; 21 aftr adjustmentsConvergence achieved after7 iterationsVariableCaefti cientStd Enort-9tatisticPrati.C2610.3131926.3641.3536410.1947X124,908302.3435811C,52830o.oocaX2-0.2893960.073680-3.9345180.0012AR(1)1.39930205990884.637498O.OOC3AR-1.1

37、527360.465390-2.4769240 0248R-squared0.996549Mean dependent /ar圜 46348Adju s ted R-s quaredO, 9 95666S.D. dependent var9090.249S.E. of regression597.0527AJcailoe info crtterion15 82614Gum squared 1已甘id5703551Schwan enteri on18 0744Log lik&lihioad-161.1745Hannan-Guinn criter15,88012F-statistic1155.034Durbin-.Vatson stat1 7516