计量经济学回归模型实验报告.docx

1、计量经济学回归模型实验报告回归模型分析报告背景意义:教育是立国之本，强国之基。随着改革开放的进行、经济的快速发展和人们生活水平的逐步 提高，“教育”越来越受到人们的重视。一方面，人均国内生产总值的增加与教育经费收入的 增加有着某种联系，而人口的增长也必定会对教育经费收入产生影响。 本报告将从这两个方面进行分析。我国1991年2013年的教育经费收入、人均国内生产总值指数、年末城镇人口数的统计资料如下表所示。试建立教育经费收入 Y关于人均国内生产总值指数 Xi和年末城镇人口数 X2 的回归模型，并进行回归分析。年份教育经费收入Y （亿元）人均国内生产总值指数X1（1978 年=100）年末城镇人

2、口数X2 （万人）1991731.50282256.67312031992867.04905289.723217519931059.93744326.323317319941488.78126364.913416919951877.95011400.63517419962262.33935435.763730419972531.73257471.133944919982949.05918503.254160819993349.04164536.944374820003849.08058577.644590620014637.66262621.094806420025480.02776672.9

3、95021220036208.2653735.845237620047242.59892805.25428320058418.83905891.315621220069815.30865998.7958288200712148.06631134.6760633200814500.737421237.4862403200916502.70651345.0764512201019561.847071480.8766978201123869.293561613.6169079201228655.305191730.1871182201330364.718151853.9773111资料来源：中经网统

4、计数据库根据经济理论和对实际情况的分析可以知道，教育经费收入 Y依赖于人均国内生产总值指数Xi和年末城镇人口数 X的变化，因此我们设定回归模型为应用EViews的最小二乘法程序，输出结果如下表DcpencieniVana&ie: Y Method: Least SquaresDate： 12C21/15 Time： 09:30Sample： 1991 2013Included observations: 23VariableCoefficientStd Ermr t-StaUsticFranC5053.355lSeSJ77 2.6S17740.0143对28.749001.811701 15,

5、363560.0000X2-0.3981760.065569 -6 3&16390.0000R-squared0999147Mean dependentar9D59.S46Adjusted R-squareaO90SD62SO dependent var5050.681S E ofreoression9005info cntenon15.75217Sum squared res id19558484Schwarz criterior16.90028Losjiifceiihaod-189.6500Hanran-Quinn criter1578942F-statistic911.4038Durbi

6、n-Waban stat0.549B16Prob(F-stalistic)0.000000(2.68) (15.9) (-6.1)R2=0.99 2=0.99 F=911.4异方差的检验1.Goldfeld-Qua ndt 检验Xi和X2的样本观测值均已按照升序排列，去掉中间 Xi和X2各5个观测值,用第一个子样本回归:Dependent Variable: Method: Least SquaresDate: 12/21/15 Time: 0933Sample: 1991 1999lr eluded obseevati ons: 9VariableCosffldentStd. Error t

7、-StatishcPron.C-3510.568&73,0425 -5.2161160.00205 9095401.58Z534 3.7341030.0097X20.0830200 035055 2.3932850 0538R-squared0.993516Mean dpe1901.933Adjusted R-squared0.991355S.D. dependentar937J6S9S.E. of regression8721013Akaike info criterion1203572Sum squared resid45633.64Schwarz criterion12 1Q146Log

8、 likelihood-51 16074Harnan-Quinn criter.11 89385Fatalistic459 7017Durbin-Watson st al1 554407Prob(F-statistic)&.OOOODOSSE 1=45633.64用第二个子样本回归:De pendent Variable: YMethod: Least SquaresDate 12/21/15 Time: 09:34Sample 20052C13Included obsratjon; 9VariableCoeffi deniStd Errcr t-StatisbcProb.C170035.61

9、100642 1 6220220 1557X1107 36147.71512 2 254T&90 0550X2-4.7487972.706982 -1754277Q 1299Rsquared0.987065Mean dependentvar1820409Adjusted R-squared0 982753S D dependentvar7937 917S.E. of regression1049.035to ike Info criterion17.0103+Sum squared res id6602S9S.Sctiwan criterion17.076QSLog likelihood-73

10、.54652Hannari-Quinn criter.16.86347F-statistic220.9229Dufbin-Watson slat1.923931Prob (Fatalistic)Q.OOOOC2SSE 2=6602898Ho=ut具有同方差，Hi =ut具有递增型异方差构造 F 统计量。 =114.7F 0.05(9,9) =3.18所以拒绝原假设，计量模型的随机误差项存在异方差2.White 检验因为模型中含有两个解释变量，辅助回归式一般形式如下辅助回归式估计结果如下H eterasked a sti dty Test: Wh itsF-statistic2.942706Pr

11、ob F(5117)0.0430 bsR-squared10.&7089Fns ChiSquare(5；00583Scaled explained SS6726204ProD. ChhSquare(S)0241STest Equaiion:De pendent Variable- RE SIDA2Method: Least SquaresDate: 12/21/15 Time: 09:38Sample 1951 2013Included obsedations. 23VariableCoefficientSbd. Errort-Stati sticProb.C-124S277530348W0.

12、41032S06S67X1-40476.2272466.12-0.5586810.5937X1A2-18.9195728 91602-0.6 &42540.5217XFX213633402.2373120,6093650.5503X21057.4322249.S100.4744540.6412X2A2-00202350 0384670.5257700.6053Ft-squarea0.453951Meat depenaentar8503689Adjusted R-s,3451540.054423 -6.M0397o.oo&oWeighted SU1i stiesRsquared0.937992M

13、ean dependent war6585.276Adjusted R-eqiuared0.99B791S.D. dependent var4981.347S E. of regression7519206Aka ike info criterion16.20956Sum squared resid11367925Schwarz criterion16.35767Log liKelihood-1834099Hannan-Quinn enter.16.24681F-statistic8227495Durbin-Watsofi stat0 472689Pro b(F statistic)O.DOO

14、ODOAeigtited man dep5093.234Unweighted StatisticsR-squared0.9&343Mean dependentvar9059.64&Adjusted R-squared 987331S O dependentvar9O5O 6B1S E of regression1010.697Sum squared resid20754674Durbin-Watson stat0 521574估计的结果还原变量，得Hetero skedasti city Test 讥tinFstatistic2 069422Prob. F(5,17)0.1197Obssqua

15、red3 702330Prob. CtihSquare 01215Scaled explained SS3 985003Prob. Chi-Square(S)Q.5516Test Equation.Dependent Variable: WGT_RESIDJl2Method Least SquaresDate: 12/21/15 Time: 1C:12Sample: 19912013indudedobservations: 23Collinear test regressors dropped from spedficalicnVariableGo EfficientStdl Errorl-S

16、tafisticFrobC1113169.214795970.0516240.9595WGT*2157496Z15S105010.5290100.9210X忖少WGT也3.652&9217.851240.2051790 3299X1fiX2*WGTft2-01374551.253073-0,109702d.9133X2A2*WGTA20 D031780.0212530.1494310.3830X2*WGTn2-190.95511171 9364.16294008725R-squared0.378362Mea n depende nt* 白 r494257.6adjusted R-squared

17、0.195527S.D. dependents ar556180.0S.E. of regression+98S511Aka ike info criteriun2S.29746Sum squsrd resid4,212Schwarz criterion29.59368Log likelihood-330.9208Hannan-Quinn criter.23.37196Fatalist it2D69422Durbin-Watson stat2 507731Prob(F-statistic0119712由上表可知TR2=8.7 =9.236,说明以及克服了异方差性自相关的检验1.DW检验Depe

18、ndent Variable: YMeth cd- Least SquaresDatat 12/21/15 Time-10:08Samiple: 1991 2013Induded observations: 23Weighting series: 1W11Weigtil type: Inverse variance (average scaling)VariableCq efficientStl Error t-StatisticFrothc3876.2011412405 2.7458130.012&X127.024571.&82C42 16.C&6530.0000X2-0.3451540.0

19、S4423 -6.3C0397a.ooooWeighted StatisticsRSquared0 987992Mea n dependent ar5535.276Musted R-squared0.98&791S.D. jependentvar4901.347S.E. of regression753.5206Aka ike infc criterion16.20956Sum squared resid11367&25Schwarz criterion1635767Log likelihood-1B34Q99Hannan-Quinri enter.16.24681F-statistic822

20、7495Durbin-Watson stat0 472639Prob(Ftatistic)0.000000.Vsighted mean dep5093.234Unweighted StatisticsR-squared0.983483Mean depen dent var9056 64&Adjusted Rsquared0.987331S.D. depends nt var9050.681S.E. of regression1019.697Sum squared resid20764874Durbh-Wats-on 封取0521574已知DW=0.47，若给定 =0.05，查表得DW 检验的临

21、界值 dL=1.17,d u=1.54。因为DW=0.47 FCZ17)U.0&49Obs*Rsquared6 364134Prob Chi-Square2)0 0415lest Equation.Dependent Variattle: RESIOMethod Least SquaresDate: 12/21/15 Time: 12:31Sample: 19922013Included obsarvattnns: 22Presample missing value lagged residuals set to zero.VariableCoeffidertStd. Error t-Stat

22、i sti匚ProbC-706.27061164 736 -0363780 552X1-0 765*X1(-1)*4 602240331B005 -1.2054070.2446X2-0 765NX2(-1)0.1320500 151557 0.8713560.3557RESlDi-1)0.9578070 364S09 5.62910S0.0176RESID (-2)-1.2615700 576139 -2J896970.0428Rsquar&d208281Mean dependentw2.48E-13Adjusted R-squared0122053S.D dependent var652 8

23、291S.E. cf regres sion6111.0932Aka ike info crlierlon15.B6706Sum squared resid636085CScnwarz Grite non10.11502Log likelihood-16*5376Hannan-Quinn Griter.15,92547F-statistic172985QDwrtjin-Watsan stat170 9&70Pro b(Fstati-stic0JQ9832LM=6.36所以误差项存在二阶自相关3.克服自相关首先估计自相关系数对原变量做广义差分变换。令GDY t=Yt-0.765Y t-1GDX

24、it= Xit-0.765X it-iGDX 2t= X2t-0.765X 2t-i以GDYt，GDX it，GDX2t（ 19922013 年）为样本再次回归Dependent JariaDim Y-0.765-1)Method Least SquaresDate： 12/21/15 Time: 12:19Sample (adjustedy 1992 2013Included observations: 22 aft&r adjusimentsVariableCoefficientStd. Error1-StatisticProb.C241.12201257X250J918560,8499X

25、1-0.766*X1r-127 429703.&465187.522163a.ocooX2.765*X2G1)-0 30243&0.156989-1.9264900.0691R-squared0 954230Mean dependent/ar3249404Aflju steel R-squamd0.949412S D. depenaentvar3051.462S E of regression&S63290Afcaifce mfo criterion1602672Sum squared resid8949904.2匚 hwarz criterion16.17549Log livelihood-173 2939Hannan-Quinn enter.10.06176F-statistic193B535Durbin-Watsan stat1 363592Pro btF-stati stic)0.009000得到 GDYt=241.322+27.