放宽基本假定模型案例

1、第四章放宽基本假定模型案例一、异方差性1、中国农村居民人均消费支出主要由人均纯收入来决定。农村人均纯收入除从事农业经营 的收入外，还包括从事其他产业的经营性收入以及工资性收入、财产收入和转移支出收入 等。为了考察从事农业经营的收入和其他收入对中国农村居民消费支出增长的影响，可使 用如下双对数模型：ln Y = f 11nx12 1nx2 u其中丫表示农村家庭人均消费支出，X1表示从事农业经营的收入，*2表示其他收入。表4.1列出了中国2001年各地区农村居民家庭人均纯收入及消费支出的相关数据。表4.1中国2001年各地区农村居民家庭人均纯收入与消费支出地区人均消费 支出Y从事农业经营的收入x1

2、其他收入X2地区人均消费 支出Y从事农业经营的收入x1其他收入X2北京3552.1579.14446.4湖北2703.361242.92526.9天津2050.91314.62633.1湖南1550.621068.8875.6河北1429.8928.81674.8广东1357.431386.7839.8山西1221.6609.81346.2广西1475.16883.21088内家占1554.61492.8480.5海南1497.52919.31067.7辽宁1786.31254.31303.6重庆1098.39764647.8吉林1661.71634.6547.6四川1336.25889.46

3、44.3黑龙江1604.51684.1596.2贵州1123.71589.6814.4上海4753.2652.55218.4云南1331.03614.8876江苏2374.71177.62607.2西藏1127.37621.6887浙江3479.2985.83596.6陕西1330.45803.8753.5安徽1412.41013.11006.9甘肃1388.79859.6963.4福建2503.110532327.7青海1350.231300.1410.3江西17201027.81203.8宁夏2703.361242.92526.9山东190512931511.6新疆1550.621068.

4、8875.6河南1375.61083.81014.1用OLS法进行估计，结果如下:Dependent variable: LOG(Y)Method： Least SquaresDate: D7/D3/O8 Time: 16:31Sample: 1 31Included obsetvations: 31VariableCoefficientStd Errort-StatisticProb.C1.6025260.8609731.8612890.0732LOG(X1)0.3254160 10376931359550.0040LOG(X2)0.507078004859910.433850.0000R-

5、squared0796506Mean dependent var7.448704Adjusted R-squared0.78197,S.D. dependent var0.364648S.E, of regression0.170267Akaike info criterionfl.611120Sum squared resid0.811747Schwarz criterion0 472356Log likelihood1247249F-statistic54 79806Durbun-Watson stat1.964720Pmbf statistic)0.000000对应的表达式为:InY -

6、1.603 0.325ln X1 0.507ln X2(1.86) (3.14)(10.43)R2 =0.7965,R =0.78,RSS= 0.8117不同地区农村人均消费支出的差别主要来源于非农经营收入及其他收入的差别，因此，如果存在异方差性，则可能是*2引起的。对异方差性的检验：做OLS回归得到的残差平方项与ln X2的散点图：20.16-.12-.04-,005.5 6.0 6.5 7.0III7.58.08.59.0LOG(X2)从散点图可以看出，两者存在异方差性。下面进行统计检验。采用White异方差检验：EViews提供了包含交叉项和没有交叉项两个选择。本例选择没有包含交叉项。E

7、Views Equation: UBTITLED Workfile: UlTTITLED: :UntitleFil a Edit Ohjact Visw Froc Quick Options Window HelpM嘲的箕1。回虱PrintName(Rreeze Estimate Forecast StatsIUrf e s ent a七 i onsEstimatiioii Outputtuelj Fi tted.KesiduU ARMA Structure. r.Gradi ents and Derivatives C ovar i axic e M air i 求t Std. Error

8、t-Statistic Prob.ResidualTestsStabili tf TestsLabelR-squared0 796SCoefficient TestsCorrelogrCorrelogrAdjusted R-squared S.E. of regressiion Sum squared resid Log likelihood Durbin-Watson stat0.78190.1702o.aii7.adriamQ-statistiesSquared ResidualsKi- Kormality Test ferial Correlation LN Test. ARCH LM

9、Test.White Het&roskediEtici ty Cno cross t电rms)White Meteroskedasticity (cross terms)12,47249- F-slatistic1.964720 Prob(F-statistic)54,798060.000000得到如下结果：White Heteroskedasticity Test:F-st atistic4 920996Prob F(4,26)0.004339Obs*R-squared13.35705Prob. Chi*Square(4)。口09657Test Equation:Dependent Vari

10、able: RESIDEMethod: Least SquaresDate: 07/03/08 Time: 16:51Sample: 1 31Included observations: 31VariableCoefficientStd. Errort-StatisticProbC3.9B21372.8828511.3813190.17B9LOG(X1)-0 5792890.916069-0.6323640 5327(LOGp(1)f20 0418390 0668660 6257100.5370LOG(X2)-0.5636560.2032282.7735140.0101(LOG(X2)n20

11、0402800.0138792.9D21730.0075R-squared0.430B73Mean dependent var0 026186Adjusted R-squared0.343315S.D. dependent var0 038823S.E. of regression0.031460Akaike info criterion-3.933482Sum squared resid0.025734Schwarz criterion-3.702194Log likelihood65.96898F-statistic4 920995Durbin-Watson stat1.526222Pro

12、bfF-statistic)0.004339所以辅助回归结果为:e=3.982-0.5791nxi 0.042(1nxi)2 - 0.563ln X2 0.04(lnX2)2(1.38) (-0.63)(0.63)(-2.77)(2.9)其他收入x2与X2的平方项的参数的t检验是显著的，且 White统计量为13.36,在5%的 显著性水平下，拒绝同方差性这一原假设，方程确实存在异方差性。用加权最小二乘法对异方差性进行修正，重新进行回归估计，过程如下:在EViews工作窗口输入如下命令，定义加权数:估计过程如下:得到加权后消除异方差性的估计结果:Dependent Variable: LOG(

13、Y)Method： Least SquaresDate: 03/30/09 Tima: 11:56Sairiph: 1 31Included abservations: 31Weighting series: WVariableCoefficientStd. Error bStatisticProb.C1.2279290 29726B4.13070S 0003LOG(X1)0.3757400.0566306.6117340.0000LOG(X2)0510120001778128.E80470 0000Weighted StatisticsR-squared0 999990Mean depend

14、ent var7.55857BAdjusted R-squared0 999989S.D. dependent var12.31758S E. of regression0.041062Akaike info criterion-3 455703Sum squared resid0.047210Schwarz criterion-3.316930Log likelihood55 56339F-statistic1960.131Durbin-Watson stat2 487309Prob(F-statistic)0 000000UnweightedStatisticsR-squared0.794

15、514Mean dependent var7.448704Adjusted squared0 779836S D dependent var0.364648S E of regression0 171099Sum squared resid0819694Durbin-Watson slat2.007122回归表达式为：lnY? = 1.228 0.3761nxi 0.51lnX2（4.13） （6.61）（28.69）R2 =0.999,R =0.999,RSS=0.047从上面的结果看出，运用加权最小二乘法估计的结果不论拟合度，残差，还是各参数的t统计量的值都有了显著的改善。 2、表4.2列

16、出了 2000年中国部分省市城镇居民每个家庭平均全年可支配收入（ X）与消费 性支出（Y）的统计数据。表4.2 2000年中国部分省市城镇居民每个家庭平均全年可支配收入（X）与消费性支出（Y）单位：元地区可支配收入X消费性支出Y地区可支配收入X消费性支出Y北京10349.698493.49浙江9279.167020.22天津8140.56121.04山东6489.975022河北5661.164348.47河南4766.263830.71山西4724.113941.87湖北5524.544644.5内家占5129.053927.75湖南6218.735218.79辽宁5357.794356.0

17、6广东9761.578016.91吉林48104020.87陕西5124.244276.67黑龙江4912.883824.44甘肃4916.254126.47上海11718.018868.19青海5169.964185.73江苏6800.235323.18新疆5644.864422.93(1) 试用OLS法建立居民人均消费支出与可支配收入的线性模型(2) 检验模型是否存在异方差性(3) 如果存在异方差性，试采用适当的方法估计模型对数。采用OLS法建立线性模型，结果如下:Dependent Variable: YMeth ad: Lea st SquaresDate: O7/O3AJ8 Time

18、: 17:31Sample: 1 20Included observations: 20VariableCoefficientStd Error /StatisticProb.C272.3635159.67731 7057130 1053X07561250.02331632.386900.0000R*squared0.983129Mean dependent var5199.515Adjusted R-squared0 982192S.D. dependent var1625.275S E. of regression216.8900Akaike info criterion13 69130S

19、um squared residS46743.0Schwarz criterion13,79087Log likelihood-134.9130F-statistic1048912Durbin-Wat son st at1,301684Prob(F-statistic)0,000000进行异方差性的检验，本例采用White检验，过程如下:EVievs - Equation: UBTITLED Vorkfile: UNTITLED:UntitledO file Edit Object yiew Ftrsc Quick QtionE ”口dow Help瓦遮ftp也口bjeut PnintNjmE

20、 RFmere EstinnateHFore匚日式151日凶ResidsR电电recent应t i on莒Estimation OutputActual Pitted, Resi dual AENk Structure.Gr4iicuts wd Derivatives .Covari met Mitrixt Std. Error t-Statistic ProbCoefficient TestsResidual IestsStability TastsLabnAdjusted (squared S.E of regression Sum squared resid Log likelihood

21、 Durbin-Watson stat0 98211216 8984674三-134.91：Correlogram - g_statistics Correlogram Square! Resi Histogrn - ITormiLity Test Serial Ccrrelation LN Test. ARCH UI Ttst.Whi te Heteroskedastici ty (no cross te-rms JWhj_七守 Hetroskedsticity (cross terms)1.301684 Prob(FsFatisticJrroooooo得到如下部分输出结果：White Hd

22、eraskeelasticity Test:F-statistic14.63595Prob. FP,17)0.000201Obs*R-squared12.65213Prob. Chi-Square(2)。.口017a2从伴随概率值可以看出，在 5%的显著性水平下，原模型存在异方差性采用加权最小二乘法进行估计，过程如下：得到如下结果:Dependent Variable: YMethod: Least SquaresDate: D7/03/08 Time: 17:39Sample: 1 20Included observations: 20Weighting series: WVariableC

23、oefficientStd. Error t-StatieticProbC415 6603116 97913.5532080.0023X0 729026002242932 503490.0000Weighted StatisticsR-squared0.983248Mean dependent var4471 606Adjusted R-squared0.982317S.D dependent var7313.160S.E of regression77.04S31Akaike info criterion11 62138Sum squared resid106856.0Schwarz cri

24、terion11,72096Log likelihood-1U2138F-statistic1056.477Durbin-Watson stat1.545424Prob(F-statistic)0.000000UnweightedStatisticsR-squared0.9S1664Mean dependent var5199.515Adjusted R-squared0 980645S.D dependent var1625.275S.E. of regression226.1101Sum squared resid920263.9Durbin-Watson slat1.306360此时的回

25、归表达式为:y =415.66 0.729x(3.55) (32.5)拟合度和残差都有所改善。二、 序列相关性1、经济理论指出，商品进口主要由进口国的经济发展水平，以及商品进口价格指数与国内 价格指数对比因素决定。由于无法取得中国商品进口价格指数，我们主要研究中国商品进 口 M与国内生产总值 GDP的关系，数据见表 4.3。表4.3 1978-2001年中国商品进口与国内生产总值年份国内生产总 值/亿元商品进口 /亿 美儿年份国内生产总值 /亿元商品进口 /亿 美儿19783624.1108.9199018547.9533.519794038.2156.7199121617.8637.9198

26、04517.8200.2199226638.1805.919814862.4220.2199334634.41039.619825294.7192.9199446759.41156.119835934.5213.9199558478.11320.819847171274.1199667884.61388.319858964.4422.5199774462.61423.7198610202.2429.1199878345.21402.4198711962.5432.1199982067.461657198814928.3552.7200089442.22250.9198916909.2591.4

27、200195933.32436.1用OLS法建立中国商品进口方程，回归结果如下:Dependent Variable: MMethod: Least SquaresDate: 03/2B/09 Time: 13:29Sample: 1970 2001Included observations: 24VariableCoefficientStd. Error t-StatisticProb.C152 905746.07B4B33103760 0031GDP0.0203940.00101420.116810.0000R-squared0 948440Mean dependent var026.95

28、42Adjusted R-squared0.9460%S.D. dependent var667.4365S.E. of regression164.9600Akaike info criterion13.00387Sum squared resid520277.4Schwarz criterion13,10204Log likelihood-154 0464F-statistic404.6960Durbin-Watson stat0.B27922Prab(F-statistic)0 000000对应的表达式为:M?t =152.91 0.02GDPt(3.32) (20.11)_2R2 =0

29、.948,R =0.946,DW =0.627进行序列相关性检验，作残差项e与时间t以及东与e的关系图，如下:O Equation: UKTIILED Tarkflie: UNTITLED:U. UlSJBForecast5tats Resids)Actual, Fi Ited, Re 4 dual TableActual Fi tt2 dli R”i dual GraphResi dual GrsphSt&ndardized RsidukL GraphR电2&ent atiQUEEstim4ticn Output|Actual, Fitted Resi dualARMA Structure.

30、Gradints and DerivativesCcvariMatrixP A ff 1 r 1 .Ti* TxtkIL 310. LIFUII-JldllSTIT l-IUO.Residual Tests434.511735 6456570 0000Stability Tests0 O.OOO9B0 18.123B10 0000LabelB Mean dependent var 642,9952v|得到如下关系图:400 rO O89699429908868 弘288078M Residuals- - o O o O 3 2o o o O o o O 12 3 一 - 一一(T5W山 a-4

31、00 41r!-400-300-200-100 0 100 200 300 400RESID从上图可以看出，随即干扰项呈现正序列相关性。DW检验结果表明，在 5%的显著性水平下，n=24, k=2 ,查表得dl =1.274=1.45,由于DW=0.627Ydl ,故存在正自相关。下面进行拉格朗日乘数检验。含1阶滞后残差项的辅助回归过程如下：Equation: UNTITLED orkfHe; UNTITLED; ;Untitledl叵Edi Object View Free Qui ck 0DtLons finiow Help0目l:, Print 随m日忻自蛇引 归.如石周归口也应帆总出归

32、官与咸.Rer es entat i onsEstimation OutputActual, Fitted, ReEidual )iRMA Structure.Gradients and Beriv&tivts 卜Covari ance Matrixit Std. Error t-Statistic Prob.Residual TestsCorrelogrami Q=statisticsStability TestsCorrelogrami Squared Re si dualsLabelstocram = Hormali ty TestSferial CorrelAtian UI TestA

33、djusted R7squared S.E. of regression ,9424110 32ABCH LM Test. , PSum squared resid231262Whi te Ktrosk&distici ty (no cross termi)Log likelihood-127.51Vb.i_te Het er oske Jasti ci ty (cross terrnsjDurbin-Wats on stat0.374721 Prob(Fstafrstic) 000000Lag Specificat ion输入滞后阶数:得到如下结果:Breusch-Godfrey Seria

34、l Correlation LM Test:F-statisticObs*R-squared0.0006740.00130715,87518 Probability10.33227 ProbabilityTest Equation:Dependent Variable: RESIDMethod: Least SquaresDate: 03/28/09 Time: 13:43Presample missing value lagged residuals set to zerc.Variable Coefficient Std. Error t-Statistic Prob.C GDP RESI

35、D(-1)-10.220050.0006190.75283035 6S349 -0.2864080.00079807757270.18B9463.984367 7774 0.44660.0007R-squared0.430511Mean dependent var-1.47E-13Adjusted R-squared0.376274S D. dependent var151.5539S.E. of regression119.6917Akaike info criterion12.52419Sum squared resid300848.0Schwarz criterion12.67144Lo

36、g likelihood-147.2902F-statietic7 937590Durbin-Watson st al1 164220Prob(F-statistic)0.002708辅助回归表达式为：et = -10.22 0.0008GDP 0.75货(-0.286) (0.776)(3.98)LM=10.33 ,从伴随概率值可以看出，在显著性为5%的水平下，模型存在 1阶序列相关性作2阶滞后残差项的辅助回归结果如下：BreuschGodfrey Serial Correlation LM Test:F-statistic19.52905Probability0.0000200b8*R-s

37、quared15.07241Probability0.00D358Test Equation:Dependent Variable： RESIDMethod： Least SquaresDate: O3Z28/D9 Time: 13:52Presample missing value lagged resiiduals set to zero.VariableCoefficientStd. Errort-StatisticProb.C6.59475028.561860.2308940.8197GDP-0,0003440 000683-0.5040090.6198RESID(-1)1.09359

38、90.1755246 2304590.0000RESID -0.7657760.212016-3.6022700.0014R-sqjared0.661350Mean dependent var-1.J7E-13Adjusted R-squared0.610553S.D depandeint var151.5539S.E of regression94 57826Akaike info criterion1208774Sum squared resid170900.9Schwarz criterion12,26409Log likelihood-141.0529F-statistic13,019

39、37Durbin-Watson stat1 873142Prob(F-st atistic)0.000061辅助回归表达式为:& =6.59-0.0003GDP 1.094吼 -0.78嗨/(0.231) (-0.504)(6.231)(-3.692)2阶序列相LM值的伴随概率说明模型仍然存在序列相关性，&二的参数显著，说明存在关性。作3阶滞后残差项的辅助回归结果如下：Breusch-Godfrey Serial Correlation LM TestF-statisticObs*R-squared12.3757615.87561Probability Probability0.0001020

40、.001203Test Equation:Dependent Variable: RESIDMethod: Least SquaresDate: 03/2809 Time: 13:57Presample missing vsdug lagged residuals set to zero.VariableCoefficientStd. Error t-StatisticProb.C6 69163829.319490 2282320 8219GDP-0.0003490.000703 -0.4967110.6251RESIDE)1.10783802439554 5411510 0002RESID

41、田-0 8192950 444735 *1.8422100 0811RESID 谕0.0322970.3733510.0065070.9320R-squared0 661484Mean dependent var-1.47E-13Adjusted R-squared0.590217S.D. dependent var151.5539S E of regression97.01614Akaike info criterion12.17068Sum squared resid170B3O.5Schwarz criterion12.41611Log likelihood-141.0482F-stat

42、istic9.2B1B22Durbin Watson stat1 888605Prob(F-statistic)0.000247辅助回归表达式为:J =6.692-0.0003GDP 1.104-0.8194/ 0.032口(0.228) (-0.497)(4.541)(-1.842)(0.087)LM值的伴随概率说明模型仍然存在序列相关性，但#二的参数不显著，说明不存在序列相关性。运用广义差分法进行自相关的处理，采用科克伦一奥科特迭代法。2阶广义差分的估计过程为:Equation EstimationSpecification OptionsEquation specif!cationDep

43、endent variable followed by list of regressors and FDL terms,. OR m explicit equation likem c gdp 轨(1) ar 02)Method: LS - Lsast Squares (HLS and kKMA)Sample 1978 2001取消确定回归结果如下:Dependent Variable: DMethod: Least SquaresDate: 03/28W Time: 14:07Sample (adjusted): 1980 2001Included observations: 22 aft

44、er adjustmentsConvergence achieved after5 iterationsVariableCoefficientStd. Errort-Statist icProb.C169,321044.390073.8143390.0013GDIP0.0197920.00107310,452500 0000AR(1)1.110817701812456 1142270 0000AR(2)-0 8011940221892-3.6107360.0020R-squared0.982325Mean dependent var890.0591Adjusted R-squared0.979

45、379S.D. dependent var661.6499S.E of regression95 01304Akaike info criterion12,108B7Sum squared resid162494.6Schwarz criterion12,30724Log likelihood-129.1976F-statistic333.4596Durbin-Watson stat1.053364Prob (F-statistic)0 000000Inverted AR Roots55+7Di55-.70i表明模型已经不存在序列相关性。2、中国19802000年投资总额 X与工业总产值 丫的

46、统计资料如表 4.4所示。表4.4 中国1980 2000年投资总额X与工业总产值丫单位：亿元年份全社会固定资产投资X工业增加值Y年份全社会固定资产投资X工业增加值Y1980910.90001996.50019915594.5008087.1001981961.00002048.40019928080.10010284.5019821230.4002162.300199313072.3014143.8019831430.1002375.600199417042.1019359.6019841832.9002789.000199520019.3024718.3019852543.2003448.

47、700199622913.5029082.6019863120.6003967.000199724941.1032412.1019873791.7004585.800199828406.2033387.9019884753.8005777.200199929854.7135087.2119894410.4006484.000200032917.7339570.3019904517.0006858.000(1)当设定模型为ln Y = P0 +&ln Xt+ut时，是否存在序列相关性若按一阶自相关假设，使用广义最小二乘法估计原模型。米用差分形式Xt =Xt -Xt，Yt=Y-丫作为新数据，估计模

48、型_ * _ _ * 丫 =0 +ct1Xt +vt,该模型是否存在序列相关？对方程进行回归分析，结果如下：Dependent Variable: LOG(Y)Method: Least SquaresDate: O7/D3DS Time: 19:30Sample: 1980 2000Included obserratione: 21VariableCoefficientStd. ErrorbStatisticProbC14521090.1909257,6056450.0000LOG的0 8704190.02172740 061870 0000R-squared0.908300Mean dep

49、endent var9.031179Adjusted R-squared0 9876B4S.D dependent var1.062296S.E. of regression0117SS9Akaike info criterion-1.347752Sum squared resid0.264059Schwarz criterion-1.248274Log likelihood16.15140F-statistic1604.953Durbin-Watson stat0.451709Prob(F-statistic)0.000000由上面的结果可以看出，DW=0.45，小于显著性水平为 5%下，样

50、本容量为 21的DW分布的下限临界值di =1.22。因此，可判定模型存在一阶序列相关。运用广义最小二乘法估计模型，过程如下：得到如下输出结果:Dependent Variable: LOG(Y)Method: Least SquaresDate： 07AJ3/D8 Time： 19:44Sample (adjusted)： 1981 2000Included observations: 20 after adjustmentsConvergence achieved after 21 iterationsVariable Coefficient Std. Error t-Statistiic

51、 ProbC LOG因 AR(1)1.1262130.9035380.6495610,41419427190470.04430320.357950.1456794 4588360.01460.00000.0003R-squared0.995681Mean dependent var9102781Adjusted R-squared0.995061S D. dependent var1.036599S.E. of regression0 072853Akaike info criterion-2.263273Sum squared resid0.090228Schwarz criterion-2

52、.113913Log likelihood25 63273F-statistic191J.828Durbin-Watson stat1.348354Prob(F-statistic)0.000000Inverted AR Roots,65则回归模型表达式为:lnY =1.126 0.904lnXt 0.65AR(1)运用拉格朗日乘数检验模型是否还存在一阶序列相关性，过程如下: EViews - Equation: UWTITLED Torkfile： UUTITLEP: ：Uitt itledFile Edi t Obj ect 1 e* Proc Quick 口卫 tionw Iff ind

53、o* Help(Proc object旧血| 柞依Q E&timateForecastStats jResidsM迹IRepresent ationsEstimation OutputArtual,. Fi tted, Residual卜ARMA Structura.&di&ntw and Dtriratives .Covariance MatrixCoafficisnt TestsRasidual Testi，St&hili ty Tests卜LabelR-squared19955；Adjusted R-squared0.99501S.E. of regression0.0728:pjust

54、menls erationsIt Std. Error Statistic Prob.Carrelogram - Q-stati sti cs Correlogram Squared Kesiduals HiEtoram - Hormali ty Test Srial Correlation LM Test. - u ARCH LM Test. .c i:mi cncrm检验一阶滞后项检验部分结果如下:White Meteroskedasticity (no ross terms) HYPERLINK mailto:K4ter0Ekda.Eti K4ter0Ekda.Eti city (cro

55、ss terms) c - - _.4 d nin nBreusch-Godfrey Serial Correlation LM Test:F-statistic2.197567Prob. F(1J6)0.157666Obs*R-squared2 415232Prob. Chi-Square(l)0.120160从伴随概率值可以看出，此时已经不存在一阶序列相关性了。采用差分形式估计模型，过程如下：Equation EstionSpeci fication Opti onsEquation ficationviriible followed by list of regressors and P

56、DL terms, OR an eyplici t e (juat i on Liked) c d&)|确定取消回归结果如下：Dependent Variable: D(Y)Method: Least SquaresDate: 0743308 Time: 19:55Sample (adjusted): 1901 2000Included observations： 20 after adjustmentsVariableCoefficientStd. Error StatisticProbC291.0347350.10330.8312820.41 E7D的0.9920730 1602356.1

57、913800.0000R-squared0.680473Mean dependent var1878.690Adjusted R-squared0.662721S.D. dependent var1835.505S.E. of regression1065.983Akaike info criterion16.87502Sum squared resid20453746Schwarz criterion16.97539Log likelihood-166.7582F-statistic38,33318Durbin-Watsam stat1 620070Prab(F-statistic)0.00

58、0008此时的DW 值为1.62,大于5%的显著性水平下容量为20的DW 检验的临界值上限 名=1.41,因此差分形式的模型不存在一阶序列相关性。3、某上市公司的子公司的年销售额Y与其总公司年销售额 X的观测数据见表 4.5.表4.5某上市公司的子公司的年销售额Y与其总公司年销售额X序号XY序号XY1127.320.9611148.324.54213021.412146.424.33132.721.9613150.2254129.421.5214153.125.64513522.3915157.326.366137.122.7616160.726.987141.223.4817164.227.

59、528142.823.6618165.627.789145.524.119168.728.2410145.324.0120171.728.78用最小二乘法估计 Y关于X的回归方程；用DW检验分析随机干扰项的一阶自相关性；直接用差分法估计回归模型的参数。首先运用OLS法估计Y关于X的回归方程，结果如下:Dependent Variable: YMethod: Least SqunesDate: 07AJ3/D8 Time 20:09Sample: 1 20Included observations: 20VariableCoefficientStd. Error /StatisticProbC-

60、1 4547500214146 -6 7932610.0000X0 1762830 001445122.01700.0000R-squared0998792Mean dependent var24,56900Adjusled R-squared0 998725S. D dependent var2.410396S.E of regression0.086056Akaike info criterion-1.972991Sum squared resid0133302Schwarz criterion-1.873418Log likelihood21,72991F-statistic14888