《计量经济学》(庞浩第二版)四五章部分习题答案,亲手奉献!!.doc 33页

'第四章多重共线性习题五解答（1）在回归模型中，如果解释变量之间存在某种相关性，而不是满足经典假定中的互不相关，则称这种现象为多重共线性。判断模型是否存在多重共线性的方法有（1）在方程线性显著性检验中F检验值显著，但针对个别解释变量参数估计量检验中全部或部分t-检验值不显著；（2）参数估计量的符号不符合经济意义。按照这两种方法判定本题中的模型：F=189.9，线性显著，计算t-值，t1=-0.531/0.34=-1.562，t2=0.91/0.14=6.5，t3=0.047/0.021=2.238，显然t1不显著，可判定可能存在多重共线性，从参数估计量符号来看可得到同样的结论。（2）模型（1）是由C-D生产函数取对数得到，只不过是生产投入中，除了资本K、劳动L之外，还包含了时间T而已，取对数是对模型线性化处理，更好估计。模型（1）中的解释变量的系数在经济学中的解释为弹性。意思是其他条件不变的情况下，K、L、T变化百分之一，Y变化百分之几。由经济学理论知，一般情况下，资本投入的增加，必然引起产值的增加（在资本多得还不至于影响生产的条件下）。因此LogK的先验符号为正，显然与模型结果与预期的不一样，两种解释：（1）模型存在多重共线性，（2）资本投入所产生的效应已经达到最大，再继续增加投入影响了生产，导致产值下滑。不过这种解释没有现实依据，现实生活中有钱投入多的影响生产吗？没有，除非钱多得让生产员工没心思工作，只关心钱的问题了。就我们所知的现实经济中，大多数的经济体，都存在资本投入不足的问题，而没有出现资本投入过多的问题（有位经济学家做过实证研究）。（3）理由很简单，模型假定该国制造业生产规模报酬不变，则就有，为产值Y对资本K的弹性，LogK的系数，为产值Y对劳动的弹性,LogL的系数。如果存在，则模型（1）显然是不合适的，因为存在完全多重共线性。而为了消除多重共线性，就有了模型（2）。因此模型（2）的估计是在模型（1）存在多重共线性条件下进行的。（4）现实经济中，大多数经济行为都会随着时间呈现出一定的趋势，而这种趋势解释变量却不能加以解释，因此模型中常加入时间趋势变量以便处理此类型的问题，模型（1）和（2）即为此意。习题六解答（1）对理论模型进行回归得到如下方程（软件回归结果见附录图1）：t值3.530.79-0.08结果分析：方程整体解释能力较好，消费支出的96%能得到解释，33 为调整的解释能力，防止模型因解释变量的增多而虚假的提高解释能力。F值显著，业反映出方程通过显著性检验。但是从t检验值看，却发现参数估计量都不能通过检验。说明模型存在多重共线性。（2）模型显然不可靠，一般地说，一个家庭的可支配收入和家庭财富具有正相关性（当然也存在例外，一个吃老本的没有多少收入的败家子就是例外），因此模型把可支配收入和财富都加进来肯定不行，从回归结果可得到同样的结论。做收入和财富的相关性检验，得到两者相关系数居然高到0.9986，可以肯定模型不可靠。为可以试着改进模型，只做支出对可支配收入的回归模型。得到回归方程（输出结果见附附录图2）：t值3.8114.24习题七解答（1）估计模型得到如下方程（输出结果见附录图3）：t值3.011.21.60.13结果分析：整体解释能力较好，达到89%，方程线性显著，但各t检验值都小于2，不显著。模型存在多重共线性。（2）模型估计得到如下方程（输出结果见附录图4）：t值3.579.51根据，得到，，，。（3）对Z可以理解为某种意义上的总收入，它是由全部的工资收入、75%的非工资、非农业收入和62.5%的农业收入之和构成。就是说，在对收入构成的分类中，存在某种程度的重复，亦即它们之间存在某种程度的相关性，不能把所有的非工资、非农业收入和所有的农业收入加入模型。但须注意，工资收入与非工资、非农业收入及农业收入之间不存在因果关系。习题八解答（1）估计模型得到如下方程（输出结果见附录图5）：t值-0.462.21.02-0.11-0.4430.22833 结果分析：解释能力较好，达到89.3%，F检验显著（F临界值3.97），但t检验值通不过检验。可能存在多重共线性。（2）先做解释变量的相关系数得到表1：表1相关系数（correlation）x2x3x4x5x6x2x31-0.35183-0.3518310.56724-0.676090.97046-0.399580.6878490.216498x4x5x60.567240.97046-0.67609-0.3995810.6624760.66247610.2877870.6273990.6878490.2164980.2877870.6273991可以看到，变量之间高度相关，X2与X5之间相关系数达到0.97。因此模型存在多重共线性。当然还有其他检验方法，如辅助回归，即自变量之间做回归，检验其显著性判别是否存在多重共线性；还有可以计算VIF或TOL来判断。在此不一一列出。但需提醒一个问题，解释变量之间简单相关系大小不是判别多重共线性的充要条件。就是说，如果存在存在多重共线性，解释变量之间不一定存在很高的简单相关系数，反之则成立。因此简单相关系数判别多重共线性不能当做教条！用相关系数检验多重共线性时，还需要考虑偏相关系数，这样才能准确的判别。（3）本题使用逐步回归法进行修正。首先做Y对每一个解释变量的个别回归（输出结果见附录图6-图10），选取回归效果最好的一个方程。经对比，选取Y对X2的回归方程如下：t值25.478.65其次，在上述模型下分别加入其它解释变量回归（输出结果见附录图11-图14），选取效果最好的方程，经对比，选取Y对X2、X3的回归，方程如下：t值-1.30411.723.01可以看到，解释能力显著提高，而且F检验和t检验都显著（常数项除外，无实际意义）。再次，在上述模型下，继续照搬上述方法，进行回归（输出结果见附录图15-图1733 ），选取效果最好的。经分析，没有得到较好回归结果，逐步回归法停止。因此最终模型为Y对X2、X3的回归模型。不过为了模型得到跟好结果，采取无截距项的回归（输出见附录图18），回归方程如下：t值11.83532.613结果分析：对比有截距项和无截距项的回归，发现解释能力为发生显著的下降，因此无截距项回归，在方方程F检验和t检验全部显著的条件下获得了较好的效果。多重共线性的修正方法还有岭回归，数据结合等。最后说明：对于多重共线性的修正不能盲目进行，要考虑经济意义，多重共线性是一种样本现象，多数情况下的多重共线性，只要增大样本都会取得较好的效果，但不可奢求消除多重共线性，只能说可以减小其程度，使模型在误差项容许的范围下达到最好。第五章异方差性习题五解答（1）估计回归模型得到如下方程（输出结果见附录图19）：t值2.56932结果分析：模型拟合较好，解释能力达到94.6%，显著性均通过。（2）检验异方差性的方法有多种，以下采取①图示法，②怀特检验。首先图示法检验得到：图1Y与X散点图图2误差项平方和R与X的散点图从图1可以看出，Y与X得散点图似乎看不出异方差性，但从残差项与X的散点图可以看出存在异方差。其次再用怀特检验得到：图3white检验输出结果33 HeteroskedasticityTest:WhiteF-statisticObs*R-squaredScaledexplainedSS6.30137310.864019.912825Prob.F(2,57)Prob.Chi-Square(2)Prob.Chi-Square(2)0.00340.00440.007TestEquationDependentVariable:RESID^2Method:LeastSquaresDate:12/21/09Time:00:41Sample:160Includedobservations:60　VariableCXX^2Coefficient-10.036140.1659770.0018Std.Error131.14241.6198560.004587t-Statistic-0.0765290.1024640.392469Prob.0.93930.91870.6962R-squaredAdjustedR-squaredS.E.ofregressionSumsquaredresidLoglikelihoodF-statisticProb(F-statistic)0.1810670.152332102.3231596790.5-361.28566.3013730.00337MeandependentvarS.D.dependentvarAkaikeinfocriterionSchwarzcriterionHannan-Quinncriter.Durbin-Watsonstat　78.86225111.137512.1428512.2475712.183811.442328　从表中的前四行可以看出，模型存在异方差，Obs*R-squared值为10.86，大于临界值。（3）对异方差性修正有多种方法，本题采取①WLS,②对数变换法两种方法。首先采用WLS法，取W=1/resid，得到如下方程（输出结果见附录图20）：t值28.59372.51对比加权和为加权的两个回归结果，发现33 ，结果大有改进，DW统计量都显著改善！接下来对数变换法进行修正，最后把钟方法的输出结果做对比。对数变换得到如下方程（输出结果见附录图21）：t值1.0534.45结果分析：我们看到，对数变换并没有显著改善模型，解释能力提高不到1%。因此对数变换不适合本题的修正，我们最好采用WLS修正。当然这只是本题的结论。由凯恩斯消费理论知，消费和收入之间大致成线性关系。习题六解答（1）首先做散点图分析数据之间的关系，得到下图：图4Y与X、Z散点图我们看到，Y与利润Z、Y与销量X之间大致呈线性关系，但是，Y对销量X的回归明显存在异方差，这符合本题的出题目的。因此我们建立线性回归模型：，估计得到如下方程（输出结果见附录图22）：t值0.1953.83结果分析：拟合效果不太好，解释能力才47.8%，不到50%，虽然显著性检验通过。在截面数据的回归中，异方差性一直是个萦绕心头的问题。本题抽取的不同部门的销售量和R&D费用的数据，因为不同部分用于R&D费用的比列不同，所以在销量中，R&D费用占有的比列就存在差异。（2）为了说明如何运用Glerjser方法检验异方差，下面以本题为例说明。其基本思想是用残差项的绝对值对解释变量的不同形式做回归，判断回归方程的显著性33 ，以此来界定原回归模型是否存在异方差。依次做如下模型的回归估计（输出结果见附录图23-图27）：，，，，。经估计得到，对解释变量平方根的回归最为显著，系数通过检验。必须说明，Glerjser检验只有在大样本情况下才会得到较好的拟合效果，在小样本情况下，则只能作为了解异方差性某种信息的一种手段。（3）采用WLS和对数变换法进行修正。WLS修正，W=1/X，得到如下方程（输出结果见附录图28）：t值-1.85.525对比原回归结果，解释能力有显著改善。在用对数变换法做修正，得到如下方程（输出结果见附录图29）：t值-3.9857.869可以看出，在本题的修正中，对数变换方法比加权得到得到了更好的效果。这就说明，不同的数据模型，其适应的修正方法也不同。习题七解答（1）首先做散点图分析，通过图示粗略地分析Y与X得关系，散点图如下：图5Y与X的散点图图6LOG(Y)与LOG(X)散点图从散点图分析我们发现，股票价格Y与X之间，线性关系相当微弱，其对数化后的线性关系33 也不见得好转，但这也只是粗略地分析而已，具体的需要回归估计。分别估计以下两模型：得到如下两方程（输出结果见附录图30-图31）：t值4.255.05t值3.5971.91结果分析：由估计可以看出，Y对X的线性回归显著，但拟合效果不太好，对数化后的模型估计效果更次，不能通过检验。对残差进行分析：画出残差对解释变量的散点图，试着分析两者关系：图7残差项与X得散点图从散点图看不出残差与X得关系，因为存在异常点干扰整体关系。（2）重做回归得到如下方程（输出结果见附录图32）：t值2.830.398结果分析：结果非常令人意想不到！剔除点后，居然模型回归由显著变为不显著！，可以说原模型是个伪回归。也即说明，Y与X之间的线性关系微弱，或者说消费者价格变化率会影响股票价格，但是影响股票价格的主要因素不是消费者价格变化率，而是其他因素。所以，本题找的两个数据没有实质意义，无非是锻炼我们掌握异方差性的相关内容。但是这样的工作可能会影响同学们的现实思考能力，以为回归模型可以利用在任何场合，也就是说方法能论！实事求是才是解决问题的前提33 和出发点。习题八解答（1）先验分析，12个样本，有五个解释变量，如把所有解释变量都纳入进来估计结果肯定不显著，存在多重共线性，为了更合理的分析，先做产值Y对所有解释变量的回归，得到如下方程（输出结果见附录图33）：t值0.521.45-0.470.482.711.63结果分析：模型整体拟合效果较好，F检验显著，但是大部分t值却不显著，这是多重共线性的典型现象，为此运用逐步回归法得到如下较好的方程（简要输出结果见附录，步骤省略）：t值3.462.62.5对比上述两方程，我们看到逐步回归法得到的方程，所有系数都显著，解释能力相比于原方程并没有显著下降。这可以作为最终建立的模型，下面的分析将基于上述模型进行。（2）运用Glejser检验和white检验分析异方差，得到如下结果（图8、图9）：图8Glejser检验结果HeteroskedasticityTest:GlejserF-statistic1.671343    Prob.F(3,8)0.2494Obs*R-squared4.623345    Prob.Chi-Square(3)0.2015ScaledexplainedSS2.702259    Prob.Chi-Square(3)0.4398TestEquation:DependentVariable:ARESIDMethod:LeastSquaresDate:12/21/09Time:15:41Sample:112Includedobservations:12VariableCoefficientStd.Errort-StatisticProb.  33 C7.7598203.9188321.9801360.0830X3-0.1642620.121134-1.3560330.2121X4-0.0019300.001782-1.0829890.3104X50.0121510.0062191.9539690.0865R-squared0.385279    Meandependentvar11.94158AdjustedR-squared0.154758    S.D.dependentvar7.839495S.E.ofregression7.207399    Akaikeinfocriterion7.049295Sumsquaredresid415.5728    Schwarzcriterion7.210930Loglikelihood-38.29577    Hannan-Quinncriter.6.989452F-statistic1.671343    Durbin-Watsonstat1.985993Prob(F-statistic)0.249381图9white检验结果HeteroskedasticityTest:WhiteF-statistic9.463925    Prob.F(6,5)0.0130Obs*R-squared11.02887    Prob.Chi-Square(6)0.0875ScaledexplainedSS5.292628    Prob.Chi-Square(6)0.5069TestEquation:DependentVariable:RESID^2Method:LeastSquaresDate:12/21/09Time:15:47Sample:112Includedobservations:12VariableCoefficientStd.Errort-StatisticProb.  C-29.0542156.72871-0.5121610.6304X3^20.6986110.2295393.0435420.0286X3*X4-0.0054540.008398-0.6494160.5447X3*X5-0.0626640.023860-2.6262930.046733 X4^25.25E-065.38E-050.0976760.9260X4*X50.0002900.0003020.9613910.3805X5^20.0013400.0005532.4255060.0597R-squared0.919072    Meandependentvar198.9376AdjustedR-squared0.821959    S.D.dependentvar271.4158S.E.ofregression114.5236    Akaikeinfocriterion12.61064Sumsquaredresid65578.31    Schwarzcriterion12.89350Loglikelihood-68.66382    Hannan-Quinncriter.12.50591F-statistic9.463925    Durbin-Watsonstat1.459409Prob(F-statistic)0.013029结果分析，两种检验，在0.05的显著性水平下（95%置信水平），均不能拒绝无异方差性的假设。因此逐步回归法得到的模型在0.05的显著性水平下不能拒绝无异方差性的假设。（3）如果把显著性水平降低到0.1，则white检验将得到异方差性的结果。这时如果要修正模型，可采用WLS法。下面以WLS作简要修正，W=1/resid，resid为Y对X3、X4、X5回归得到的残差。修正得到如下结果（输出结果见附录图34）：t值5.54.32.62结果分析：虽然加权之后回归拟合效果提高了3%，但是，必须看到，这里做的修正是在降低显著性水平条件下进行的，即只是一个练习操作而已，没有实质意义。在实际研究中，当原模型可以很好的拟合数据时，我们再继续对它做些画蛇添足的行为时愚蠢的。33 附录图1DependentVariable:YMethod:LeastSquaresDate:12/20/09Time:20:25Sample:110Includedobservations:10VariableCoefficientStd.Errort-StatisticProb.  C24.551586.9523483.5314080.0096X20.5684250.7160980.7937810.4534X3-0.0058330.070294-0.0829750.9362R-squared0.962099    Meandependentvar111.0000AdjustedR-squared0.951270    S.D.dependentvar31.42893S.E.ofregression6.937901    Akaikeinfocriterion6.955201Sumsquaredresid336.9413    Schwarzcriterion7.045976Loglikelihood-31.77600    F-statistic88.84545Durbin-Watsonstat2.708154    Prob(F-statistic)0.000011图2DependentVariable:YMethod:LeastSquaresDate:12/20/09Time:20:40Sample:110Includedobservations:10VariableCoefficientStd.Errort-StatisticProb.  C24.454556.4138173.8127910.0051X20.5090910.03574314.243170.000033 R-squared0.962062    Meandependentvar111.0000AdjustedR-squared0.957319    S.D.dependentvar31.42893S.E.ofregression6.493003    Akaikeinfocriterion6.756184Sumsquaredresid337.2727    Schwarzcriterion6.816701Loglikelihood-31.78092    F-statistic202.8679Durbin-Watsonstat2.680127    Prob(F-statistic)0.000001图3DependentVariable:YMethod:LeastSquaresDate:12/20/09Time:21:39Sample:114Includedobservations:14VariableCoefficientStd.Errort-StatisticProb.  C22.734637.5505873.0109760.0131X20.4110800.3433391.1973030.2588X31.3028420.7929391.6430550.1314X40.1959431.5442240.1268880.9015R-squared0.894442    Meandependentvar87.76429AdjustedR-squared0.862774    S.D.dependentvar18.06057S.E.ofregression6.690349    Akaikeinfocriterion6.874166Sumsquaredresid447.6078    Schwarzcriterion7.056753Loglikelihood-44.11916    Hannan-Quinncriter.6.857264F-statistic28.24485    Durbin-Watsonstat1.439495Prob(F-statistic)0.000034图4DependentVariable:YMethod:LeastSquaresDate:12/20/09Time:21:5233 Sample:114Includedobservations:14VariableCoefficientStd.Errort-StatisticProb.  C24.537476.8642673.5746670.0038Z0.6784000.0713059.5141170.0000R-squared0.882948    Meandependentvar87.76429AdjustedR-squared0.873194    S.D.dependentvar18.06057S.E.ofregression6.431349    Akaikeinfocriterion6.691809Sumsquaredresid496.3470    Schwarzcriterion6.783103Loglikelihood-44.84266    Hannan-Quinncriter.6.683358F-statistic90.51842    Durbin-Watsonstat1.446036Prob(F-statistic)0.000001图5DependentVariable:YMethod:LeastSquaresDate:12/20/09Time:22:28Sample:19831995Includedobservations:13VariableCoefficientStd.Errort-StatisticProb.  C-15327.6033512.84-0.4573650.6613X25.4876152.4948432.1995840.0638X30.3930320.3839941.0235370.3401X4-0.0093480.084285-0.1109100.9148X5-0.1230430.277870-0.4428060.6713X60.1122540.4931960.2276060.8265R-squared0.937310    Meandependentvar42010.15AdjustedR-squared0.892532    S.D.dependentvar2948.71433 S.E.ofregression966.6556    Akaikeinfocriterion16.88960Sumsquaredresid6540962.    Schwarzcriterion17.15035Loglikelihood-103.7824    Hannan-Quinncriter.16.83600F-statistic20.93228    Durbin-Watsonstat2.807954Prob(F-statistic)0.000444图6DependentVariable:YMethod:LeastSquaresDate:12/20/09Time:23:12Sample:19831995Includedobservations:13VariableCoefficientStd.Errort-StatisticProb.  C31605.331240.94225.468830.0000X24.2277540.4886818.6513610.0000R-squared0.871864    Meandependentvar42010.15AdjustedR-squared0.860215    S.D.dependentvar2948.714S.E.ofregression1102.461    Akaikeinfocriterion16.98912Sumsquaredresid13369621    Schwarzcriterion17.07603Loglikelihood-108.4293    Hannan-Quinncriter.16.97125F-statistic74.84604    Durbin-Watsonstat2.366188Prob(F-statistic)0.000003图7DependentVariable:YMethod:LeastSquaresDate:12/20/09Time:23:13Sample:19831995Includedobservations:13VariableCoefficientStd.Errort-StatisticProb.  33 C62268.0362353.060.9986360.3394X3-0.1820290.560228-0.3249200.7513R-squared0.009506    Meandependentvar42010.15AdjustedR-squared-0.080539    S.D.dependentvar2948.714S.E.ofregression3065.158    Akaikeinfocriterion19.03422Sumsquaredresid1.03E+08    Schwarzcriterion19.12114Loglikelihood-121.7225    Hannan-Quinncriter.19.01636F-statistic0.105573    Durbin-Watsonstat0.493997Prob(F-statistic)0.751337图8DependentVariable:YMethod:LeastSquaresDate:12/20/09Time:23:13Sample:19831995Includedobservations:13VariableCoefficientStd.Errort-StatisticProb.  C38647.752569.91815.038510.0000X40.1559160.1134111.3747780.1966R-squared0.146626    Meandependentvar42010.15AdjustedR-squared0.069047    S.D.dependentvar2948.714S.E.ofregression2845.094    Akaikeinfocriterion18.88522Sumsquaredresid89040158    Schwarzcriterion18.97213Loglikelihood-120.7539    Hannan-Quinncriter.18.86735F-statistic1.890015    Durbin-Watsonstat0.865140Prob(F-statistic)0.196557图9DependentVariable:Y33 Method:LeastSquaresDate:12/20/09Time:23:13Sample:19831995Includedobservations:13VariableCoefficientStd.Errort-StatisticProb.  C29425.912129.91813.815510.0000X50.4660810.0773956.0221060.0001R-squared0.767273    Meandependentvar42010.15AdjustedR-squared0.746116    S.D.dependentvar2948.714S.E.ofregression1485.765    Akaikeinfocriterion17.58588Sumsquaredresid24282463    Schwarzcriterion17.67280Loglikelihood-112.3083    Hannan-Quinncriter.17.56802F-statistic36.26576    Durbin-Watsonstat1.551952Prob(F-statistic)0.000086图10DependentVariable:YMethod:LeastSquaresDate:12/20/09Time:23:14Sample:19831995Includedobservations:13VariableCoefficientStd.Errort-StatisticProb.  C-16028.2414238.56-1.1256920.2843X61.8017820.4417154.0790640.0018R-squared0.602008    Meandependentvar42010.15AdjustedR-squared0.565827    S.D.dependentvar2948.714S.E.ofregression1942.961    Akaikeinfocriterion18.12245Sumsquaredresid41526060    Schwarzcriterion18.2093733 Loglikelihood-115.7959    Hannan-Quinncriter.18.10459F-statistic16.63876    Durbin-Watsonstat0.900150Prob(F-statistic)0.001823图11DependentVariable:YMethod:LeastSquaresDate:12/20/09Time:23:23Sample:19831995Includedobservations:13VariableCoefficientStd.Errort-StatisticProb.C-24206.5818567.18-1.3037300.2215X24.6477380.39661111.718640.0000X30.4922160.1635363.0098270.0131R-squared0.932769Meandependentvar42010.15AdjustedR-squared0.919323S.D.dependentvar2948.714S.E.ofregression837.5463Akaikeinfocriterion16.49800Sumsquaredresid7014837.Schwarzcriterion16.62838Loglikelihood-104.2370Hannan-Quinncriter.16.47121F-statistic69.37022Durbin-Watsonstat2.618267Prob(F-statistic)0.000001图12DependentVariable:YMethod:LeastSquaresDate:12/20/09Time:23:24Sample:19831995Includedobservations:13VariableCoefficientStd.Errort-StatisticProb.33 C32137.561166.30827.554960.0000X24.7834060.5397748.8618660.0000X4-0.0880910.048541-1.8147790.0996R-squared0.903609Meandependentvar42010.15AdjustedR-squared0.884331S.D.dependentvar2948.714S.E.ofregression1002.862Akaikeinfocriterion16.85828Sumsquaredresid10057321Schwarzcriterion16.98865Loglikelihood-106.5788Hannan-Quinncriter.16.83148F-statistic46.87216Durbin-Watsonstat2.303967Prob(F-statistic)0.000008图13DependentVariable:YMethod:LeastSquaresDate:12/20/09Time:23:24Sample:19831995Includedobservations:13VariableCoefficientStd.Errort-StatisticProb.C33449.241981.11216.884080.0000X26.5084731.9901493.2703450.0084X5-0.2761810.233876-1.1808880.2650R-squared0.887545Meandependentvar42010.15AdjustedR-squared0.865054S.D.dependentvar2948.714S.E.ofregression1083.208Akaikeinfocriterion17.01242Sumsquaredresid11733403Schwarzcriterion17.14279Loglikelihood-107.5807Hannan-Quinncriter.16.98562F-statistic39.46238Durbin-Watsonstat2.551133Prob(F-statistic)0.000018图1433 DependentVariable:YMethod:LeastSquaresDate:12/20/09Time:23:24Sample:19831995Includedobservations:13VariableCoefficientStd.Errort-StatisticProb.C14578.089048.5531.6110950.1382X23.4378780.6055795.6770090.0002X60.5889540.3105891.8962470.0872R-squared0.905753Meandependentvar42010.15AdjustedR-squared0.886903S.D.dependentvar2948.714S.E.ofregression991.6488Akaikeinfocriterion16.83579Sumsquaredresid9833673.Schwarzcriterion16.96616Loglikelihood-106.4326Hannan-Quinncriter.16.80899F-statistic48.05189Durbin-Watsonstat2.862048Prob(F-statistic)0.000007图15DependentVariable:YMethod:LeastSquaresDate:12/20/09Time:23:32Sample:19831995Includedobservations:13VariableCoefficientStd.Errort-StatisticProb.C-18285.7724890.72-0.7346420.4813X24.7334400.47205410.027330.0000X30.4410920.2175562.0274870.0732X4-0.0205030.053931-0.3801670.712633 R-squared0.933831Meandependentvar42010.15AdjustedR-squared0.911775S.D.dependentvar2948.714S.E.ofregression875.8469Akaikeinfocriterion16.63592Sumsquaredresid6903970.Schwarzcriterion16.80975Loglikelihood-104.1335Hannan-Quinncriter.16.60019F-statistic42.33870Durbin-Watsonstat2.551112Prob(F-statistic)0.000012图16DependentVariable:YMethod:LeastSquaresDate:12/20/09Time:23:34Sample:19831995Includedobservations:13VariableCoefficientStd.Errort-StatisticProb.C-19387.0119995.69-0.9695590.3576X25.8219831.5933053.6540300.0053X30.4582900.1729062.6505130.0265X5-0.1456990.191196-0.7620410.4655R-squared0.936844Meandependentvar42010.15AdjustedR-squared0.915792S.D.dependentvar2948.714S.E.ofregression855.6773Akaikeinfocriterion16.58932Sumsquaredresid6589653.Schwarzcriterion16.76315Loglikelihood-103.8306Hannan-Quinncriter.16.55359F-statistic44.50128Durbin-Watsonstat2.795472Prob(F-statistic)0.000010图17DependentVariable:YMethod:LeastSquares33 Date:12/20/09Time:23:34Sample:19831995Includedobservations:13VariableCoefficientStd.Errort-StatisticProb.C-22269.1220711.67-1.0751970.3103X24.4724430.7587275.8946640.0002X30.4488400.2326001.9296660.0857X60.1031090.3731060.2763530.7885R-squared0.933334Meandependentvar42010.15AdjustedR-squared0.911113S.D.dependentvar2948.714S.E.ofregression879.1292Akaikeinfocriterion16.64340Sumsquaredresid6955813.Schwarzcriterion16.81723Loglikelihood-104.1821Hannan-Quinncriter.16.60767F-statistic42.00078Durbin-Watsonstat2.679392Prob(F-statistic)0.000013图18DependentVariable:YMethod:LeastSquaresDate:12/21/09Time:17:42Sample:19831995Includedobservations:13VariableCoefficientStd.Errort-StatisticProb.  X24.4422350.37533911.835260.0000X30.2792840.00856432.612900.0000R-squared0.921341    Meandependentvar42010.15AdjustedR-squared0.914191    S.D.dependentvar2948.714S.E.ofregression863.7738    Akaikeinfocriterion16.5011433 Sumsquaredresid8207158.    Schwarzcriterion16.58805Loglikelihood-105.2574    Hannan-Quinncriter.16.48327Durbin-Watsonstat2.680964图19DependentVariable:YMethod:LeastSquaresDate:12/20/09Time:23:59Sample:160Includedobservations:60VariableCoefficientStd.Errort-StatisticProb.C9.3475223.6384372.5691040.0128X0.6370690.01990332.008810.0000R-squared0.946423Meandependentvar119.6667AdjustedR-squared0.945500S.D.dependentvar38.68984S.E.ofregression9.032255Akaikeinfocriterion7.272246Sumsquaredresid4731.735Schwarzcriterion7.342058Loglikelihood-216.1674Hannan-Quinncriter.7.299553F-statistic1024.564Durbin-Watsonstat1.790431Prob(F-statistic)0.000000图20DependentVariable:YMethod:LeastSquaresDate:12/21/09Time:10:26Sample:160Includedobservations:60Weightingseries:1/RESIDVariableCoefficientStd.Errort-StatisticProb.33 C10.205070.35693328.591030.0000X0.6331700.001700372.51350.0000WeightedStatisticsR-squared0.999582Meandependentvar120.4524AdjustedR-squared0.999575S.D.dependentvar931.0901S.E.ofregression1.729654Akaikeinfocriterion3.966484Sumsquaredresid173.5187Schwarzcriterion4.036296Loglikelihood-116.9945Hannan-Quinncriter.3.993792F-statistic138766.3Durbin-Watsonstat0.192262Prob(F-statistic)0.000000UnweightedStatisticsR-squared0.946365Meandependentvar119.6667AdjustedR-squared0.945441S.D.dependentvar38.68984S.E.ofregression9.037146Sumsquaredresid4736.860Durbin-Watsonstat1.794290图21DependentVariable:LOG(Y)Method:LeastSquaresDate:12/21/09Time:10:41Sample:160Includedobservations:60VariableCoefficientStd.Errort-StatisticProb.C0.1401990.1335721.0496170.2982LOG(X)0.9015470.02616834.452160.0000R-squared0.953412Meandependentvar4.730314AdjustedR-squared0.952609S.D.dependentvar0.339103S.E.ofregression0.073821Akaikeinfocriterion-2.34157733 Sumsquaredresid0.316075Schwarzcriterion-2.271765Loglikelihood72.24731Hannan-Quinncriter.-2.314270F-statistic1186.951Durbin-Watsonstat1.947104Prob(F-statistic)0.000000图22DependentVariable:YMethod:LeastSquaresDate:12/21/09Time:11:02Sample:118Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.C192.9944990.98450.1947500.8480X0.0319000.0083293.8300440.0015R-squared0.478305Meandependentvar3056.861AdjustedR-squared0.445699S.D.dependentvar3705.973S.E.ofregression2759.150Akaikeinfocriterion18.78767Sumsquaredresid1.22E+08Schwarzcriterion18.88660Loglikelihood-167.0890Hannan-Quinncriter.18.80131F-statistic14.66924Durbin-Watsonstat3.015597Prob(F-statistic)0.001476图23DependentVariable:RMethod:LeastSquaresDate:12/21/09Time:11:23Sample:118Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.33 C578.5686678.69490.8524720.4065X0.0119390.0057042.0930560.0526R-squared0.214951Meandependentvar1650.427AdjustedR-squared0.165885S.D.dependentvar2069.045S.E.ofregression1889.657Akaikeinfocriterion18.03062Sumsquaredresid57132855Schwarzcriterion18.12955Loglikelihood-160.2756Hannan-Quinncriter.18.04426F-statistic4.380883Durbin-Watsonstat1.743304Prob(F-statistic)0.052634图24DependentVariable:RMethod:LeastSquaresDate:12/21/09Time:12:02Sample:118Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.SQRX6.4435141.4112684.5657620.0003R-squared0.248189Meandependentvar1650.427AdjustedR-squared0.248189S.D.dependentvar2069.045S.E.ofregression1794.007Akaikeinfocriterion17.87624Sumsquaredresid54713861Schwarzcriterion17.92571Loglikelihood-159.8862Hannan-Quinncriter.17.88306Durbin-Watsonstat1.742094图25DependentVariable:RMethod:LeastSquaresDate:12/21/09Time:12:06Sample:11833 Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.X19589750.126400820.7586780.4584R-squared-0.618902Meandependentvar1650.427AdjustedR-squared-0.618902S.D.dependentvar2069.045S.E.ofregression2632.572Akaikeinfocriterion18.64326Sumsquaredresid1.18E+08Schwarzcriterion18.69273Loglikelihood-166.7894Hannan-Quinncriter.18.65008Durbin-Watsonstat0.794335图26DependentVariable:RMethod:LeastSquaresDate:12/21/09Time:11:26Sample:118Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.X0.0156080.0037134.2034670.0006R-squared0.179294Meandependentvar1650.427AdjustedR-squared0.179294S.D.dependentvar2069.045S.E.ofregression1874.406Akaikeinfocriterion17.96392Sumsquaredresid59727790Schwarzcriterion18.01339Loglikelihood-160.6753Hannan-Quinncriter.17.97074Durbin-Watsonstat1.713357图27DependentVariable:RMethod:LeastSquaresDate:12/21/09Time:12:0133 Sample:118Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.1/SQRX174610.9104554.51.6700470.1132R-squared-0.437823Meandependentvar1650.427AdjustedR-squared-0.437823S.D.dependentvar2069.045S.E.ofregression2480.977Akaikeinfocriterion18.52465Sumsquaredresid1.05E+08Schwarzcriterion18.57411Loglikelihood-165.7218Hannan-Quinncriter.18.53147Durbin-Watsonstat0.894315图28DependentVariable:YMethod:LeastSquaresDate:12/21/09Time:12:38Sample:118Includedobservations:18Weightingseries:1/XVariableCoefficientStd.Errort-StatisticProb.C-243.4910135.2946-1.7997090.0908X0.0366980.0066425.5254750.0000WeightedStatisticsR-squared0.656142Meandependentvar929.6678AdjustedR-squared0.634651S.D.dependentvar738.5199S.E.ofregression694.2181Akaikeinfocriterion16.02789Sumsquaredresid7711020.Schwarzcriterion16.12682Loglikelihood-142.2510Hannan-Quinncriter.16.04153F-statistic30.53087Durbin-Watsonstat2.64308833 Prob(F-statistic)0.000046UnweightedStatisticsR-squared0.467483Meandependentvar3056.861AdjustedR-squared0.434201S.D.dependentvar3705.973S.E.ofregression2787.620Sumsquaredresid1.24E+08Durbin-Watsonstat2.963758图29DependentVariable:LOG(Y)Method:LeastSquaresDate:12/21/09Time:12:43Sample:118Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.C-7.3646981.847999-3.9852290.0011LOG(X)1.3222400.1680377.8687330.0000R-squared0.794653Meandependentvar7.109988AdjustedR-squared0.781819S.D.dependentvar1.606121S.E.ofregression0.750216Akaikeinfocriterion2.367529Sumsquaredresid9.005196Schwarzcriterion2.466459Loglikelihood-19.30776Hannan-Quinncriter.2.381170F-statistic61.91696Durbin-Watsonstat2.398776Prob(F-statistic)0.000001图30DependentVariable:YMethod:LeastSquaresDate:12/21/09Time:13:11Sample:12033 Includedobservations:20VariableCoefficientStd.Errort-StatisticProb.C4.6102821.0849064.2494780.0005X0.7574330.1499415.0515590.0001R-squared0.586380Meandependentvar8.530000AdjustedR-squared0.563402S.D.dependentvar5.131954S.E.ofregression3.390969Akaikeinfocriterion5.374748Sumsquaredresid206.9761Schwarzcriterion5.474321Loglikelihood-51.74748Hannan-Quinncriter.5.394186F-statistic25.51825Durbin-Watsonstat2.607212Prob(F-statistic)0.000083图31DependentVariable:LOG(Y)Method:LeastSquaresDate:12/21/09Time:13:12Sample:120Includedobservations:20VariableCoefficientStd.Errort-StatisticProb.C1.3226240.3676533.5974800.0021LOG(X)0.4578650.2393111.9132590.0718R-squared0.168997Meandependentvar1.982564AdjustedR-squared0.122830S.D.dependentvar0.607609S.E.ofregression0.569070Akaikeinfocriterion1.805014Sumsquaredresid5.829139Schwarzcriterion1.904587Loglikelihood-16.05014Hannan-Quinncriter.1.824452F-statistic3.660559Durbin-Watsonstat2.643006Prob(F-statistic)0.07175733 图32DependentVariable:YMethod:LeastSquaresDate:12/21/09Time:13:35Sample:120IFX<=26Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.C6.7380822.3848602.8253580.0117X0.2214840.5555680.3986630.6951R-squared0.009262Meandependentvar7.636842AdjustedR-squared-0.049016S.D.dependentvar3.310457S.E.ofregression3.390619Akaikeinfocriterion5.379203Sumsquaredresid195.4371Schwarzcriterion5.478618Loglikelihood-49.10243Hannan-Quinncriter.5.396028F-statistic0.158932Durbin-Watsonstat2.656146Prob(F-statistic)0.695105图33DependentVariable:YMethod:LeastSquaresDate:12/21/09Time:15:10Sample:112Includedobservations:12VariableCoefficientStd.Errort-StatisticProb.C4.7171989.1257550.5169100.6237X10.0396150.0272701.4526970.1965X2-0.0368950.077705-0.4748130.6517X30.2632560.5494760.4791040.6488X40.0134630.0049632.7129970.035033 X50.0254690.0156631.6259930.1551R-squared0.974539Meandependentvar96.62750AdjustedR-squared0.953321S.D.dependentvar77.06446S.E.ofregression16.65001Akaikeinfocriterion8.769552Sumsquaredresid1663.338Schwarzcriterion9.012005Loglikelihood-46.61731Hannan-Quinncriter.8.679787F-statistic45.93047Durbin-Watsonstat1.969898Prob(F-statistic)0.000105图34DependentVariable:YMethod:LeastSquaresDate:12/21/09Time:15:59Sample:112Includedobservations:12Weightingseries:1/BVariableCoefficientStd.Errort-StatisticProb.X31.0374460.1885275.5029030.0004X40.0089590.0020874.2936450.0020X50.0211620.0080892.6162610.0280WeightedStatisticsR-squared0.992089Meandependentvar82.95636AdjustedR-squared0.990332S.D.dependentvar239.5237S.E.ofregression17.52356Akaikeinfocriterion8.777287Sumsquaredresid2763.675Schwarzcriterion8.898514Loglikelihood-49.66372Hannan-Quinncriter.8.732405Durbin-Watsonstat0.474622UnweightedStatistics33 R-squared0.959618Meandependentvar96.62750AdjustedR-squared0.950644S.D.dependentvar77.06446S.E.ofregression17.12075Sumsquaredresid2638.082Durbin-Watsonstat1.92369033'