计量经济学 综合案例1 我国农民收入影响因素的回归分析

综合案例1 我国农民收入影响因素的回归分析

自改革开放以来,虽然中国经济平均增长速度为9.5 % ,但二元经济结构给经济发展带来的问题仍然很突出。农村人口占了中国总人口的70 %多,农业产业结构不合理,经济不发达,以及农民收入增长缓慢等问题势必成为我国经济持续稳定增长的障碍。正确有效地解决好“三农”问题是中国经济走出困境,实现长期稳定增长的关键。其中,农民收入增长是核心,也是解决“三农”问题的关键。本文力图应用适当的多元线性回归模型,对有关农民收入的历史数据和现状进行分析,寻找其根源,探讨影响农民收入的主要因素,并在此基础上对如何增加农民收入提出相应的政策建议。

农民收入水平的度量，通常采用人均纯收入指标。影响农民收入增长的因素是多方面的，既有结构性矛盾因素，又有体制性障碍因素。但可以归纳为以下几个方面：一是农产品收购价格水平。目前农业收入仍是中西部地区农民收入的主要来源。二是农业剩余劳动力转移水平。中国的农业目前仍以农户分散经营为主，农业比较效益低，尽快地把农业剩余劳动力转移出去是有效改善农民收入状况的重要因素。三是城市化、工业化水平。中国多数地区城市化、工业化水平落后于世界平均水平，这种状况极大地影响了农民收入的增长。四是农业产业结构状况。农林牧渔业对农民收入增长贡献率是不同的。随着我国“入世”后农产品市场的开放和人民生活水平的提高、农产品需求市场的改变，农业结构状况直接影响着农民收入的增长。五是农业投入水平。农民收入与财政农业支出、农村集体投入、农户个人投入以及信贷投入都有显著的正相关关系。农业投入是农民收入增长的重要保证。但考虑到农业投入主体的多元性，既有国家、集体和农户的投入，又有银行、企业和外资的投入，考虑到复杂性和可行性，所以对农业投入与农民收入，本文暂不作讨论。因此，以全国为例，把农民收入与各影响因素关系进行线性回归分析，并建立数学模型。

一、计量经济模型分析 (一)、数据搜集

根据以上分析，我们在影响农民收入因素中引入7个解释变量。即： x2-财

政用于农业的支出的比重，三产业从业人数占全社会从业人数的比重，x3 -第二、

x4 -非农村人口比重，x5 -乡村从业人员占农村人口的比重，x6 -农业总产值

占农林牧总产值的比重，x7 -农作物播种面积，x8—农村用电量。

资料来源《中国统计年鉴2006》。

(二)、计量经济学模型建立 我们设定模型为下面所示的形式：

Yt 1 2X2 3X3 4X4 5X5 6X6 7X7 8X8 ut

利用Eviews软件进行最小二乘估计，估计结果如下表所示：

Dependent Variable: Y Method: Least Squares Date: 06/08/07 Time: 21:51 Sample: 1986 2004 Included observations: 19

C

-1102.373

375.8283

-2.933184

0.0136

X2 X3 X4 X5 X6 X7 X8

R-squared

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

-6.635393 18.22942 2.430039 -16.23737 -2.155208 0.009962 0.063389

3.781349 2.066617 8.370337 5.894109 2.770834 0.002328 0.021276

-1.754769 8.820899 0.290316 -2.754847 -0.777819 4.278810 2.979348

0.1071 0.0000 0.7770 0.0187 0.4531 0.0013 0.0125 345.5232 139.7117 8.026857 8.424516 374.6600 0.000000

0.995823 Mean dependent var 0.993165 S.D. dependent var 11.55028 Akaike info criterion 1467.498 Schwarz criterion -68.25514 F-statistic 1.993270 Prob(F-statistic)

表1 最小二乘估计结果

回归分析报告为：

-1102.373-6.6354X+18.2294X+2.4300X-16.2374X-2.1552X+0.0100X+0.0634XYi2345678SE 375.83 t -2.933 R 0.995823

2

3.7813 2.06661 8.37034 5.8941 2.7708 0.00233 0.02128 1.755 8.82090 0.20316 2.755 0.778 4.27881 2.9793

R 0.993165

2

Df 19DW 1.99327F 374.66

二、计量经济学检验

(一)、多重共线性的检验及修正

①、检验多重共线性 (a)、直观法

从“表1 最小二乘估计结果”中可以看出，虽然模型的整体拟合的很好，但是x4 x6的t统计量并不显著，所以可能存在多重共线性。

(b)、相关系数矩阵

X2 X3 X4 X5 X6 X7 X8

X2

X3

X4

X5

X6

X7

X8

1.000000 -0.717662 -0.695257 -0.731326 0.737028 -0.332435 -0.594699 -0.717662 1.000000 0.922286 0.935992 -0.945701 0.742251 0.883804 -0.695257 0.922286 1.000000 0.986050 -0.937751 0.753928 0.974675 -0.731326 0.935992 0.986050 1.000000 -0.974750 0.687439 0.940436 0.737028 -0.945701 -0.937751 -0.974750 1.000000 -0.603539 -0.887428 -0.332435 0.742251 0.753928 0.687439 -0.603539 1.000000 0.742781 -0.594699 0.883804 0.974675 0.940436 -0.887428 0.742781 1.000000

表2 相关系数矩阵

从“表2 相关系数矩阵”中可以看出，个个解释变量之间的相关程度较高，所以应该存在多重共线性。

②、多重共线性的修正——逐步迭代法 A、

一元回归

Dependent Variable: Y Method: Least Squares Date: 06/08/07 Time: 21:52 Sample: 1986 2004 Variable C X2

R-squared

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Coefficient 820.3133 -51.37836

Std. Error 151.8712 16.18923

t-Statistic 5.401374 -3.173614

Prob. 0.0000 0.0056 345.5232 139.7117 12.40822 12.50763 10.07183 0.372041 Mean dependent var 0.335102 S.D. dependent var 113.9227 Akaike info criterion 220632.4 Schwarz criterion -115.8781 F-statistic 表3 y对x2的回归结果

Dependent Variable: Y Method: Least Squares Date: 06/08/07 Time: 21:52 Sample: 1986 2004 C R-squared

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

-525.8891 64.11333 -8.202492 0.0000 345.5232 139.7117 10.37950 10.47892 188.8628 0.000000

0.917421 Mean dependent var 0.912563 S.D. dependent var 41.31236 Akaike info criterion 29014.09 Schwarz criterion -96.60526 F-statistic 0.598139 Prob(F-statistic)

表4 y对x3的回归结果

Dependent Variable: Y Method: Least Squares Date: 06/08/07 Time: 21:52 Sample: 1986 2004 Included observations: 19

Variable C

Coefficient -223.1905

Std. Error 69.92322

t-Statistic -3.191937

Prob. 0.0053

R-squared

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

345.5232 139.7117 11.25018 11.34959 69.18839 0.000000

0.802758 Mean dependent var 0.791155 S.D. dependent var 63.84760 Akaike info criterion 69300.77 Schwarz criterion -104.8767 F-statistic 0.282182 Prob(F-statistic)

表5 y对x4的回归结果

Dependent Variable: Y Method: Least Squares Date: 06/08/07 Time: 21:52 Sample: 1986 2004 Variable C X5

R-squared

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Coefficient -494.1440 15.77978

Std. Error 118.1449 2.198711

t-Statistic -4.182526 7.176832

Prob. 0.0006 0.0000 345.5232 139.7117 11.47978 11.57919 51.50691 0.751850 Mean dependent var 0.737253 S.D. dependent var 71.61463 Akaike info criterion 87187.14 Schwarz criterion -107.0579 F-statistic 表6 y对x5的回归结果

Dependent Variable: Y Method: Least Squares Date: 06/08/07 Time: 21:52 Sample: 1986 2004 Included observations: 19

C X6

R-squared

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

1288.009 -15.52398

143.8088 2.351180

8.956395 -6.602635

0.0000 0.0000 345.5232 139.7117 11.60250 11.70192 43.59479 0.000004

0.719448 Mean dependent var 0.702945 S.D. dependent var 76.14674 Akaike info criterion 98571.54 Schwarz criterion -108.2238 F-statistic 0.395893 Prob(F-statistic)

表7 y对x6的回归结果

Dependent Variable: Y Method: Least Squares

Date: 06/08/07 Time: 21:52 Sample: 1986 2004 Variable C X7

R-squared

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Coefficient -4417.766 0.031528

Std. Error 681.1678 0.004507

t-Statistic -6.485577 6.994943

Prob. 0.0000 0.0000 345.5232 139.7117 11.51813 11.61754 48.92923 0.742148 Mean dependent var 0.726980 S.D. dependent var 73.00119 Akaike info criterion 90595.96 Schwarz criterion -107.4222 F-statistic 表8 y对x7的回归结果

Dependent Variable: Y Method: Least Squares Date: 06/08/07 Time: 21:52 Sample: 1986 2004 C X8

R-squared

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

140.1625 0.119827

28.96616 0.014543

4.838835 8.239503

0.0002 0.0000 345.5232 139.7117 11.26536 11.36478 67.88941 0.000000

0.799739 Mean dependent var 0.787959 S.D. dependent var 64.33424 Akaike info criterion 70361.21 Schwarz criterion -105.0209 F-statistic 0.203711 Prob(F-statistic)

表9 y对x8的回归结果

综合比较表3~9的回归结果，发现加入x3的回归结果最好。以x3为基础顺次加入其他解释变量，进行二元回归，具体的回归结果如下表10~15所示：

Dependent Variable: Y Method: Least Squares Date: 06/08/07 Time: 21:53 Sample: 1986 2004 Variable C X3 Coefficient -754.4481 21.78865 Std. Error 149.1701 1.932689 t-Statistic -5.057637 11.27375 Prob. 0.0001 0.0000

R-squared

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood 0.929787 Mean dependent var 0.921010 S.D. dependent var 39.26619 Akaike info criterion 24669.34 Schwarz criterion -95.06417 F-statistic 345.5232 139.7117 10.32254 10.47167 105.9385 Dependent Variable: Y Method: Least Squares Date: 06/08/07 Time: 21:53 Sample: 1986 2004 Included observations: 19

Variable C X3 R-squared

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

Coefficient -508.6781 17.88200 Std. Error 75.73220 3.752121 t-Statistic -6.716802 4.765837 Prob. 0.0000 0.0002 345.5232 139.7117 10.47185 10.62097 90.13613 0.000000

0.918481 Mean dependent var 0.908291 S.D. dependent var 42.30965 Akaike info criterion 28641.71 Schwarz criterion -96.48254 F-statistic 0.596359 Prob(F-statistic)

Dependent Variable: Y Method: Least Squares Date: 06/08/07 Time: 21:54 Sample: 1986 2004 Included observations: 19

Variable C X3 X5

R-squared

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

Coefficient -498.1550 23.97516 -4.320566

Std. Error 67.21844 3.967183 3.553466

t-Statistic -7.410986 6.043370 -1.215874

Prob. 0.0000 0.0000 0.2417 345.5232 139.7117 10.39639 10.54551 97.82772 0.000000

0.924405 Mean dependent var 0.914956 S.D. dependent var 40.74312 Akaike info criterion 26560.02 Schwarz criterion -95.76570 F-statistic 0.607882 Prob(F-statistic)

Dependent Variable: Y Method: Least Squares

Date: 06/08/07 Time: 21:54 Sample: 1986 2004 Variable C X3 R-squared

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

Coefficient -1600.965 29.93768 Std. Error 346.9265 3.534753 t-Statistic -4.614709 8.469528 Prob. 0.0003 0.0000 345.5232 139.7117 10.00606 10.15518 148.3576 0.000000

0.948835 Mean dependent var 0.942440 S.D. dependent var 33.51927 Akaike info criterion 17976.66 Schwarz criterion -92.05754 F-statistic 1.125188 Prob(F-statistic)

Dependent Variable: Y Method: Least Squares Date: 06/08/07 Time: 21:54 Sample: 1986 2004 Included observations: 19

C X3 X7

R-squared

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

-2153.028 14.40497 0.012268

327.1248 1.358355 0.002447

-6.581673 10.60472 5.014015

0.0000 0.0000 0.0001 345.5232 139.7117 9.540364 9.689485 241.0961 0.000000

0.967884 Mean dependent var 0.963869 S.D. dependent var 26.55648 Akaike info criterion 11283.94 Schwarz criterion -87.63345 F-statistic 0.690413 Prob(F-statistic)

Dependent Variable: Y Method: Least Squares Date: 06/08/07 Time: 21:54 Sample: 1986 2004 Included observations: 19

Variable C X3 X8

R-squared

Adjusted R-squared

Coefficient -400.5635 15.54271 0.029233

Std. Error 103.0301 2.916358 0.019233

t-Statistic -3.887832 5.329493 1.519929

Prob. 0.0013 0.0001 0.1480 345.5232 139.7117

0.927840 Mean dependent var 0.918820 S.D. dependent var

S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

39.80687 Akaike info criterion 25353.40 Schwarz criterion -95.32401 F-statistic 0.559772 Prob(F-statistic)

10.34990 10.49902 102.8643 0.000000

综合表10~15所示，加入x7的模型的R最大,以x3、x7为基础顺次加入其他解释变量，进行三元回归，具体回归结果如下表16~20所示：

Dependent Variable: Y Method: Least Squares Date: 06/08/07 Time: 21:55 Sample: 1986 2004 Variable C X3 X7 X2

R-squared

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

Coefficient -2133.921 14.96023 0.011843 2.195243

Std. Error 340.6965 2.094645 0.002786 6.170403

t-Statistic -6.263406 7.142134 4.250908 0.355770

Prob. 0.0000 0.0000 0.0007 0.7270 345.5232 139.7117 9.637224 9.836053 151.9988 0.000000

0.968153 Mean dependent var 0.961783 S.D. dependent var 27.31242 Akaike info criterion 11189.52 Schwarz criterion -87.55363 F-statistic 0.712258 Prob(F-statistic)

Dependent Variable: Y Method: Least Squares Date: 06/08/07 Time: 21:55 Sample: 1986 2004 Variable C X3 X7 R-squared

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

Coefficient -2226.420 15.66729 0.012703 Std. Error 353.4425 2.443113 0.002589 t-Statistic -6.299243 6.412839 4.906373 Prob. 0.0000 0.0000 0.0002 345.5232 139.7117 9.619741 9.818571 154.7677 0.000000

0.968705 Mean dependent var 0.962445 S.D. dependent var 27.07472 Akaike info criterion 10995.60 Schwarz criterion -87.38754 F-statistic 0.704178 Prob(F-statistic)

表17 加入x4的回归结果

Dependent Variable: Y Method: Least Squares Date: 06/08/07 Time: 21:55 Sample: 1986 2004 Included observations: 19

Variable C X3 X7 X5

R-squared

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

Coefficient -2110.381 18.60156 0.012139 -3.964878

Std. Error 306.2690 2.617381 0.002285 2.163262

t-Statistic -6.890613 7.106937 5.311665 -1.832823

Prob. 0.0000 0.0000 0.0001 0.0868 345.5232 139.7117 9.443544 9.642373 185.5507 0.000000

0.973760 Mean dependent var 0.968512 S.D. dependent var 24.79152 Akaike info criterion 9219.289 Schwarz criterion -85.71367 F-statistic 0.733972 Prob(F-statistic)

Dependent Variable: Y Method: Least Squares Date: 06/08/07 Time: 21:55 Sample: 1986 2004 C X3 X7 X6

R-squared

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood -2418.859 20.99887 0.009920 5.359184

323.7240 3.397120 0.002495 2.571950

-7.471979 6.181374 3.976660 2.083705

0.0000 0.0000 0.0012 0.0547 345.5232 139.7117 9.391407 9.590236 195.7489 0.975093 Mean dependent var 0.970112 S.D. dependent var 24.15359 Akaike info criterion 8750.940 Schwarz criterion -85.21837 F-statistic Dependent Variable: Y Method: Least Squares Date: 06/08/07 Time: 21:56 Sample: 1986 2004 Included observations: 19

Variable

Coefficient

Std. Error

t-Statistic

Prob.

X3 X7 X8

R-squared

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

13.01578 0.011615 0.012375

2.032420 0.002558 0.013416

6.404078 4.540322 0.922401

0.0000 0.0004 0.3709 345.5232 139.7117 9.590455 9.789285 159.5158 0.000000

0.969608 Mean dependent var 0.963529 S.D. dependent var 26.68115 Akaike info criterion 10678.26 Schwarz criterion -87.10933 F-statistic 0.672264 Prob(F-statistic)

综合上述表16~20的回归结果所示，其中加入x6的回归结果最好，以x3 x6 x7为基础一次加入其他解释变量，作四元回归估计，估计结果如表21~24所示：

Dependent Variable: Y Method: Least Squares Date: 06/08/07 Time: 21:57 Sample: 1986 2004 Included observations: 19

Variable C X3 X6 X7 X2

R-squared

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Coefficient -2405.108 21.26850 5.310543 0.009689 1.302605

Std. Error 339.7396 3.699787 2.665569 0.002766 5.655390

t-Statistic -7.079269 5.748573 1.992273 3.503386 0.230330

Prob. 0.0000 0.0001 0.0662 0.0035 0.8212 345.5232 139.7117 9.492888 9.741424 137.5567 0.975187 Mean dependent var 0.968098 S.D. dependent var 24.95411 Akaike info criterion 8717.904 Schwarz criterion -85.18244 F-statistic Dependent Variable: Y Method: Least Squares Date: 06/08/07 Time: 21:57 Sample: 1986 2004 Variable C X3 X6

Coefficient -2401.402 22.10570 9.089033

Std. Error 316.2980 3.420783 3.781330

t-Statistic -7.592215 6.462174 2.403660

Prob. 0.0000 0.0000 0.0307

X4

R-squared

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

4.417678

3.348889

1.319147

0.2083 345.5232 139.7117 9.379513 9.628049 154.4909 0.000000

0.977847 Mean dependent var 0.971517 S.D. dependent var 23.57887 Akaike info criterion 7783.481 Schwarz criterion -84.10537 F-statistic 1.580301 Prob(F-statistic)

Dependent Variable: Y Method: Least Squares Date: 06/08/07 Time: 21:57 Sample: 1986 2004 Included observations: 19

C X3 X6 X7 X5

R-squared

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

-2375.188 20.83493 4.629196 0.010217 -0.693692

430.7065 3.657414 5.252860 0.003171 4.304485

-5.514631 5.696629 0.881272 3.221953 -0.161156

0.0001 0.0001 0.3930 0.0061 0.8743 345.5232 139.7117 9.494817 9.743353 137.2849 0.000000

0.975139 Mean dependent var 0.968036 S.D. dependent var 24.97818 Akaike info criterion 8734.736 Schwarz criterion -85.20076 F-statistic 1.023211 Prob(F-statistic)

Dependent Variable: Y Method: Least Squares Date: 06/08/07 Time: 21:57 Sample: 1986 2004 Variable C X3 X6 X7 X8

R-squared

Adjusted R-squared S.E. of regression

Coefficient -2212.242 22.06629 9.595653 0.006115 0.036923

Std. Error 259.5324 2.662231 2.380088 0.002260 0.011239

t-Statistic -8.523951 8.288647 4.031638 2.705978 3.285354

Prob. 0.0000 0.0000 0.0012 0.0171 0.0054 345.5232 139.7117 8.925144

0.985936 Mean dependent var 0.981918 S.D. dependent var 18.78702 Akaike info criterion

Log likelihood Durbin-Watson stat

-79.78887 F-statistic 2.186293 Prob(F-statistic)

245.3639 0.000000

综合表21~24所示的回归结果，其中加入x8的回归结果最好，以x3 x6 x7 x8为基础顺次加入其他的解释变量，其回归结果如表25~27所示：

Dependent Variable: Y Method: Least Squares Date: 06/08/07 Time: 23:38 Sample: 1986 2004 Included observations: 19

Variable C X3 X6 X7 X8 R-squared

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

Coefficient -2207.020 22.17495 9.566731 0.006028 0.036846 Std. Error 272.6061 2.903190 2.480057 0.002451 0.011674 t-Statistic -8.096005 7.638133 3.857464 2.458949 3.156195 Prob. 0.0000 0.0000 0.0020 0.0287 0.0076 345.5232 139.7117 9.029279 9.327523 182.4791 0.000000

0.985952 Mean dependent var 0.980549 S.D. dependent var 19.48522 Akaike info criterion 4935.759 Schwarz criterion -79.77815 F-statistic 2.180501 Prob(F-statistic)

Dependent Variable: Y Method: Least Squares Date: 06/08/07 Time: 23:39 Sample: 1986 2004 Included observations: 19

C X3 X6 X7 X8 X5

R-squared

Adjusted R-squared S.E. of regression

-1373.136 20.09330 0.480401 0.008497 0.060502 -11.23292

279.4825 1.928486 2.845972 0.001692 0.009873 2.844094

-4.913137 10.41921 0.168800 5.021410 6.128146 -3.949560

0.0003 0.0000 0.8686 0.0002 0.0000 0.0017 345.5232 139.7117 8.241984

0.993607 Mean dependent var 0.991148 S.D. dependent var 13.14457 Akaike info criterion

Log likelihood Durbin-Watson stat

-72.29885 F-statistic 1.704834 Prob(F-statistic)

404.1009 0.000000

Dependent Variable: Y Method: Least Squares Date: 06/08/07 Time: 23:38 Sample: 1986 2004 Included observations: 19

Variable C X3 X6 X7 X8 R-squared

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

Coefficient -2056.366 20.60220 5.264834 0.008853 0.071742 Std. Error 236.8112 2.413096 2.804292 0.002306 0.018026 t-Statistic -8.683569 8.537661 1.877420 3.839446 3.980036 Prob. 0.0000 0.0000 0.0831 0.0020 0.0016 345.5232 139.7117 8.687938 8.986182 257.7752 0.000000

0.990014 Mean dependent var 0.986174 S.D. dependent var 16.42798 Akaike info criterion 3508.420 Schwarz criterion -76.53541 F-statistic 1.965748 Prob(F-statistic)

据表25~27所示，分别加入x2 x4 x5后R均有所增加，但是参数的T检验均不显著，所以最终的计量模型如下表所示：

Dependent Variable: Y Method: Least Squares Date: 06/08/07 Time: 23:43 Sample: 1986 2004 Included observations: 19

C X3 X6 X7 X8

R-squared

Adjusted R-squared S.E. of regression Sum squared resid

-2212.242 22.06629 9.595653 0.006115 0.036923

259.5324 2.662231 2.380088 0.002260 0.011239

-8.523951 8.288647 4.031638 2.705978 3.285354

0.0000 0.0000 0.0012 0.0171 0.0054 345.5232 139.7117 8.925144 9.173681

0.985936 Mean dependent var 0.981918 S.D. dependent var 18.78702 Akaike info criterion 4941.332 Schwarz criterion

Log likelihood Durbin-Watson stat

-79.78887 F-statistic 2.186293 Prob(F-statistic)

245.3639 0.000000

回归分析报告为：

-2212.242+22.0663X+9.5956X+0.00612X+0.03692XYi3678SE 259.5324 t 8.523951 R 0.985936

2

2.6622 2.380 0.00226 0.011239 8.28865 4.032 2.70598 3.285354

R 0.981918

2

Df 19DW 2.186293F 245.3639

(二)、异方差的检验 A、相关图形分析

图1

图

2

图3

图4

从图1~4可以看出y 并不随着x的增大而变得更离散，表明模型可能不存在异方差。

B、残差分析图

图

5

图6

图

7

图 8

从图5~8看出，e2并不随x的增大而变化，表明模型可能不存在异方差。 C、ARCH检验

ARCH Test: F-statistic

Test Equation:

Dependent Variable: RESID^2 Method: Least Squares Date: 06/09/07 Time: 00:04 Sample(adjusted): 1989 2004

Included observations: 16 after adjusting endpoints

C RESID^2(-1) RESID^2(-2) RESID^2(-3)

R-squared

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

279.7407 0.051971 -0.223409 -0.157992

120.1889 0.251414 0.241815 0.249154

2.327509 0.206717 -0.923887 -0.634115

0.0382 0.8397 0.3737 0.5379 204.2351 286.6884 14.45940 14.65255 0.558635 0.652331

0.558635 Probability

0.652331

0.122544 Mean dependent var -0.096820 S.D. dependent var 300.2464 Akaike info criterion 1081774. Schwarz criterion -111.6752 F-statistic 1.767931 Prob(F-statistic)

在显著性水平 0.05的情况下，

2

3 7.81473, n p R2

1.960709,则有

n p R

2

1.960709

2

3 7.81473,所以接受源假设，表明模型中不存在异方差。

D、White检验

F-statistic

Test Equation:

Dependent Variable: RESID^2 Method: Least Squares Date: 06/09/07 Time: 00:05 Sample: 1986 2004 C

83312.19

792151.1

0.105172

0.9213

5.378778 Probability

0.058152

X3 X3^2 X3*X6 X3*X7 X3*X8 X6 X6^2 X6*X7 X6*X8 X7 X7^2 X7*X8 X8 R-squared

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

8939.976 92.15690 -23.05086 -0.094926 -0.965260 14984.21 -53.86422 -0.045905 -0.395631 -10.35154 5.76E-05 -7.38E-06 62.90965 3785.514 56.34778 26.32794 0.045467 0.775504 4130.063 41.43287 0.033365 0.371854 12.19311 4.21E-05 0.000266 32.25761 2.361628 1.635502 -0.875529 -2.087801 -1.244688 3.628083 -1.300036 -1.375837 -1.063942 -0.848966 1.369855 -0.027789 1.950226 0.0775 0.1773 0.4307 0.1051 0.2812 0.0222 0.2634 0.2409 0.3473 0.4437 0.2426 0.9792 0.1229 260.0701 337.4753 13.01876 13.76437 5.378778 0.058152

0.949560 Mean dependent var 0.773022 S.D. dependent var 160.7806 Akaike info criterion 103401.7 Schwarz criterion -108.6782 F-statistic 3.254288 Prob(F-statistic)

在显著性水平 0.05的情况下，

2

14 23.6848, n p R2

18.04165,则有

n p R2

18.04165

2

3 23.6848,所以接受源假设，表明模型中不存在异方差。

综合上述4种方法得出的结论，说明模型中不存在异方差。

(三)、自相关检验及修正 ①自相关的检验 A、DW检验

已知DW= 2.18535949259，查表得DL=0.859 ，DU=1.848，所以4-DU=2.152 <DW<4-DL=3.141，因此不能确定是否存在自相关性

B、图示法：

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