计量经济学第三版课后习题答案

第二章 简单线性回归模型 2.1 （1） ①首先分析人均寿命与人均GDP的数量关系，用Eviews分析： Dependent Variable: Y Method: Least Squares Date: 12/23/15 Time: 14:37 Sample: 1 22 Included observations: 22 Variable Coefficient Std. Error t-Statistic Prob.   C 56.64794 1.960820 28.88992 0.0000 X1 0.128360 0.027242 4.711834 0.0001 R-squared 0.526082     Mean dependent var 62.50000 Adjusted R-squared 0.502386     S.D. dependent var 10.08889 S.E. of regression 7.116881     Akaike info criterion 6.849324 Sum squared resid 1013.000     Schwarz criterion 6.948510 Log likelihood -73.34257     Hannan-Quinn criter. 6.872689 F-statistic 22.20138     Durbin-Watson stat 0.629074 Prob(F-statistic) 0.000134 有上可知，关系式为y=56.64794+0.128360x1 ②关于人均寿命与成人识字率的关系，用Eviews分析如下： Dependent Variable: Y Method: Least Squares Date: 12/23/15 Time: 15:01 Sample: 1 22 Included observations: 22 Variable Coefficient Std. Error t-Statistic Prob.   C 38.79424 3.532079 10.98340 0.0000 X2 0.331971 0.046656 7.115308 0.0000 R-squared 0.716825     Mean dependent var 62.50000 Adjusted R-squared 0.702666     S.D. dependent var 10.08889 S.E. of regression 5.501306     Akaike info criterion 6.334356 Sum squared resid 605.2873     Schwarz criterion 6.433542 Log likelihood -67.67792     Hannan-Quinn criter. 6.357721 F-statistic 50.62761     Durbin-Watson stat 1.846406 Prob(F-statistic) 0.000001 由上可知，关系式为y=38.79424+0.331971x2 ③关于人均寿命与一岁儿童疫苗接种率的关系，用Eviews分析如下： Dependent Variable: Y Method: Least Squares Date: 12/23/14 Time: 15:20 Sample: 1 22 Included observations: 22 Variable Coefficient Std. Error t-Statistic Prob.   C 31.79956 6.536434 4.864971 0.0001 X3 0.387276 0.080260 4.825285 0.0001 R-squared 0.537929     Mean dependent var 62.50000 Adjusted R-squared 0.514825     S.D. dependent var 10.08889 S.E. of regression 7.027364     Akaike info criterion 6.824009 Sum squared resid 987.6770     Schwarz criterion 6.923194 Log likelihood -73.06409     Hannan-Quinn criter. 6.847374 F-statistic 23.28338     Durbin-Watson stat 0.952555 Prob(F-statistic) 0.000103 由上可知，关系式为y=31.79956+0.387276x3 （2）①关于人均寿命与人均GDP模型，由上可知，可决系数为0.526082，说明所建模型整体上对样本数据拟合较好。 对于回归系数的t检验：t（β1）=4.711834>t0.025(20)=2.086，对斜率系数的显著性检验 表 关于同志近三年现实表现材料材料类招标技术评分表图表与交易pdf视力表打印pdf用图表说话 pdf 明，人均GDP对人均寿命有显著影响。 ②关于人均寿命与成人识字率模型，由上可知，可决系数为0.716825，说明所建模型整体上对样本数据拟合较好。 对于回归系数的t检验：t（β2）=7.115308>t0.025(20)=2.086，对斜率系数的显著性检验表明，成人识字率对人均寿命有显著影响。 ③关于人均寿命与一岁儿童疫苗的模型，由上可知，可决系数为0.537929，说明所建模型整体上对样本数据拟合较好。 对于回归系数的t检验：t（β3）=4.825285>t0.025(20)=2.086，对斜率系数的显著性检验表明，一岁儿童疫苗接种率对人均寿命有显著影响。 2.2 （1） ①对于浙江省预算收入与全省生产总值的模型，用Eviews分析结果如下： Dependent Variable: Y Method: Least Squares Date: 12/23/15 Time: 17:46 Sample (adjusted): 1 33 Included observations: 33 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   X 0.176124 0.004072 43.25639 0.0000 C -154.3063 39.08196 -3.948274 0.0004 R-squared 0.983702     Mean dependent var 902.5148 Adjusted R-squared 0.983177     S.D. dependent var 1351.009 S.E. of regression 175.2325     Akaike info criterion 13.22880 Sum squared resid 951899.7     Schwarz criterion 13.31949 Log likelihood -216.2751     Hannan-Quinn criter. 13.25931 F-statistic 1871.115     Durbin-Watson stat 0.100021 Prob(F-statistic) 0.000000 ②由上可知，模型的参数：斜率系数0.176124，截距为—154.3063 ③关于浙江省财政预算收入与全省生产总值的模型，检验模型的显著性： 1）可决系数为0.983702，说明所建模型整体上对样本数据拟合较好。 2）对于回归系数的t检验：t（β2）=43.25639>t0.025(31)=2.0395，对斜率系数的显著性检验表明，全省生产总值对财政预算总收入有显著影响。 ④用规范形式写出检验结果如下： Y=0.176124X—154.3063 (0.004072) (39.08196) t= (43.25639) （-3.948274） R2=0.983702 F=1871.115 n=33 ⑤经济意义是：全省生产总值每增加1亿元，财政预算总收入增加0.176124亿元。 （2）当x=32000时， ①进行点预测，由上可知Y=0.176124X—154.3063，代入可得： Y= Y=0.176124*32000—154.3063=5481.6617 ②进行区间预测： 先由Eviews分析： X Y  Mean  6000.441  902.5148  Median  2689.280  209.3900  Maximum  27722.31  4895.410  Minimum  123.7200  25.87000  Std. Dev.  7608.021  1351.009  Skewness  1.432519  1.663108  Kurtosis  4.010515  4.590432  Jarque-Bera  12.69068  18.69063  Probability  0.001755  0.000087  Sum  198014.5  29782.99  Sum Sq. Dev.  1.85E+09  58407195  Observations  33  33 由上表可知， ∑x2=∑（Xi—X）2=δ2x(n—1)=  7608.0212 x (33—1)=1852223.473 (Xf—X)2=(32000— 6000.441)2=675977068.2 当Xf=32000时，将相关数据代入计算得到： 5481.6617—2.0395x175.2325x√1/33+1852223.473/675977068.2≤ Yf≤5481.6617+2.0395x175.2325x√1/33+1852223.473/675977068.2 即Yf的置信区间为（5481.6617—64.9649, 5481.6617+64.9649） (3) 对于浙江省预算收入对数与全省生产总值对数的模型，由Eviews分析结果如下： Dependent Variable: LNY Method: Least Squares Date: 12/23/15 Time: 18:04 Sample (adjusted): 1 33 Included observations: 33 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   LNX 0.980275 0.034296 28.58268 0.0000 C -1.918289 0.268213 -7.152121 0.0000 R-squared 0.963442     Mean dependent var 5.573120 Adjusted R-squared 0.962263     S.D. dependent var 1.684189 S.E. of regression 0.327172     Akaike info criterion 0.662028 Sum squared resid 3.318281     Schwarz criterion 0.752726 Log likelihood -8.923468     Hannan-Quinn criter. 0.692545 F-statistic 816.9699     Durbin-Watson stat 0.096208 Prob(F-statistic) 0.000000 ①模型方程为：lnY=0.980275lnX-1.918289 ②由上可知，模型的参数：斜率系数为0.980275，截距为-1.918289 ③关于浙江省财政预算收入与全省生产总值的模型，检验其显著性： 1）可决系数为0.963442，说明所建模型整体上对样本数据拟合较好。 2）对于回归系数的t检验：t（β2）=28.58268>t0.025(31)=2.0395，对斜率系数的显著性检验表明，全省生产总值对财政预算总收入有显著影响。 ④经济意义：全省生产总值每增长1%，财政预算总收入增长0.980275% 2.4 （1）对建筑面积与建造单位成本模型，用Eviews分析结果如下： Dependent Variable: Y Method: Least Squares Date: 12/23/15 Time: 20:11 Sample: 1 12 Included observations: 12 Variable Coefficient Std. Error t-Statistic Prob.   X -64.18400 4.809828 -13.34434 0.0000 C 1845.475 19.26446 95.79688 0.0000 R-squared 0.946829     Mean dependent var 1619.333 Adjusted R-squared 0.941512     S.D. dependent var 131.2252 S.E. of regression 31.73600     Akaike info criterion 9.903792 Sum squared resid 10071.74     Schwarz criterion 9.984610 Log likelihood -57.42275     Hannan-Quinn criter. 9.873871 F-statistic 178.0715     Durbin-Watson stat 1.172407 Prob(F-statistic) 0.000000 由上可得：建筑面积与建造成本的回归方程为： Y=1845.475--64.18400X （2）经济意义：建筑面积每增加1万平方米，建筑单位成本每平方米减少64.18400元。 （3） ①首先进行点预测，由Y=1845.475--64.18400X得，当x=4.5，y=1556.647 ②再进行区间估计： 用Eviews分析： Y X  Mean  1619.333  3.523333  Median  1630.000  3.715000  Maximum  1860.000  6.230000  Minimum  1419.000  0.600000  Std. Dev.  131.2252  1.989419  Skewness  0.003403 -0.060130  Kurtosis  2.346511  1.664917  Jarque-Bera  0.213547  0.898454  Probability  0.898729  0.638121  Sum  19432.00  42.28000  Sum Sq. Dev.  189420.7  43.53567  Observations  12  12 由上表可知， ∑x2=∑（Xi—X）2=δ2x(n—1)=  1.9894192 x (12—1)=43.5357 (Xf—X)2=(4.5— 3.523333)2=0.95387843 当Xf=4.5时，将相关数据代入计算得到： 1556.647—2.228x31.73600x√1/12+43.5357/0.95387843≤ Yf≤1556.647+2.228x31.73600x√1/12+43.5357/0.95387843 即Yf的置信区间为（1556.647—478.1231, 1556.647+478.1231） 3.1 （1） ①对百户拥有家用汽车量计量经济模型，用Eviews分析结果如下： Dependent Variable: Y Method: Least Squares Date: 12/23/15 Time: 20:59 Sample: 1 31 Included observations: 31 Variable Coefficient Std. Error t-Statistic Prob.   X2 5.996865 1.406058 4.265020 0.0002 X3 -0.524027 0.179280 -2.922950 0.0069 X4 -2.265680 0.518837 -4.366842 0.0002 C 246.8540 51.97500 4.749476 0.0001 R-squared 0.666062     Mean dependent var 16.77355 Adjusted R-squared 0.628957     S.D. dependent var 8.252535 S.E. of regression 5.026889     Akaike info criterion 6.187394 Sum squared resid 682.2795     Schwarz criterion 6.372424 Log likelihood -91.90460     Hannan-Quinn criter. 6.247709 F-statistic 17.95108     Durbin-Watson stat 1.147253 Prob(F-statistic) 0.000001 ②得到模型得： Y=246.8540+5.996865X2-　0.524027 X3-2.265680 X4 ③对模型进行检验： 1） 可决系数是0.666062，修正的可决系数为0.628957，说明模型对样本拟合较好 2） F检验，F=17.95108>F（3,27）=3.65，回归方程显著。 3）t检验，t统计量分别为4.749476，4.265020，-2.922950，-4.366842，均大于 t（27）=2.0518，所以这些系数都是显著的。 ④依据： 1） 可决系数越大，说明拟合程度越好 2） F的值与临界值比较，若大于临界值，则否定原假设，回归方程是显著的；若小于临界值，则接受原假设，回归方程不显著。 3） t的值与临界值比较，若大于临界值，则否定原假设，系数都是显著的；若小于临界值，则接受原假设，系数不显著。 （2）经济意义：人均ＧＤＰ增加１万元，百户拥有家用汽车增加5.996865辆，城镇人口比重增加１个百分点，百户拥有家用汽车减少0.524027辆，交通工具消费价格指数每上升１，百户拥有家用汽车减少2.265680辆。 （3）用EViews分析得： Dependent Variable: Y Method: Least Squares Date: 12/23/15 Time: 21:09 Sample: 1 31 Included observations: 31 Variable Coefficient Std. Error t-Statistic Prob.   X2 5.135670 1.010270 5.083465 0.0000 LNX3 -22.81005 6.771820 -3.368378 0.0023 LNX4 -230.8481 49.46791 -4.666624 0.0001 C 1148.758 228.2917 5.031974 0.0000 R-squared 0.691952     Mean dependent var 16.77355 Adjusted R-squared 0.657725     S.D. dependent var 8.252535 S.E. of regression 4.828088     Akaike info criterion 6.106692 Sum squared resid 629.3818     Schwarz criterion 6.291723 Log likelihood -90.65373     Hannan-Quinn criter. 6.167008 F-statistic 20.21624     Durbin-Watson stat 1.150090 Prob(F-statistic) 0.000000 模型方程为： Y=5.135670 X2-22.81005 LNX3-230.8481 LNX4+1148.758 此分析得出的可决系数为0.691952>0.666062，拟合程度得到了提高，可这样改进。 3.2 （１）对出口货物总额计量经济模型，用Eviews分析结果如下：： Dependent Variable: Y Method: Least Squares Date: 12/24/15 Time: 08:23 Sample: 1994 2011 Included observations: 18 Variable Coefficient Std. Error t-Statistic Prob.   X2 0.135474 0.012799 10.58454 0.0000 X3 18.85348 9.776181 1.928512 0.0729 C -18231.58 8638.216 -2.110573 0.0520 R-squared 0.985838     Mean dependent var 6619.191 Adjusted R-squared 0.983950     S.D. dependent var 5767.152 S.E. of regression 730.6306     Akaike info criterion 16.17670 Sum squared resid 8007316.     Schwarz criterion 16.32510 Log likelihood -142.5903     Hannan-Quinn criter. 16.19717 F-statistic 522.0976     Durbin-Watson stat 1.173432 Prob(F-statistic) 0.000000 ①由上可知，模型为： Y = 0.135474X2 + 18.85348X3 - 18231.58 ②对模型进行检验： 1）可决系数是0.985838，修正的可决系数为0.983950，说明模型对样本拟合较好 2）F检验，F=522.0976>F（2,15）=4.77，回归方程显著 3）t检验，t统计量分别为X2的系数对应t值为10.58454，大于t（15）=2.131，系数是显著的，X3的系数对应t值为1.928512，小于t（15）=2.131，说明此系数是不显著的。 （2）对于对数模型，用Eviews分析结果如下： Dependent Variable: LNY Method: Least Squares Date: 12/24/15 Time: 08:47 Sample: 1994 2011 Included observations: 18 Variable Coefficient Std. Error t-Statistic Prob.   LNX2 1.564221 0.088988 17.57789 0.0000 LNX3 1.760695 0.682115 2.581229 0.0209 C -20.52048 5.432487 -3.777363 0.0018 R-squared 0.986295     Mean dependent var 8.400112 Adjusted R-squared 0.984467     S.D. dependent var 0.941530 S.E. of regression 0.117343     Akaike info criterion -1.296424 Sum squared resid 0.206540     Schwarz criterion -1.148029 Log likelihood 14.66782     Hannan-Quinn criter. -1.275962 F-statistic 539.7364     Durbin-Watson stat 0.686656 Prob(F-statistic) 0.000000 ①由上可知，模型为： LNY=-20.52048+1.564221 LNX2+1.760695 LNX3 ②对模型进行检验： 1）可决系数是0.986295，修正的可决系数为0.984467，说明模型对样本拟合较好。 2）F检验，F=539.7364> F（2,15）=4.77，回归方程显著。 3）t检验，t统计量分别为-3.777363，17.57789，2.581229，均大于t（15）=2.131，所以这些系数都是显著的。 （3） ①（1）式中的经济意义：工业增加1亿元，出口货物总额增加0.135474亿元，人民币汇率增加1，出口货物总额增加18.85348亿元。 ②（2）式中的经济意义：工业增加额每增加1%，出口货物总额增加1.564221%，人民币汇率每增加1%，出口货物总额增加1.760695% 3.3 （1）对家庭书刊消费对家庭月平均收入和户主受教育年数计量模型，由Eviews分析结果如下： Dependent Variable: Y Method: Least Squares Date: 12/24/15 Time: 09:03 Sample: 1 18 Included observations: 18 Variable Coefficient Std. Error t-Statistic Prob.   X 0.086450 0.029363 2.944186 0.0101 T 52.37031 5.202167 10.06702 0.0000 C -50.01638 49.46026 -1.011244 0.3279 R-squared 0.951235     Mean dependent var 755.1222 Adjusted R-squared 0.944732     S.D. dependent var 258.7206 S.E. of regression 60.82273     Akaike info criterion 11.20482 Sum squared resid 55491.07     Schwarz criterion 11.35321 Log likelihood -97.84334     Hannan-Quinn criter. 11.22528 F-statistic 146.2974     Durbin-Watson stat 2.605783 Prob(F-statistic) 0.000000 ①模型为：Y = 0.086450X + 52.37031T-50.01638 ②对模型进行检验： 1）可决系数是0.951235，修正的可决系数为0.944732，说明模型对样本拟合较好。 2）F检验，F=539.7364> F（2,15）=4.77，回归方程显著。 3）t检验，t统计量分别为2.944186，10.06702，均大于t（15）=2.131，所以这些系数都是显著的。 ③经济意义：家庭月平均收入增加1元，家庭书刊年消费支出增加0.086450元，户主受教育年数增加1年，家庭书刊年消费支出增加52.37031元。 （2）用Eviews分析： ① Dependent Variable: Y Method: Least Squares Date: 12/24/15 Time: 09:18 Sample: 1 18 Included observations: 18 Variable Coefficient Std. Error t-Statistic Prob.   T 63.01676 4.548581 13.85416 0.0000 C -11.58171 58.02290 -0.199606 0.8443 R-squared 0.923054     Mean dependent var 755.1222 Adjusted R-squared 0.918245     S.D. dependent var 258.7206 S.E. of regression 73.97565     Akaike info criterion 11.54979 Sum squared resid 87558.36     Schwarz criterion 11.64872 Log likelihood -101.9481     Hannan-Quinn criter. 11.56343 F-statistic 191.9377     Durbin-Watson stat 2.134043 Prob(F-statistic) 0.000000 ② Dependent Variable: X Method: Least Squares Date: 12/24/15 Time: 09:34 Sample: 1 18 Included observations: 18 Variable Coefficient Std. Error t-Statistic Prob.   T 123.1516 31.84150 3.867644 0.0014 C 444.5888 406.1786 1.094565 0.2899 R-squared 0.483182     Mean dependent var 1942.933 Adjusted R-squared 0.450881     S.D. dependent var 698.8325 S.E. of regression 517.8529     Akaike info criterion 15.44170 Sum squared resid 4290746.     Schwarz criterion 15.54063 Log likelihood -136.9753     Hannan-Quinn criter. 15.45534 F-statistic 14.95867     Durbin-Watson stat 1.052251 Prob(F-statistic) 0.001364 以上分别是y与T，X与T的一元回归 模型分别是： Y = 63.01676T - 11.58171 X = 123.1516T + 444.5888 （3）对残差进行模型分析，用Eviews分析结果如下： Dependent Variable: E1 Method: Least Squares Date: 12/24/15 Time: 09:39 Sample: 1 18 Included observations: 18 Variable Coefficient Std. Error t-Statistic Prob.   E2 0.086450 0.028431 3.040742 0.0078 C 3.96E-14 13.88083 2.85E-15 1.0000 R-squared 0.366239     Mean dependent var 2.30E-14 Adjusted R-squared 0.326629     S.D. dependent var 71.76693 S.E. of regression 58.89136     Akaike info criterion 11.09370 Sum squared resid 55491.07     Schwarz criterion 11.19264 Log likelihood -97.84334     Hannan-Quinn criter. 11.10735 F-statistic 9.246111     Durbin-Watson stat 2.605783 Prob(F-statistic) 0.007788 模型为： E1 = 0.086450E2 + 3.96e-14 参数：斜率系数α为0.086450，截距为3.96e-14 （3）由上可知，β2与α2的系数是一样的。回归系数与被解释变量的残差系数是一样的，它们的变化规律是一致的。 3.6 （1）预期的符号是X1，X2,X3,X4,X5的符号为正，X6的符号为负 （2）根据Eviews分析得到数据如下： Dependent Variable: Y Method: Least Squares Date: 12/24/15 Time: 10:13 Sample: 1994 2011 Included observations: 18 Variable Coefficient Std. Error t-Statistic Prob.   X2 0.001382 0.001102 1.254330 0.2336 X3 0.001942 0.003960 0.490501 0.6326 X4 -3.579090 3.559949 -1.005377 0.3346 X5 0.004791 0.005034 0.951671 0.3600 X6 0.045542 0.095552 0.476621 0.6422 C -13.77732 15.73366 -0.875659 0.3984 R-squared 0.994869     Mean dependent var 12.76667 Adjusted R-squared 0.992731     S.D. dependent var 9.746631 S.E. of regression 0.830963     Akaike info criterion 2.728738 Sum squared resid 8.285993     Schwarz criterion 3.025529 Log likelihood -18.55865     Hannan-Quinn criter. 2.769662 F-statistic 465.3617     Durbin-Watson stat 1.553294 Prob(F-statistic) 0.000000 ①与预期不相符。 ②评价： 1） 可决系数为0.994869，数据相当大，可以认为拟合程度很好。 2） F检验，F=465.3617>F（5.12）=3,89，回归方程显著 3） T检验，X1，X2,X3,X4,X5，X6 系数对应的t值分别为：1.254330，0.490501，-1.005377，0.951671，0.476621，均小于t（12）=2.179，所以所得系数都是不显著的。 （3）根据Eviews分析得到数据如下： Dependent Variable: Y Method: Least Squares Date: 12/24/15 Time: 10:20 Sample: 1994 2011 Included observations: 18 Variable Coefficient Std. Error t-Statistic Prob.   X5 0.001032 2.20E-05 46.79946 0.0000 X6 -0.054965 0.031184 -1.762581 0.0983 C 4.205481 3.335602 1.260786 0.2266 R-squared 0.993601     Mean dependent var 12.76667 Adjusted R-squared 0.992748     S.D. dependent var 9.746631 S.E. of regression 0.830018     Akaike info criterion 2.616274 Sum squared resid 10.33396     Schwarz criterion 2.764669 Log likelihood -20.54646     Hannan-Quinn criter. 2.636736 F-statistic 1164.567     Durbin-Watson stat 1.341880 Prob(F-statistic) 0.000000 ①得到模型的方程为： Y=0.001032 X5-0.054965 X6+4.205481 ②评价： 1） 可决系数为0.993601，数据相当大，可以认为拟合程度很好。 2） F检验，F=1164.567>F（5.12）=3,89，回归方程显著 3） T检验，X5 系数对应的t值为46.79946，大于t（12）=2.179，所以系数是显著的，即人均GDP对年底存款余额有显著影响。 X6 系数对应的t值为-1.762581，小于t（12）=2.179，所以系数是不显著的。 4.3 （1）根据Eviews分析得到数据如下： Dependent Variable: LNY Method: Least Squares Date: 12/24/15 Time: 10:39 Sample: 1985 2011 Included observations: 27 Variable Coefficient Std. Error t-Statistic Prob.   LNGDP 1.338533 0.088610 15.10582 0.0000 LNCPI -0.421791 0.233295 -1.807975 0.0832 C -3.111486 0.463010 -6.720126 0.0000 R-squared 0.988051     Mean dependent var 9.484710 Adjusted R-squared 0.987055     S.D. dependent var 1.425517 S.E. of regression 0.162189     Akaike info criterion -0.695670 Sum squared resid 0.631326     Schwarz criterion -0.551689 Log likelihood 12.39155     Hannan-Quinn criter. -0.652857 F-statistic 992.2582     Durbin-Watson stat 0.522613 Prob(F-statistic) 0.000000 得到的模型方程为： LNY=1.338533 LNGDPt-0.421791 LNCPIt-3.111486 （2） 1 该模型的可决系数为0.988051，可决系数很高，F检验值为992.2582， 明显显著。但当α=0.05时，t（24）=2.064，LNCPI的系数不显著，可能存在多重共线性。 ②得到相关系数矩阵如下： LNY LNGDP LNCPI LNY  1.000000  0.993189  0.935116 LNGDP  0.993189  1.000000  0.953740 LNCPI  0.935116  0.953740  1.000000 LNGDP， LNCPI之间的相关系数很高，证实确实存在多重共线性。 （3）由Eviews得： a） Dependent Variable: LNY Method: Least Squares Date: 12/24/15 Time: 10:41 Sample: 1985 2011 Included observations: 27 Variable Coefficient Std. Error t-Statistic Prob.   LNGDP 1.185739 0.027822 42.61933 C -3.750670 0.312255 -12.01156 0.0000 R-squared 0.986423     Mean dependent var 9.484710 Adjusted R-squared 0.985880     S.D. dependent var 1.425517 S.E. of regression 0.169389     Akaike info criterion -0.642056 Sum squared resid 0.717312     Schwarz criterion -0.546068 Log likelihood 10.66776     Hannan-Quinn criter. -0.613514 F-statistic 1816.407     Durbin-Watson stat 0.471111 Prob(F-statistic) 0.000000 b) Dependent Variable: LNY Method: Least Squares Date: 12/24/15 Time: 10:55 Sample: 1985 2011 Included observations: 27 Variable Coefficient Std. Error t-Statistic Prob.   LNCPI 2.939295 0.222756 13.19511 0.0000 C -6.854535 1.242243 -5.517871 0.0000 R-squared 0.874442     Mean dependent var 9.484710 Adjusted R-squared 0.869419     S.D. dependent var 1.425517 S.E. of regression 0.515124     Akaike info criterion 1.582368 Sum squared resid 6.633810     Schwarz criterion 1.678356 Log likelihood -19.36196     Hannan-Quinn criter. 1.610910 F-statistic 174.1108     Durbin-Watson stat 0.137042 Prob(F-statistic) 0.000000 c) Dependent Variable: LNGDP Method: Least Squares Date: 12/24/15 Time: 11:07 Sample: 1985 2011 Included observations: 27 Variable Coefficient Std. Error t-Statistic Prob.   LNCPI 2.511022 0.158302 15.86227 0.0000 C -2.796381 0.882798 -3.167634 0.0040 R-squared 0.909621     Mean dependent var 11.16214 Adjusted R-squared 0.906005     S.D. dependent var 1.194029 S.E. of regression 0.366072     Akaike info criterion 0.899213 Sum squared resid 3.350216     Schwarz criterion 0.995201 Log likelihood -10.13938     Hannan-Quinn criter. 0.927755 F-statistic 251.6117     Durbin-Watson stat 0.099623 Prob(F-statistic) 0.000000 ①得到的回归方程分别为 1）LNY=1.185739 LNGDPt-3.750670 2）LNY=2.939295 LNCPIt-6.854535 3）LNGDPt=2.511022 LNCPIt-2.796381 ②对多重共线性的认识： 单方程拟合效果都很好，回归系数显著，判定系数较高，GDP和CPI对进口的显著的单一影响，在这两个变量同时引入模型时影响方向发生了改变，这只有通过相关系数的分析才能发现。 （4）建议：如果仅仅是作预测，可以不在意这种多重共线性，但如果是进行结构分析，还是应该引起注意的。 4.4 （1）按照设计的理论模型，由Eviews分析得： Dependent Variable: CZSR Method: Least Squares Date: 12/24/15 Time: 11:23 Sample: 1985 2011 Included observations: 27 Variable Coefficient Std. Error t-Statistic Prob.   CZZC 0.090114 0.044367 2.031129 0.0540 GDP -0.025334 0.005069 -4.998036 0.0000 SSZE 1.176894 0.062162 18.93271 0.0000 C -221.8540 130.6532 -1.698038 0.1030 R-squared 0.999857     Mean dependent var 22572.56 Adjusted R-squared 0.999838     S.D. dependent var 27739.49 S.E. of regression 353.0540     Akaike info criterion 14.70707 Sum squared resid 2866884.     Schwarz criterion 14.89905 Log likelihood -194.5455     Hannan-Quinn criter. 14.76416 F-statistic 53493.93     Durbin-Watson stat 1.458128 Prob(F-statistic) 0.000000 从回归结果可见，可决系数为0.999857，校正的可决系数为0.999838，模型拟合的很好。F的统计量为53493.93，说明在α=0.05,水平下，回归方程回归方程整体上是显著的。但是t检验结果表明，国内生产总值对财政收入的影响显著，但回归系数的符号为负，与实际不符合。由此可得知，该方程可能存在多重共线性。 （2）得到相关系数矩阵如下： CZSR CZZC GDP SSZE CZSR  1.000000  0.998729  0.992838  0.999832 CZZC  0.998729  1.000000  0.992536  0.998575 GDP  0.992838  0.992536  1.000000  0.994370 SSZE  0.999832  0.998575  0.994370  1.000000 由上表可知，CZZC与GDP，CZZC与SSZE，GDP与SSZE之间的相关系数都非常高，说明确实存在多重共线性。 （3）做辅助回归 被解释变量 可决系数 方差扩大因子 CZZC 0.997168 353 GDP 0.988833 90 SSZE 0.997862 468 方差扩大因子均大于10，存在严重多重共线性。并且通过以上分析，两两被解释变量之间相关性都很高。 （4）解决方式：分别作出财政收入与财政支出、国内生产总值、税收总额之间的一元回归。 5.2 （1） ①用图形法检验 绘制e2的散点图，用Eviews分析如下： 由上图可知，模型可能存在异方差， 2 Goldfeld-Quanadt检验 1）定义区间为1-7时，由软件分析得： Dependent Variable: Y Method: Least Squares Date: 12/24/15 Time: 14:52 Sample: 1 7 Included observations: 7 Variable Coefficient Std. Error t-Statistic Prob.   T 35.20664 4.901492 7.182843 0.0020 X 0.109949 0.061965 1.774380 0.1507 C 77.12588 82.32844 0.936807 0.4019 R-squared 0.943099     Mean dependent var 565.6857 Adjusted R-squared 0.914649     S.D. dependent var 108.2755 S.E. of regression 31.63265     Akaike info criterion 10.04378 Sum squared resid 4002.499     Schwarz criterion 10.02060 Log likelihood -32.15324     Hannan-Quinn criter. 9.757267 F-statistic 33.14880     Durbin-Watson stat 1.426262 Prob(F-statistic) 0.003238 得∑e1i2=4002.499 2）定义区间为12-18时，由软件分析得： Dependent Variable: Y Method: Least Squares Date: 12/24/15 Time: 14:55 Sample: 12 18 Included observations: 7 Variable Coefficient Std. Error t-Statistic Prob.   T 52.40588 6.923378 7.569409 0.0016 X 0.068689 0.053763 1.277635 0.2705 C -8.789265 79.92542 -0.109968 0.9177 R-squared 0.984688     Mean dependent var 887.6143 Adjusted R-squared 0.977032     S.D. dependent var 274.4148 S.E. of regression 41.58810     Akaike info criterion 10.59103 Sum squared resid 6918.280     Schwarz criterion 10.56785 Log likelihood -34.06861     Hannan-Quinn criter. 10.30451 F-statistic 128.6166     Durbin-Watson stat 2.390329 Prob(F-statistic) 0.000234 得∑e2i2=6918.280 3）根据Goldfeld-Quanadt检验，F统计量为： F=∑e2i2 /∑e1i2 =6918.280/4002.499=1.7285 在α=0.05水平下，分子分母的自由度均为4，查分布表得临界值F0.05（4,4）=6.39，因为F=1.7285< F0.05（4,4）=6.39，所以接受原假设，此检验表明模型不存在异方差。 （2）存在异方差，估计参数的方法： ①可以对模型进行变换 ②使用加权最小二乘法进行计算，得出模型方程，并对其进行相关检验 ③对模型进行对数变换，进行分析 （3）评价： 3.3所得结论是可以相信的，随机扰动项之间不存在异方差。回归方程是显著的。 5.3 (1)由Eviews软件分析得： Dependent Variable: Y Method: Least Squares Date: 12/24/15 Time: 16:00 Sample: 1 31 Included observations: 31 Variable Coefficient Std. Error t-Statistic Prob.   X 1.244281 0.079032 15.74411 0.0000 C 242.4488 291.1940 0.832602 0.4119 R-squared 0.895260     Mean dependent var 4443.526 Adjusted R-squared 0.891649     S.D. dependent var 1972.072 S.E. of regression 649.1426     Akaike info criterion 15.85152 Sum squared resid 12220196     Schwarz criterion 15.94404 Log likelihood -243.6986     Hannan-Quinn criter. 15.88168 F-statistic 247.8769     Durbin-Watson stat 1.078581 Prob(F-statistic) 0.000000 由上表可知，2007年我国农村居民家庭人均消费支出（x）对人均纯收入（y）的模型为： Y=1.244281X+242.4488 （2） ①由图形法检验 由上图可知，模型可能存在异方差。 ②Goldfeld-Quanadt检验 1）定义区间为1-12时，由软件分析得： Dependent Variable: Y1 Method: Least Squares Date: 12/24/15 Time: 16:05 Sample: 1 12 Included observations: 12 Variable Coefficient Std. Error t-Statistic Prob.   X1 1.485296 0.500386 2.968297 0.0141 C -550.5492 1220.063 -0.451247 0.6614 R-squared 0.468390     Mean dependent var 3052.950 Adjusted R-squared 0.415229     S.D. dependent var 550.5148 S.E. of regression 420.9803     Akaike info criterion 15.07406 Sum squared resid 1772245.     Schwarz criterion 15.15488 Log likelihood -88.44437     Hannan-Quinn criter. 15.04414 F-statistic 8.810789     Durbin-Watson stat 2.354167 Prob(F-statistic) 0.014087 得∑e1i2=1772245. 2）定义区间为20-31时，由软件分析得： Dependent Variable: Y1 Method: Least Squares Date: 12/24/15 Time: 16:16 Sample: 20 31 Included observations: 12 Variable Coefficient Std. Error t-Statistic Prob.   X1 1.086940 0.148863 7.301623 0.0000 C 1173.307 733.2520 1.600141 0.1407 R-squared 0.842056     Mean dependent var 6188.329 Adjusted R-squared 0.826262     S.D. dependent var 2133.692 S.E. of regression 889.3633     Akaike info criterion 16.56990 Sum squared resid 7909670.     Schwarz criterion 16.65072 Log likelihood -97.41940     Hannan-Quinn criter. 16.53998 F-statistic 53.31370     Durbin-Watson stat 2.339767 Prob(F-statistic) 0.000026 得∑e2i2=7909670. 3）根据Goldfeld-Quanadt检验，F统计量为： F=∑e2i2 /∑e1i2 =7909670./ 1772245=4.4631 在α=0.05水平下，分子分母的自由度均为10，查分布表得临界值F0.05（10,10）=2.98，因为F=4.4631> F0.05（10,10）=2.98，所以拒绝原假设，此检验表明模型存在异方差。 （3） 1）采用WLS法估计过程中， ①用权数w1=1/X,建立回归得： Dependent Variable: Y Method: Least Squares Date: 12/24/15 Time: 16:29 Sample: 1 31 Included observations: 31 Weighting series: W1 Variable Coefficient Std. Error t-Statistic Prob.   X 1.425859 0.119104 11.97157 0.0000 C -334.8131 344.3523 -0.972298 0.3389 Weighted Statistics R-squared 0.831707     Mean dependent var 3946.082 Adjusted R-squared 0.825904     S.D. dependent var 536.1907 S.E. of regression 536.6796     Akaike info criterion 15.47102 Sum squared resid 8352726.     Schwarz criterion 15.56354 Log likelihood -237.8008     Hannan-Quinn criter. 15.50118 F-statistic 143.3184     Durbin-Watson stat 1.369081 Prob(F-statistic) 0.000000 Unweighted Statistics R-squared 0.875855     Mean dependent var 4443.526 Adjusted R-squared 0.871574     S.D. dependent var 1972.072 S.E. of regression 706.7236     Sum squared resid 14484289 Durbin-Watson stat 1.532908 对此模型进行White检验得： Heteroskedasticity Test: White F-statistic 0.299395     Prob. F(2,28) 0.7436 Obs*R-squared 0.649065     Prob. Chi-Square(2) 0.7229 Scaled explained SS 1.798067     Prob. Chi-Square(2) 0.4070 Test Equation: Dependent Variable: WGT_RESID^2 Method: Least Squares Date: 12/24/15 Time: 16:34 Sample: 1 31 Included observations: 31 Collinear test regressors dropped from specification Variable Coefficient Std. Error t-Statistic Prob.   C 61927.89 1045682. 0.059222 0.9532 WGT^2 -593927.9 1173622. -0.506064 0.6168 X*WGT^2 282.4407 747.9780 0.377606 0.7086 R-squared 0.020938     Mean dependent var 269442.8 Adjusted R-squared -0.048995     S.D. dependent var 689166.5 S.E. of regression 705847.6     Akaike info criterion 29.86395 Sum squared resid 1.40E+13     Schwarz criterion 30.00273 Log likelihood -459.8913     Hannan-Quinn criter. 29.90919 F-statistic 0.299395     Durbin-Watson stat 1.922336 Prob(F-statistic) 0.743610 从上可知，nR2=0.649065，比较计算的统计量的临界值，因为nR2=0.649065<0.05（2）=5.9915，所以接受原假设，该模型消除了异方差。 估计结果为： Y=1.425859X-334.8131 t=（11.97157）（-0.972298） R2=0.875855 F=143.3184 DW=1.369081 ②用权数w2=1/x2,用回归分析得： Dependent Variable: Y Method: Least Squares Date: 12/24/15 Time: 16:40 Sample: 1 31 Included observations: 31 Weighting series: W2 Variable Coefficient Std. Error t-Statistic Prob.   X 1.557040 0.145392 10.70922 0.0000 C -693.1946 376.4760 -1.841272 0.0758 Weighted Statistics R-squared 0.798173     Mean dependent var 3635.028 Adjusted R-squared 0.791214     S.D. dependent var 1029.830 S.E. of regression 466.8513     Akaike info criterion 15.19224 Sum squared resid 6320554.     Schwarz criterion 15.28475 Log likelihood -233.4797     Hannan-Quinn criter. 15.22240 F-statistic 114.6875     Durbin-Watson stat 1.562975 Prob(F-statistic) 0.000000 Unweighted Statistics R-squared 0.834850     Mean dependent var 4443.526 Adjusted R-squared 0.829156     S.D. dependent var 1972.072 S.E. of regression 815.1229     Sum squared resid 19268334 Durbin-Watson stat 1.678365 对此模型进行White检验得： Heteroskedasticity Test: White F-statistic 0.299790     Prob. F(3,27) 0.8252 Obs*R-squared 0.999322     Prob. Chi-Square(3) 0.8014 Scaled explained SS 1.789507     Prob. Chi-Square(3) 0.6172 Test Equation: Dependent Variable: WGT_RESID^2 Method: Least Squares Date: 12/24/15 Time: 16:45 Sample: 1 31 Included observations: 31 Variable Coefficient Std. Error t-Statistic Prob.   C -111661.8 549855.7 -0.203075 0.8406 WGT^2 426220.2 2240181. 0.190262 0.8505 X^2*WGT^2 0.194888 0.516395 0.377402 0.7088 X*WGT^2 -583.2151 2082.820 -0.280012 0.7816 R-squared 0.032236     Mean dependent var 203888.8 Adjusted R-squared -0.075293     S.D. dependent var 419282.0 S.E. of regression 434780.1     Akaike info criterion 28.92298 Sum squared resid 5.10E+12     Schwarz criterion 29.10801 Log likelihood -444.3062     Hannan-Quinn criter. 28.98330 F-statistic 0.299790     Durbin-Watson stat 1.835854 Prob(F-statistic) 0.825233 从上可知，nR2=0.999322，比较计算的统计量的临界值，因为nR2=0.999322<0.05（2）=5.9915，所以接受原假设，该模型消除了异方差。 估计结果为： Y=1.557040X-693.1946 t=（10.70922）（-1.841272） R2=0.798173 F=114.6875 DW=1.562975 ③用权数w3=1/sqr（x）,用回归分析得： Dependent Variable: Y Method: Least Squares Date: 12/24/15 Time: 16:49 Sample: 1 31 Included observations: 31 Weighting series: W3 Variable Coefficient Std. Error t-Statistic Prob.   X 1.330130 0.098345 13.52507 0.0000 C -47.40242 313.1154 -0.151390 0.8807 Weighted Statistics R-squared 0.863161     Mean dependent var 4164.118 Adjusted R-squared 0.858442     S.D. dependent var 991.2079 S.E. of regression 586.9555     Akaike info criterion 15.65012 Sum squared resid 9990985.     Schwarz criterion 15.74263 Log likelihood -240.5768     Hannan-Quinn criter. 15.68027 F-statistic 182.9276     Durbin-Watson stat 1.237664 Prob(F-statistic) 0.000000 Unweighted Statistics R-squared 0.890999     Mean dependent var 4443.526 Adjusted R-squared 0.887240     S.D. dependent var 1972.072 S.E. of regression 662.2171     Sum squared resid 12717412 Durbin-Watson stat 1.314859 对此模型进行White检验得： Heteroskedasticity Test: White F-statistic 0.423886     Prob. F(2,28) 0.6586 Obs*R-squared 0.911022     Prob. Chi-Square(2) 0.6341 Scaled explained SS 2.768332     Prob. Chi-Square(2) 0.2505 Test Equation: Dependent Variable: WGT_RESID^2 Method: Least Squares Date: 12/24/15 Time: 16:57 Sample: 1 31 Included observations: 31 Collinear test regressors dropped from specification Variable Coefficient Std. Error t-Statistic Prob.   C 1212308. 2141958. 0.565981 0.5759 WGT^2 -715673.0 1301839. -0.549740 0.5869 X^2*WGT^2 -0.015194 0.082276 -0.184677 0.8548 R-squared 0.029388     Mean dependent var 322289.8 Adjusted R-squared -0.039942     S.D. dependent var 863356.7 S.E. of regression 880429.8     Akaike info criterion 30.30597 Sum squared resid 2.17E+13     Schwarz criterion 30.44475 Log likelihood -466.7426     Hannan-Quinn criter. 30.35121 F-statistic 0.423886     Durbin-Watson stat 1.887426 Prob(F-statistic) 0.658628 从上可知，nR2=0.911022，比较计算的统计量的临界值，因为nR2=0.911022<0.05（2）=5.9915，所以接受原假设，该模型消除了异方差。 估计结果为： Y=1.330130X-47.40242 t=（13.52507）（-0.151390） R2=0.863161 F=182.9276 DW=1.237664 经过检验发现，用权数w1的效果最好，所以综上可知，即修改后的结果为： Y=1.425859X-334.8131 t=（11.97157）（-0.972298） R2=0.875855 F=143.3184 DW=1.369081 5.6 (1) a)用Eviews模型分析得： Dependent Variable: Y Method: Least Squares Date: 12/24/15 Time: 19:16 Sample: 1978 2011 Included observations: 34 Variable Coefficient Std. Error t-Statistic Prob.   X 0.746241 0.019120 39.03027 0.0000 C 92.55422 42.80529 2.162215 0.0382 R-squared 0.979426     Mean dependent var 1295.802 Adjusted R-squared 0.978783     S.D. dependent var 1188.791 S.E. of regression 173.1597     Akaike info criterion 13.20333 Sum squared resid 959497.2     Schwarz criterion 13.29311 Log likelihood -222.4566     Hannan-Quinn criter. 13.23395 F-statistic 1523.362     Durbin-Watson stat 1.534491 Prob(F-statistic) 0.000000 得回归模型为： Y=0.746241 X+92.55422 b)检验是否存在异方差： ①用Goldfeld-Quanadt检验如下： 1）当定义区间为1-13时，由软件分析得： Dependent Variable: Y Method: Least Squares Date: 12/24/15 Time: 19:27 Sample: 1 13 Included observations: 13 Variable Coefficient Std. Error t-Statistic Prob.   X 0.967839 0.026879 36.00771 0.0000 C -18.86861 8.963780 -2.104984 0.0591 R-squared 0.991587     Mean dependent var 280.1377 Adjusted R-squared 0.990823     S.D. dependent var 127.0409 S.E. of regression 12.17039     Akaike info criterion 7.976527 Sum squared resid 1629.301     Schwarz criterion 8.063442 Log likelihood -49.84742     Hannan-Quinn criter. 7.958662 F-statistic 1296.555     Durbin-Watson stat 1.071505 Prob(F-statistic) 0.000000 得∑e1i2=1629.301 2）当定义区间为1-13时，由软件分析得： Dependent Variable: Y Method: Least Squares Date: 12/24/15 Time: 19:34 Sample: 22 34 Included observations: 13 Variable Coefficient Std. Error t-Statistic Prob.   X 0.719567 0.058312 12.33998 0.0000 C 179.3950 202.8764 0.884258 0.3955 R-squared 0.932629     Mean dependent var 2496.127 Adjusted R-squared 0.926504     S.D. dependent var 1022.591 S.E. of regression 277.2250     Akaike info criterion 14.22817 Sum squared resid 845390.4     Schwarz criterion 14.31509 Log likelihood -90.48313     Hannan-Quinn criter. 14.21031 F-statistic 152.2752     Durbin-Watson stat 1.658418 Prob(F-statistic) 0.000000 得∑e2i2=845390.4 3）根据Goldfeld-Quanadt检验，F统计量为： F=∑e2i2 /∑e1i2 =845390.4/ 1629.301=518.8669 在α=0.05水平下，分子分母的自由度均为11，查分布表得临界值F0.05（11,11）=4.47，因为F=518.8669> F0.05（11,11）=4.47，所以拒绝原假设，此检验表明模型存在异方差。 ②White检验 用EViews软件分析得： Heteroskedasticity Test: White F-statistic 10.36759     Prob. F(2,31) 0.0004 Obs*R-squared 13.62701     Prob. Chi-Square(2) 0.0011 Scaled explained SS 76.13635     Prob. Chi-Square(2) 0.0000 Test Equation: Dependent Variable: RESID^2 Method: Least Squares Date: 12/24/15 Time: 19:56 Sample: 1 34 Included observations: 34 Variable Coefficient Std. Error t-Statistic Prob.   C 11581.11 26117.11 0.443430 0.6605 X -27.69901 27.86540 -0.994029 0.3279 X^2 0.012230 0.005156 2.371861 0.0241 R-squared 0.400795     Mean dependent var 28220.51 Adjusted R-squared 0.362136     S.D. dependent var 101738.9 S.E. of regression 81255.15     Akaike info criterion 25.53267 Sum squared resid 2.05E+11     Schwarz criterion 25.66735 Log likelihood -431.0554     Hannan-Quinn criter. 25.57860 F-statistic 10.36759     Durbin-Watson stat 3.021651 Prob(F-statistic) 0.000357 从上图中可以看出，nR2=13.62701，比较计算的统计量的临界值，因为nR2=13.62701>0.05（2）=5.9915，所以拒绝原假设，不拒绝备择假设，表明模型存在异方差。 用以上两种方法，可以检验模型是存在异方差的。 c)修正模型 1）用加权二乘法修正异方差现象步骤如下： ①当权数w1=1/x时，用软件分析得： Dependent Variable: Y Method: Least Squares Date: 12/24/15 Time: 20:22 Sample: 1 34 Included observations: 34 Weighting series: W1 Variable Coefficient Std. Error t-Statistic Prob.   X 0.821013 0.016866 48.67993 0.0000 C 17.69318 6.283256 2.815926 0.0083 Weighted Statistics R-squared 0.986676     Mean dependent var 457.8505 Adjusted R-squared 0.986260     S.D. dependent var 41.70384 S.E. of regression 37.91285     Akaike info criterion 10.16548 Sum squared resid 45996.29     Schwarz criterion 10.25527 Log likelihood -170.8132     Hannan-Quinn criter. 10.19610 F-statistic 2369.735     Durbin-Watson stat 0.605852 Prob(F-statistic) 0.000000 Unweighted Statistics R-squared 0.968070     Mean dependent var 1295.802 Adjusted R-squared 0.967072     S.D. dependent var 1188.791 S.E. of regression 215.7175     Sum squared resid 1489089. Durbin-Watson stat 1.079107 得方程模型为： Y=0.821013X-17.69318 t=（48.67993）（2.815926） R2=0.986676 F=2369.735 DW=0.605852 对此模型进行White检验如下： Heteroskedasticity Test: White F-statistic 1.348072     Prob. F(2,31) 0.2745 Obs*R-squared 2.720457     Prob. Chi-Square(2) 0.2566 Scaled explained SS 1.221901     Prob. Chi-Square(2) 0.5428 Test Equation: Dependent Variable: WGT_RESID^2 Method: Least Squares Date: 12/24/15 Time: 20:29 Sample: 1 34 Included observations: 34 Collinear test regressors dropped from specification Variable Coefficient Std. Error t-Statistic Prob.   C 1678.870 416.5417 4.030498 0.0003 WGT^2 -32.13071 187.6175 -0.171257 0.8651 X*WGT^2 -0.484040 1.279449 -0.378319 0.7078 R-squared 0.080013     Mean dependent var 1352.832 Adjusted R-squared 0.020659     S.D. dependent var 1382.825 S.E. of regression 1368.467     Akaike info criterion 17.36487 Sum squared resid 58053732     Schwarz criterion 17.49955 Log likelihood -292.2027     Hannan-Quinn criter. 17.41080 F-statistic 1.348072     Durbin-Watson stat 1.199640 Prob(F-statistic) 0.274545 从上图中可以看出，nR2=2.720457，比较计算的统计量的临界值， 因为nR2=2.720457<0.05（2）=5.9915，所以接受原假设，即该模型消除了异方差的影响。 ②当权数w2=1/x2时，用软件分析得： Dependent Variable: Y Method: Least Squares Date: 12/24/15 Time: 20:41 Sample: 1 34 Included observations: 34 Weighting series: W2 Variable Coefficient Std. Error t-Statistic Prob.   X 0.852193 0.020150 42.29335 0.0000 C 8.890886 3.604301 2.466744 0.0192 Weighted Statistics R-squared 0.982425     Mean dependent var 230.2433 Adjusted R-squared 0.981875     S.D. dependent var 247.1718 S.E. of regression 16.20273     Akaike info criterion 8.465259 Sum squared resid 8400.912     Schwarz criterion 8.555045 Log likelihood -141.9094     Hannan-Quinn criter. 8.495879 F-statistic 1788.728     Durbin-Watson stat 0.604647 Prob(F-statistic) 0.000000 Unweighted Statistics R-squared 0.954142     Mean dependent var 1295.802 Adjusted R-squared 0.952709     S.D. dependent var 1188.791 S.E. of regression 258.5207     Sum squared resid 2138654. Durbin-Watson stat 0.781788 得方程模型为： Y=0.852193X+8.890886 t=（42.29335）（2.466744） R2=0.982425 F=1788.728 DW=0.604647 用White检验模型得： Heteroskedasticity Test: White F-statistic 7.462185     Prob. F(3,30) 0.0007 Obs*R-squared 14.52935     Prob. Chi-Square(3) 0.0023 Scaled explained SS 19.40139     Prob. Chi-Square(3) 0.0002 Test Equation: Dependent Variable: WGT_RESID^2 Method: Least Squares Date: 12/24/15 Time: 20:55 Sample: 1 34 Included observations: 34 Variable Coefficient Std. Error t-Statistic Prob.   C -7.684700 85.76169 -0.089605 0.9292 WGT^2 64.20016 96.11160 0.667975 0.5093 X^2*WGT^2 0.006306 0.003431 1.838317 0.0759 X*WGT^2 -1.247222 1.163558 -1.071903 0.2923 R-squared 0.427334     Mean dependent var 247.0857 Adjusted R-squared 0.370067     S.D. dependent var 435.4791 S.E. of regression 345.6323     Akaike info criterion 14.63876 Sum squared resid 3583851.     Schwarz criterion 14.81833 Log likelihood -244.8589     Hannan-Quinn criter. 14.70000 F-statistic 7.462185     Durbin-Watson stat 1.586012 Prob(F-statistic) 0.000712 从上图中可以看出，nR2=14.52935，比较计算的统计量的临界值，因为nR2=14.52935>0.05（2）=5.9915，所以拒绝原假设，不拒绝备择假设，表明模型存在异方差。此模型并未消除异方差。 ③当权数w3=1/sqr(x)时，用软件分析得： Dependent Variable: Y Method: Least Squares Date: 12/24/15 Time: 21:06 Sample: 1 34 Included observations: 34 Weighting series: W3 Variable Coefficient Std. Error t-Statistic Prob.   X 0.778551 0.015677 49.66347 0.0000 C 40.45770 14.57528 2.775775 0.0091 Weighted Statistics R-squared 0.987192     Mean dependent var 776.3266 Adjusted R-squared 0.986792     S.D. dependent var 367.3152 S.E. of regression 79.19828     Akaike info criterion 11.63881 Sum squared resid 200715.8     Schwarz criterion 11.72859 Log likelihood -195.8597     Hannan-Quinn criter. 11.66943 F-statistic 2466.460     Durbin-Watson stat 1.178340 Prob(F-statistic) 0.000000 Unweighted Statistics R-squared 0.977590     Mean dependent var 1295.802 Adjusted R-squared 0.976890     S.D. dependent var 1188.791 S.E. of regression 180.7210     Sum squared resid 1045123. Durbin-Watson stat 1.460832 得方程模型为： Y=0.778551X+40.45770 t=（49.66347）（2.775775） R2=0.986792 F=2466.460 DW=1.178340 对所得模型进行White检验： Heteroskedasticity Test: White F-statistic 8.158958     Prob. F(2,31) 0.0014 Obs*R-squared 11.72514     Prob. Chi-Square(2) 0.0028 Scaled explained SS 28.08353     Prob. Chi-Square(2) 0.0000 Test Equation: Dependent Variable: WGT_RESID^2 Method: Least Squares Date: 12/24/15 Time: 21:23 Sample: 1 34 Included observations: 34 Collinear test regressors dropped from specification Variable Coefficient Std. Error t-Statistic Prob.   C -7585.186 5311.263 -1.428132 0.1633 WGT^2 2468.369 1996.041 1.236632 0.2255 X^2*WGT^2 0.009139 0.002481 3.684177 0.0009 R-squared 0.344857     Mean dependent var 5903.405 Adjusted R-squared 0.302590     S.D. dependent var 13934.64 S.E. of regression 11636.97     Akaike info criterion 21.64586 Sum squared resid 4.20E+09     Schwarz criterion 21.78054 Log likelihood -364.9796     Hannan-Quinn criter. 21.69179 F-statistic 8.158958     Durbin-Watson stat 2.344068 Prob(F-statistic) 0.001423 从上图中可以看出，nR2=11.72514，比较计算的统计量的临界值，因为nR2=11.72514>0.05（2）=5.9915，所以拒绝原假设，不拒绝备择假设，表明模型存在异方差。此模型并未消除异方差。 综上所述，用加权二乘法w1的效果最好，所以模型为： 得方程模型为： Y=0.821013X-17.69318 t=（48.67993）（2.815926） R2=0.986676 F=2369.735 DW=0.605852 2）用对数模型法 用软件分析得： Dependent Variable: LNY Method: Least Squares Date: 12/24/15 Time: 21:37 Sample: 1 34 Included observations: 34 Variable Coefficient Std. Error t-Statistic Prob.   LNX 0.946887 0.011228 84.33549 0.0000 C 0.201861 0.077905 2.591100 0.0143 R-squared 0.995521     Mean dependent var 6.687779 Adjusted R-squared 0.995381     S.D. dependent var 1.067124 S.E. of regression 0.072525     Akaike info criterion -2.352753 Sum squared resid 0.168315     Schwarz criterion -2.262967 Log likelihood 41.99680     Hannan-Quinn criter. -2.322134 F-statistic 7112.475     Durbin-Watson stat 0.812150 Prob(F-statistic) 0.000000 得到模型为： LnY=0.946887 LNX+0.201861 对此模型进行White检验得： Heteroskedasticity Test: White F-statistic 1.003964     Prob. F(2,31) 0.3780 Obs*R-squared 2.068278     Prob. Chi-Square(2) 0.3555 Scaled explained SS 1.469638     Prob. Chi-Square(2) 0.4796 Test Equation: Dependent Variable: RESID^2 Method: Least Squares Date: 12/24/15 Time: 21:45 Sample: 1 34 Included observations: 34 Variable Coefficient Std. Error t-Statistic Prob.   C 0.039547 0.046759 0.845753 0.4042 LNX -0.011601 0.014012 -0.827969 0.4140 LNX^2 0.000932 0.001028 0.906774 0.3715 R-squared 0.060832     Mean dependent var 0.004950 Adjusted R-squared 0.000240     S.D. dependent var 0.006365 S.E. of regression 0.006364     Akaike info criterion -7.192271 Sum squared resid 0.001255     Schwarz criterion -7.057592 Log likelihood 125.2686     Hannan-Quinn criter. -7.146342 F-statistic 1.003964     Durbin-Watson stat 2.022904 Prob(F-statistic) 0.378027 从上图中可以看出，nR2=2.068278，比较计算的统计量的临界值，因为nR2=2.068278<0.05（2）=5.9915，所以接受原假设，此模型消除了异方差。 综合两种方法，改进后的模型最好为： LnY=0.946887 LNX+0.201861 (2) 1）考虑价格因素，首先用软件三者关系进行分析如下： Dependent Variable: Y Method: Least Squares Date: 12/24/15 Time: 21:51 Sample: 1 34 Included observations: 34 Variable Coefficient Std. Error t-Statistic Prob.   X 0.741684 0.019905 37.26095 0.0000 P 0.235025 0.271701 0.865012 0.3937 C 43.41715 71.22946 0.609539 0.5466 R-squared 0.979911     Mean dependent var 1295.802 Adjusted R-squared 0.978615     S.D. dependent var 1188.791 S.E. of regression 173.8449     Akaike info criterion 13.23830 Sum squared resid 936883.7     Schwarz criterion 13.37298 Log likelihood -222.0511     Hannan-Quinn criter. 13.28423 F-statistic 756.0627     Durbin-Watson stat 1.681521 Prob(F-statistic) 0.000000 1）用Goldfeld-Quanadt检验如下： ①当样本为1-13时，进行回归分析： Dependent Variable: P Method: Least Squares Date: 12/24/15 Time: 21:59 Sample: 1 13 Included observations: 13 Variable Coefficient Std. Error t-Statistic Prob.   X -0.170484 0.203868 -0.836247 0.4225 Y 0.458660 0.209755 2.186646 0.0536 C 59.50496 7.385841 8.056627 0.0000 R-squared 0.956255     Mean dependent var 135.3231 Adjusted R-squared 0.947506     S.D. dependent var 36.95380 S.E. of regression 8.466678     Akaike info criterion 7.309328 Sum squared resid 716.8464     Schwarz criterion 7.439701 Log likelihood -44.51063     Hannan-Quinn criter. 7.282530 F-statistic 109.2993     Durbin-Watson stat 0.637181 Prob(F-statistic) 0.000000 得∑e1i2=716.8464 ②当样本为22-34时，做回归分析得： Dependent Variable: Y Method: Least Squares Date: 12/24/15 Time:22:07 Sample: 22 34 Included observations: 13 Variable Coefficient Std. Error t-Statistic Prob.   X 0.641197 0.092678 6.918569 0.0000 P -1.206222 1.114278 -1.082514 0.3044 C 795.6887 603.8605 1.317670 0.2170 R-squared 0.939696     Mean dependent var 2496.127 Adjusted R-squared 0.927635     S.D. dependent var 1022.591 S.E. of regression 275.0847     Akaike info criterion 14.27121 Sum squared resid 756715.7     Schwarz criterion 14.40158 Log likelihood -89.76286     Hannan-Quinn criter. 14.24441 F-statistic 77.91291     Durbin-Watson stat 1.128778 Prob(F-statistic) 0.000001 得∑e2i2=756715.7 ③根据Goldfeld-Quanadt检验，F统计量为： F=∑e2i2 /∑e1i2 =756715.7/ 716.8464=1055.6176 在α=0.05水平下，分子分母的自由度均为11，查分布表得临界值F0.05（10,10）=2.98，因为F=1055.6176> F0.05（10,10）=2.98，所以拒绝原假设，此检验表明模型存在异方差。 2）用White检验，软件分析结果为： Heteroskedasticity Test: White F-statistic 7.312529     Prob. F(5,28) 0.0002 Obs*R-squared 19.25463     Prob. Chi-Square(5) 0.0017 Scaled explained SS 119.3072     Prob. Chi-Square(5) 0.0000 Test Equation: Dependent Variable: RESID^2 Method: Least Squares Date: 12/24/15 Time: 22:18 Sample: 1 34 Included observations: 34 Variable Coefficient Std. Error t-Statistic Prob.   C 79541.08 112647.3 0.706107 0.4860 X 209.4964 63.90400 3.278298 0.0028 X^2 -0.024133 0.010712 -2.252841 0.0323 X*P -0.235137 0.106647 -2.204822 0.0358 P -1175.326 1156.253 -1.016495 0.3181 P^2 1.637366 2.600020 0.629751 0.5340 R-squared 0.566313     Mean dependent var 27555.40 Adjusted R-squared 0.488869     S.D. dependent var 107990.9 S.E. of regression 77206.44     Akaike info criterion 25.50514 Sum squared resid 1.67E+11     Schwarz criterion 25.77450 Log likelihood -427.5874     Hannan-Quinn criter. 25.59700 F-statistic 7.312529     Durbin-Watson stat 2.787044 Prob(F-statistic) 0.000171 从上图中可以看出，nR2=19.25463，比较计算的统计量的临界值，因为nR2=19.25463>0.05（5）=11.0705，所以拒绝原假设，不拒绝备择假设，表明模型存在异方差。 2）修正 ①建立对数模型，用软件分析如下： Dependent Variable: LNY Method: Least Squares Date: 12/24/15 Time: 22:24 Sample: 1 34 Included observations: 34 Variable Coefficient Std. Error t-Statistic Prob.   LNX 0.939605 0.013645 68.86088 0.0000 LNP 0.026821 0.028454 0.942609 0.3532 C 0.108230 0.126322 0.856784 0.3981 R-squared 0.995646     Mean dependent var 6.687779 Adjusted R-squared 0.995365     S.D. dependent var 1.067124 S.E. of regression 0.072652     Akaike info criterion -2.322188 Sum squared resid 0.163625     Schwarz criterion -2.187509 Log likelihood 42.47720     Hannan-Quinn criter. -2.276259 F-statistic 3544.292     Durbin-Watson stat 0.930109 Prob(F-statistic) 0.000000 对此模型进行White检验： Heteroskedasticity Test: White F-statistic 3.523832     Prob. F(5,28) 0.0135 Obs*R-squared 13.13158     Prob. Chi-Square(5) 0.0222 Scaled explained SS 12.14373     Prob. Chi-Square(5) 0.0329 Test Equation: Dependent Variable: RESID^2 Method: Least Squares Date: 12/24/15 Time: 22:34 Sample: 1 34 Included observations: 34 Variable Coefficient Std. Error t-Statistic Prob.   C 0.422872 0.273746 1.544759 0.1336 LNX 0.080712 0.031833 2.535502 0.0171 LNX^2 -0.003917 0.003037 -1.289564 0.2078 LNX*LNP -0.004955 0.005136 -0.964765 0.3429 LNP -0.254992 0.129858 -1.963631 0.0596 LNP^2 0.026470 0.012675 2.088390 0.0460 R-squared 0.386223     Mean dependent var 0.004813 Adjusted R-squared 0.276620     S.D. dependent var 0.007286 S.E. of regression 0.006197     Akaike info criterion -7.170690 Sum squared resid 0.001075     Schwarz criterion -6.901332 Log likelihood 127.9017     Hannan-Quinn criter. -7.078831 F-statistic 3.523832     Durbin-Watson stat 2.264261 Prob(F-statistic) 0.013502 从上图中可以看出，nR2=13.13158，比较计算的统计量的临界值，因为nR2=13.13158>0.05（5）=11.0705，所以拒绝原假设，不拒绝备择假设，表明模型存在异方差，所以此模型没有消除异方差。 ②当w1=1/x时，用软件分析如下： Dependent Variable: Y Method: Least Squares Date: 12/24/15 Time: 22:49 Sample: 1 34 Included observations: 34 Weighting series: W1 Variable Coefficient Std. Error t-Statistic Prob.   X 0.723218 0.022965 31.49212 0.0000 P 0.719506 0.141085 5.099795 0.0000 C -44.72084 13.11268 -3.410502 0.0018 Weighted Statistics R-squared 0.992755     Mean dependent var 457.8505 Adjusted R-squared 0.992287     S.D. dependent var 41.70384 S.E. of regression 28.40494     Akaike info criterion 9.615100 Sum squared resid 25012.05     Schwarz criterion 9.749779 Log likelihood -160.4567     Hannan-Quinn criter. 9.661030 F-statistic 2123.843     Durbin-Watson stat 1.298389 Prob(F-statistic) 0.000000 Unweighted Statistics R-squared 0.977704     Mean dependent var 1295.802 Adjusted R-squared 0.976266     S.D. dependent var 1188.791 S.E. of regression 183.1446     Sum squared resid 1039800. Durbin-Watson stat 1.740795 所得模型为： Y=0.723218X+0.719506p-44.72084 对此模型进行White检验得： Heteroskedasticity Test: White F-statistic 2.088840     Prob. F(5,28) 0.0966 Obs*R-squared 9.236835     Prob. Chi-Square(5) 0.1000 Scaled explained SS 25.50696     Prob. Chi-Square(5) 0.0001 Test Equation: Dependent Variable: WGT_RESID^2 Method: Least Squares Date: 12/24/15 Time: 22:50 Sample: 1 34 Included observations: 34 Collinear test regressors dropped from specification Variable Coefficient Std. Error t-Statistic Prob.   C 3861.793 1068.806 3.613183 0.0012 WGT^2 3260.199 4309.988 0.756429 0.4557 X*WGT^2 13.72241 8.453473 1.623287 0.1157 X*P*WGT^2 -0.151725 0.061588 -2.463567 0.0202 P^2*WGT^2 0.431162 0.278315 1.549186 0.1326 P*WGT^2 -76.13221 73.40636 -1.037134 0.3085 R-squared 0.271672     Mean dependent var 735.6486 Adjusted R-squared 0.141613     S.D. dependent var 1924.655 S.E. of regression 1783.177     Akaike info criterion 17.96897 Sum squared resid 89032169     Schwarz criterion 18.23832 Log likelihood -299.4724     Hannan-Quinn criter. 18.06082 F-statistic 2.088840     Durbin-Watson stat 2.336495 Prob(F-statistic) 0.096616 因为nR2=9.236835<0.05（5）=11.0705，所以接受原假设。该模型不存在异方差，所以此模型消除了异方差。 ③当w2=1/x2，用软件分析得： Dependent Variable: Y Method: Least Squares Date: 12/24/15 Time: 23:00 Sample: 1 34 Included observations: 34 Weighting series: W2 Variable Coefficient Std. Error t-Statistic Prob.   X 0.639012 0.039216 16.29477 0.0000 P 1.200751 0.206023 5.828234 0.0000 C -81.85973 15.77499 -5.189209 0.0000 Weighted Statistics R-squared 0.991614     Mean dependent var 230.2433 Adjusted R-squared 0.991073     S.D. dependent var 247.1718 S.E. of regression 11.37136     Akaike info criterion 7.784170 Sum squared resid 4008.543     Schwarz criterion 7.918849 Log likelihood -129.3309     Hannan-Quinn criter. 7.830100 F-statistic 1832.775     Durbin-Watson stat 1.167961 Prob(F-statistic) 0.000000 Unweighted Statistics R-squared 0.956816     Mean dependent var 1295.802 Adjusted R-squared 0.954030     S.D. dependent var 1188.791 S.E. of regression 254.8849     Sum squared resid 2013955. Durbin-Watson stat 1.002870 所得模型为： Y=0.639012X+1.200751p-81.85973 对该模型进行White检验得： Heteroskedasticity Test: White F-statistic 43.19853     Prob. F(6,27) 0.0000 Obs*R-squared 30.79235     Prob. Chi-Square(6) 0.0000 Scaled explained SS 47.42430     Prob. Chi-Square(6) 0.0000 Test Equation: Dependent Variable: WGT_RESID^2 Method: Least Squares Date: 12/26/15 Time: 07:20 Sample: 1 34 Included observations: 34 Variable Coefficient Std. Error t-Statistic Prob.   C 27.51002 20.12556 1.366919 0.1829 WGT^2 -1245.193 837.2352 -1.487268 0.1485 X^2*WGT^2 0.007732 0.005450 1.418649 0.1674 X*WGT^2 7.948582 4.884597 1.627275 0.1153 X*P*WGT^2 -0.111755 0.064061 -1.744525 0.0924 P^2*WGT^2 0.184342 0.164562 1.120199 0.2725 P*WGT^2 -3.127017 23.56724 -0.132685 0.8954 R-squared 0.905657     Mean dependent var 117.8983 Adjusted R-squared 0.884692     S.D. dependent var 230.3570 S.E. of regression 78.22224     Akaike info criterion 11.73823 Sum squared resid 165205.4     Schwarz criterion 12.05248 Log likelihood -192.5498     Hannan-Quinn criter. 11.84539 F-statistic 43.19853     Durbin-Watson stat 1.794799 Prob(F-statistic) 0.000000 因为nR2=30.79235>0.05（5）=11.0705，所以拒绝原假设，不拒绝备择假设，表明模型存在异方差，所以此模型没有消除异方差。 ④当w3=1/sqr(x)时，用软件分析得： Dependent Variable: Y Method: Least Squares Date: 12/26/15 Time: 07:34 Sample: 1 34 Included observations: 34 Weighting series: W3 Variable Coefficient Std. Error t-Statistic Prob.   X 0.744661 0.019825 37.56252 0.0000 P 0.451861 0.179971 2.510739 0.0175 C -13.49643 25.37768 -0.531823 0.5986 Weighted Statistics R-squared 0.989356     Mean dependent var 776.3266 Adjusted R-squared 0.988670     S.D. dependent var 367.3152 S.E. of regression 73.35237     Akaike info criterion 11.51252 Sum squared resid 166797.7     Schwarz criterion 11.64720 Log likelihood -192.7129     Hannan-Quinn criter. 11.55845 F-statistic 1440.783     Durbin-Watson stat 1.599590 Prob(F-statistic) 0.000000 Unweighted Statistics R-squared 0.979407     Mean dependent var 1295.802 Adjusted R-squared 0.978079     S.D. dependent var 1188.791 S.E. of regression 176.0098     Sum squared resid 960362.6 Durbin-Watson stat 1.761225 所得模型为： Y=0.744661X+0.451861p-13.49643 对所得模型进行White检验得： Heteroskedasticity Test: White F-statistic 4.459272     Prob. F(5,28) 0.0041 Obs*R-squared 15.07219     Prob. Chi-Square(5) 0.0101 Scaled explained SS 72.39077     Prob. Chi-Square(5) 0.0000 Test Equation: Dependent Variable: WGT_RESID^2 Method: Least Squares Date: 12/26/15 Time: 07:43 Sample: 1 34 Included observations: 34 Collinear test regressors dropped from specification Variable Coefficient Std. Error t-Statistic Prob.   C 61163.22 27531.93 2.221538 0.0346 WGT^2 28251.98 17350.39 1.628320 0.1147 X^2*WGT^2 -0.001093 0.006624 -0.164950 0.8702 X*P*WGT^2 -0.235836 0.077110 -3.058447 0.0049 P^2*WGT^2 1.236884 0.644872 1.918030 0.0654 P*WGT^2 -503.3080 262.5884 -1.916718 0.0655 R-squared 0.443300     Mean dependent var 4905.814 Adjusted R-squared 0.343889     S.D. dependent var 16926.97 S.E. of regression 13710.96     Akaike info criterion 22.04856 Sum squared resid 5.26E+09     Schwarz criterion 22.31792 Log likelihood -368.8256     Hannan-Quinn criter. 22.14042 F-statistic 4.459272     Durbin-Watson stat 2.450171 Prob(F-statistic) 0.004103 因为nR2=15.07219>0.05（5）=11.0705，所以拒绝原假设，不拒绝备择假设，表明模型存在异方差，所以此模型没有消除异方差。 综上所述，修改后的模型为： Y= Y=0.723218X+0.719506p-44.72084 t=(31.49212) (5.099705) (-3.410502) R2=0.992755 F=2123.843 DW=1.298389 (3)体会：对于不同的模型，可采取对数模型法或者加权二乘法对具有异方差性的模型进行改进，从而消除异方差。但对于不同的模型，自由度的不同，可能导致改进的方法不同，所以要对改进的模型进行进一步的检验才行。 6.1 (1)建立居民收入-消费模型，用Eviews分析结果如下： Dependent Variable: Y Method: Least Squares Date: 12/26/15 Time: 08:22 Sample: 1 19 Included observations: 19 Variable Coefficient Std. Error t-Statistic Prob.   X 0.690488 0.012877 53.62068 0.0000 C 79.93004 12.39919 6.446390 0.0000 R-squared 0.994122     Mean dependent var 700.2747 Adjusted R-squared 0.993776     S.D. dependent var 246.4491 S.E. of regression 19.44245     Akaike info criterion 8.872095 Sum squared resid 6426.149     Schwarz criterion 8.971510 Log likelihood -82.28490     Hannan-Quinn criter. 8.888920 F-statistic 2875.178     Durbin-Watson stat 0.574663 Prob(F-statistic) 0.000000 所得模型为： Y=0.690488X+79.93004 Se=(0.012877)(12.39919) t=(53.62068)(6.446390) R2=0.994122 F=2875.178 DW=0.574663 （2） 1）检验模型中存在的问 题 快递公司问题件快递公司问题件货款处理关于圆的周长面积重点题型关于解方程组的题及答案关于南海问题 ①做出残差图如下： 残差的变动有系统模式，连续为正和连续为负，表明残差项存在一阶自相关。 ②该回归方程可决系数较高，回归系数均显著。对样本量为19，一个解释变量的模型，5%的显著水平，查DW统计表可知，dL=1.180，dU=1.401，模型中DW=0.574663,< dL,显然模型中有自相关。 ③对模型进行BG检验，用Eviews分析结果如下： Breusch-Godfrey Serial Correlation LM Test: F-statistic 4.811108     Prob. F(2,15) 0.0243 Obs*R-squared 7.425088     Prob. Chi-Square(2) 0.0244 Test Equation: Dependent Variable: RESID Method: Least Squares Date: 12/26/15 Time: 08:27 Sample: 1 19 Included observations: 19 Presample missing value lagged residuals set to zero. Variable Coefficient Std. Error t-Statistic Prob.   X -0.003275 0.010787 -0.303586 0.7656 C 1.929546 10.35593 0.186323 0.8547 RESID(-1) 0.608886 0.292707 2.080189 0.0551 RESID(-2) 0.089988 0.291120 0.309110 0.7615 R-squared 0.390794     Mean dependent var -1.65E-13 Adjusted R-squared 0.268953     S.D. dependent var 18.89466 S.E. of regression 16.15518     Akaike info criterion 8.587023 Sum squared resid 3914.848     Schwarz criterion 8.785852 Log likelihood -77.57671     Hannan-Quinn criter. 8.620672 F-statistic 3.207406     Durbin-Watson stat 1.570723 Prob(F-statistic) 0.053468 如上表显示，LM=TR2=7.425088，其p值为0.0244，表明存在自相关。 2）对模型进行处理： ①采取广义差分法 a)为估计自相关系数ρ。对et进行滞后一期的自回归，用EViews分析结果如下： Dependent Variable: E Method: Least Squares Date: 12/26/15 Time: 08:34 Sample (adjusted): 2 19 Included observations: 18 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   E(-1) 0.657352 0.177626 3.700759 0.0018 R-squared 0.440747     Mean dependent var 1.717433 Adjusted R-squared 0.440747     S.D. dependent var 17.85134 S.E. of regression 13.34980     Akaike info criterion 8.074833 Sum squared resid 3029.692     Schwarz criterion 8.124298 Log likelihood -71.67349     Hannan-Quinn criter. 8.081653 Durbin-Watson stat 1.634573 由上可知，ρ=0.657352 b)对原模型进行广义差分回归，用Eviews进行分析所得结果如下： Dependent Variable: Y-0.657352*Y(-1) Method: Least Squares Date: 12/26/15 Time: 08:41 Sample (adjusted): 2 19 Included observations: 18 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   C 35.97761 8.103546 4.439737 0.0004 X-0.657352*X(-1) 0.668695 0.020642 32.39512 0.0000 R-squared 0.984983     Mean dependent var 278.1002 Adjusted R-squared 0.984044     S.D. dependent var 105.1781 S.E. of regression 13.28570     Akaike info criterion 8.115693 Sum squared resid 2824.158     Schwarz criterion 8.214623 Log likelihood -71.04124     Hannan-Quinn criter. 8.129334 F-statistic 1049.444     Durbin-Watson stat 1.830746 Prob(F-statistic) 0.000000 由上图可知回归方程为： Yt*=35.97761+0.668695Xt* Se=(8.103546)(0.020642) t=(4.439737)(32.39512) R2=0.984983 F=1049.444 DW=1.830746 式中，Yt*=Yt-0.657352Yt-1, Xt*=Xt-0.657352Xt-1 由于使用了广义差分数据，样本容量减少了1个，为18个。查5%显著水平的DW统计表可知，dL=1.158,dU=1.391模型中DW=1,830746，du