计量经济学报告

建立多元线性回归模型 Y代表居民消费水平，X2表示年底余额，X3表示居民可支配收入，X4表示居民家庭恩格尔系数，X5表示国民总收入 Dependent Variable: Y Method: Least Squares Date: 12/03/12 Time: 22:09 Sample: 1 15 Included observations: 15 Coefficient Std. Error t-Statistic Prob.   C 839.7427 630.5823 1.331694 0.2125 X2 -0.000194 0.002408 -0.080744 0.9372 X3 0.345733 0.101229 3.415371 0.0066 X4 -3.168988 10.21463 -0.310240 0.7627 X5 0.006907 0.004240 1.628834 0.1344 R-squared 0.999311     Mean dependent var 5331.467 Adjusted R-squared 0.999035     S.D. dependent var 2347.887 S.E. of regression 72.94103     Akaike info criterion 11.67838 Sum squared resid 53203.94     Schwarz criterion 11.91440 Log likelihood -82.58786     Hannan-Quinn criter. 11.67587 F-statistic 3623.923     Durbin-Watson stat 1.739552 Prob(F-statistic) 0.000000 以上结果得出回归方程： Y=839.7427-0.000194x1+0.345733x2-3.168988x3+0.006907x4 模型的经济意义是： 1. X2表示年底余额，X3表示居民可支配收入，X4表示居民家庭恩格尔系数，X5表示国民总收入都为0时，居民消费水平为839.7427元 2. 每增加一单位的年底余额，居民消费水平便会减小，但影响更可以忽略不计 3. 每增加一单位的居民可支配收入，居民消费水平便会增加0.3单位 4. 每增加一单位的恩格尔系数，居民消费水平便会减少3个单位 5. 每增加一单位的国民收入，居民消费水平便会增加，但是影响比较小 T检验 原假设为H0:aj=0(j=1,2,3,4)，给定显著性水平α=0.05，查t分布表的自由度为n-k=11,得临界值为2.201 由上表中可知，与各个回归系数对应的t统计量分别为-0.080744、3.415371、-0.310240、1.628834，也就是说，接受原假设H0：a1=0，a3=0，a4=0。拒绝原假设H0：a2=0，所以在0.05的显著性水平下，年底余额，居民家庭恩格尔系数，国民总收入对居民消费水平没有显著性影响，只有居民可支配收入对居民消费水平有着显著的影响。 F检验 F检验：针对H0：a1=a2=a3=a4=0，给定显著性水平α=0.05，在F分布表中查出自由度为k-1=3和n-k=11临界值为8.76。由表中可得F=3623.923，由于F值大于临界值8.76，应拒绝原假设H0：a1=a2=a3=a4=0，说明回归方程显著，年底余额，居民可支配收入，居民家庭恩格尔系数，国民总收入联合起来确实对居民消费水平有着显著的影响。 现在单独对居民可支配收入和居民消费水平进行回归，结果为 Dependent Variable: Y Method: Least Squares Date: 12/04/12 Time: 11:23 Sample: 1 15 Included observations: 15 Coefficient Std. Error t-Statistic Prob.   C 367.9811 48.65441 7.563160 0.0000 X3 0.502656 0.004482 112.1529 0.0000 R-squared 0.998968     Mean dependent var 5331.467 Adjusted R-squared 0.998888     S.D. dependent var 2347.887 S.E. of regression 78.28999     Akaike info criterion 11.68228 Sum squared resid 79681.20     Schwarz criterion 11.77669 Log likelihood -85.61712     Hannan-Quinn criter. 11.68128 F-statistic 12578.28     Durbin-Watson stat 0.910663 Prob(F-statistic) 0.000000 现在单独对年底余额和居民消费水平进行回归，结果为 Dependent Variable: Y Method: Least Squares Date: 12/04/12 Time: 11:32 Sample: 1 15 Included observations: 15 Coefficient Std. Error t-Statistic Prob.   C 1715.027 122.8632 13.95884 0.0000 X2 0.028504 0.000822 34.69290 0.0000 R-squared 0.989314     Mean dependent var 5331.467 Adjusted R-squared 0.988492     S.D. dependent var 2347.887 S.E. of regression 251.8650     Akaike info criterion 14.01923 Sum squared resid 824667.5     Schwarz criterion 14.11364 Log likelihood -103.1442     Hannan-Quinn criter. 14.01822 F-statistic 1203.597     Durbin-Watson stat 1.128005 Prob(F-statistic) 0.000000 现在单独对恩格尔系数和居民消费水平进行回归，结果为 Dependent Variable: Y Method: Least Squares Date: 12/04/12 Time: 11:33 Sample: 1 15 Included observations: 15 Coefficient Std. Error t-Statistic Prob.   C 20646.57 4518.709 4.569131 0.0005 X4 -388.6444 114.0805 -3.406754 0.0047 R-squared 0.471673     Mean dependent var 5331.467 Adjusted R-squared 0.431033     S.D. dependent var 2347.887 S.E. of regression 1771.009     Akaike info criterion 17.92005 Sum squared resid 40774160     Schwarz criterion 18.01446 Log likelihood -132.4004     Hannan-Quinn criter. 17.91905 F-statistic 11.60598     Durbin-Watson stat 0.183573 Prob(F-statistic) 0.004681 现在单独对国民收入和居民消费水平进行回归，结果为 Dependent Variable: Y Method: Least Squares Date: 12/04/12 Time: 11:35 Sample: 1 15 Included observations: 15 Coefficient Std. Error t-Statistic Prob.   C 1449.020 70.60521 20.52285 0.0000 X5 0.021848 0.000343 63.65910 0.0000 R-squared 0.996802     Mean dependent var 5331.467 Adjusted R-squared 0.996556     S.D. dependent var 2347.887 S.E. of regression 137.7797     Akaike info criterion 12.81275 Sum squared resid 246782.1     Schwarz criterion 12.90716 Log likelihood -94.09566     Hannan-Quinn criter. 12.81175 F-statistic 4052.482     Durbin-Watson stat 1.192942 Prob(F-statistic) 0.000000 一元回归统计结果 变量 X2 X3 X4 X5 参数估计量 T统计量 R2 0.028504 34.69290 0.989314 0.988492 0.502656 112.1529 0.998968 0.998888 -388.6444 -3.406754 0.471673 0.431033 0.021848 63.65910 0.996802 0.996556 其中，加入X3的方程 最大，以X3为基础，顺次加入其他变量逐步回归，结果如下 变量 变量 X3 X2 X4 X5 X3，X2 0.4839 (10.6768) 0.0011 (0.4169) 0.9988 X3，X4 0.5087 (84.8649) 9.7689 (1,.4484) 0.9989 X3，X5 0.3680 (6.5665) 0.0059 (2.4077) 0.9991 经比较，新加入X3的方程 =0.9991，改进最大，而且X5的t值大于2.201，所以保留X5，再加入其他变量逐步进行回归 变量 变量 X3 X5 X2 X4 X3，X5，X2 0.3693 (5.7574) 0.0059 (2.2548) -0.0001 (-0.0479) 0.999114 X3，X5，X4 0.3442 (3.6272) 0.0068 (1.7359) -3.0757 (-0.3177) 因为X2，X4的t值小于2.201，没有通过检验，所以舍弃X2，X4，最后回归结果为 Y=652.946+0.3680*X3+0.0059*X5 WHITE检验 Heteroskedasticity Test: White F-statistic 3.233070     Prob. F(5,9) 0.0604 Obs*R-squared 9.635481     Prob. Chi-Square(5) 0.0862 Scaled explained SS 3.985030     Prob. Chi-Square(5) 0.5516 Test Equation: Dependent Variable: RESID^2 Method: Least Squares Date: 12/04/12 Time: 15:46 Sample: 1 15 Included observations: 15 Coefficient Std. Error t-Statistic Prob.   C -71381.62 71960.01 -0.991962 0.3471 X3 79.39712 65.92021 1.204443 0.2591 X3^2 -0.015487 0.014123 -1.096590 0.3013 X3*X5 0.001370 0.001209 1.133483 0.2863 X5 -3.803537 2.865545 -1.327334 0.2171 X5^2 -2.96E-05 2.58E-05 -1.146521 0.2811 R-squared 0.642365     Mean dependent var 3581.817 Adjusted R-squared 0.443679     S.D. dependent var 4214.918 S.E. of regression 3143.776     Akaike info criterion 19.23341 Sum squared resid 88949963     Schwarz criterion 19.51663 Log likelihood -138.2506     Hannan-Quinn criter. 19.23039 F-statistic 3.233070     Durbin-Watson stat 2.895691 Prob(F-statistic) 0.060359 经检验，nR2=9.635481，由WHITE检验知，，在α=0.05下，查 分布表，得临界值 0.05（5）=11.0705，比较计算的 统计量与临界值，因为nR2=9.635481< 0.05（5）=11.0705，所以接受原假设，表明模型不存在异方差。 自相关性 Breusch-Godfrey Serial Correlation LM Test: F-statistic 0.118988     Prob. F(1,11) 0.7366 Obs*R-squared 0.160521     Prob. Chi-Square(1) 0.6887 Test Equation: Dependent Variable: RESID Method: Least Squares Date: 12/17/12 Time: 17:25 Sample: 1 15 Included observations: 15 Presample missing value lagged residuals set to zero. Coefficient Std. Error t-Statistic Prob.   C -10.72510 134.3790 -0.079812 0.9378 X3 0.006134 0.060880 0.100753 0.9216 X5 -0.000284 0.002664 -0.106764 0.9169 RESID(-1) 0.122122 0.354031 0.344947 0.7366 R-squared 0.010701     Mean dependent var 4.61E-13 Adjusted R-squared -0.259107     S.D. dependent var 61.94886 S.E. of regression 69.51278     Akaike info criterion 11.54408 Sum squared resid 53152.29     Schwarz criterion 11.73289 Log likelihood -82.58058     Hannan-Quinn criter. 11.54207 F-statistic 0.039663     Durbin-Watson stat 1.686923 Prob(F-statistic) 0.988871 因为P=0.7366>0.05，所以不存在自相关 Breusch-Godfrey Serial Correlation LM Test: F-statistic 0.958920     Prob. F(2,10) 0.4159 Obs*R-squared 2.413826     Prob. Chi-Square(2) 0.2991 Test Equation: Dependent Variable: RESID Method: Least Squares Date: 12/17/12 Time: 17:26 Sample: 1 15 Included observations: 15 Presample missing value lagged residuals set to zero. Coefficient Std. Error t-Statistic Prob.   C -31.86101 130.7549 -0.243670 0.8124 X3 0.018655 0.059544 0.313300 0.7605 X5 -0.000876 0.002611 -0.335324 0.7443 RESID(-1) 0.353472 0.383187 0.922452 0.3780 RESID(-2) -0.562881 0.420682 -1.338022 0.2105 R-squared 0.160922     Mean dependent var 4.61E-13 Adjusted R-squared -0.174710     S.D. dependent var 61.94886 S.E. of regression 67.14266     Akaike info criterion 11.51272 Sum squared resid 45081.37     Schwarz criterion 11.74873 Log likelihood -81.34538     Hannan-Quinn criter. 11.51020 F-statistic 0.479460     Durbin-Watson stat 1.711104 Prob(F-statistic) 0.750577 因为P值大于0.05，所以不存在自相关，所以模型为 Y=-31.86101+0.018655*X3-0.000876*X4 _1416128041.unknown _1416128586.unknown _1416141608.unknown _1416142285.unknown _1416141453.unknown _1416128138.unknown _1416127136.unknown _1416127146.unknown _1416123346.unknown