Weighted Statistics R-squared 0.987192 Mean dependent var
Adjusted R-squared 0.986792 S.D. dependent var S.E. of regression 79.19828 Akaike info criterion Sum squared resid 200715.8 Schwarz criterion Log likelihood -195.8597 Hannan-Quinn criter. F-statistic 2466.460 Durbin-Watson stat Prob(F-statistic) 0.000000
Unweighted Statistics R-squared 0.977590 Mean dependent var
Adjusted R-squared 0.976890 S.D. dependent var S.E. of regression 180.7210 Sum squared resid 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)
Obs*R-squared 11.72514 Prob. Chi-Square(2) Scaled explained SS 28.08353 Prob. Chi-Square(2)
Test Equation: Dependent Variable: WGT_RESID^2 Method: Least Squares Date: 12/10/14 Time: 13:23 Sample: 1 34 Included observations: 34 Collinear test regressors dropped from specification
Variable Coefficient Std. Error t-Statistic C -7585.186 5311.263 -1.428132 WGT^2 2468.369 1996.041 1.236632 X^2*WGT^2 0.009139 0.002481 3.684177
R-squared 0.344857 Mean dependent var
Adjusted R-squared 0.302590 S.D. dependent var
776.3266 367.3152 11.63881 11.72859 11.66943 1.178340
1295.802 1188.791 1045123.
0.0014 0.0028 0.0000 Prob. 0.1633 0.2255 0.0009 5903.405 13934.64
S.E. of regression 11636.97 Akaike info criterion Sum squared resid 4.20E+09 Schwarz criterion Log likelihood -364.9796 Hannan-Quinn criter. F-statistic 8.158958 Durbin-Watson stat Prob(F-statistic) 0.001423
2
从上图中可以看出，nR=11.72514，比较计算的nR2=11.72514>
21.64586 21.78054 21.69179 2.344068
统计量的临界值，因为
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: 12/11/14 Time: 09:54 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: 12/11/14 Time: 09:55 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，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: 12/12/14 Time: 19:26 Sample: 1 34 Included observations: 34
Variable Coefficient Std. Error t-Statistic Prob. X 0.741684 0.019905 37.26095
0.0000
为因P 0.235025 0.271701 0.865012 C 43.41715 71.22946 0.609539 R-squared 0.979911 Mean dependent var
Adjusted R-squared 0.978615 S.D. dependent var S.E. of regression 173.8449 Akaike info criterion Sum squared resid 936883.7 Schwarz criterion Log likelihood -222.0511 Hannan-Quinn criter. F-statistic 756.0627 Durbin-Watson stat 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: 12/14/14 Time: 19:26 Sample: 1 13 Included observations: 13
Variable Coefficient Std. Error t-Statistic X -0.170484 0.203868 -0.836247 Y 0.458660 0.209755 2.186646 C 59.50496 7.385841 8.056627 R-squared 0.956255 Mean dependent var
Adjusted R-squared 0.947506 S.D. dependent var S.E. of regression 8.466678 Akaike info criterion Sum squared resid 716.8464 Schwarz criterion Log likelihood -44.51063 Hannan-Quinn criter. F-statistic 109.2993 Durbin-Watson stat Prob(F-statistic) 0.000000
2 得∑e1i=716.8464
②当样本为22-34时，做回归分析得： Dependent Variable: Y Method: Least Squares Date: 12/14/14 Time:20:39 Sample: 22 34 Included observations: 13
Variable Coefficient Std. Error t-Statistic
0.3937
0.5466 1295.802 1188.791 13.23830 13.37298 13.28423 1.681521
Prob. 0.4225 0.0536 0.0000 135.3231 36.95380 7.309328 7.439701 7.282530 0.637181
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
2 得∑e2i=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: 12/12/14 Time: 19:31 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
