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 S.E. of regression 11636.97 Akaike info criterion Sum squared resid 4.20E+09 Schwarz criterion Log likelihood -364.9796 Hannan-Quinn criter.

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 21.64586 21.78054 21.69179

F-statistic 8.158958 Durbin-Watson stat Prob(F-statistic) 0.001423

从上图中可以看出，nR2=11.72514，比较计算的nR2=11.72514>

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 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

为因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 X 0.641197 0.092678 6.918569 P -1.206222 1.114278 -1.082514 C 795.6887 603.8605 1.317670

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. 0.0000 0.3044 0.2170