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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 X 0.852193 0.020150 42.29335 C 8.890886 3.604301 2.466744 Weighted Statistics R-squared 0.982425 Mean dependent var
Adjusted R-squared 0.981875 S.D. dependent var S.E. of regression 16.20273 Akaike info criterion Sum squared resid 8400.912 Schwarz criterion Log likelihood -141.9094 Hannan-Quinn criter. F-statistic 1788.728 Durbin-Watson stat Prob(F-statistic) 0.000000
Unweighted Statistics R-squared 0.954142 Mean dependent var
Adjusted R-squared 0.952709 S.D. dependent var S.E. of regression 258.5207 Sum squared resid 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
Prob. 0.0000 0.0192 230.2433 247.1718 8.465259 8.555045 8.495879 0.604647
1295.802 1188.791 2138654.
用White检验模型得：
Heteroskedasticity Test: White
F-statistic 7.462185 Prob. F(3,30) Obs*R-squared 14.52935 Prob. Chi-Square(3) Scaled explained SS 19.40139 Prob. Chi-Square(3)
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 C -7.684700 85.76169 -0.089605 WGT^2 64.20016 96.11160 0.667975 X^2*WGT^2 0.006306 0.003431 1.838317 X*WGT^2 -1.247222 1.163558 -1.071903
R-squared 0.427334 Mean dependent var
Adjusted R-squared 0.370067 S.D. dependent var S.E. of regression 345.6323 Akaike info criterion Sum squared resid 3583851. Schwarz criterion Log likelihood -244.8589 Hannan-Quinn criter. F-statistic 7.462185 Durbin-Watson stat Prob(F-statistic) 0.000712
从上图中可以看出，nR2=14.52935，比较计算的nR2=14.52935>
0.0007 0.0023 0.0002 Prob. 0.9292 0.5093 0.0759 0.2923 247.0857 435.4791 14.63876 14.81833 14.70000 1.586012
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。
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 X 0.778551 0.015677 49.66347 C 40.45770 14.57528 2.775775 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
Prob. 0.0000 0.0091 776.3266 367.3152 11.63881 11.72859 11.66943 1.178340
1295.802 1188.791 1045123.
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: 12/24/15 Time: 21:23 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. 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>
0.0014 0.0028 0.0000
Prob. 0.1633 0.2255 0.0009 5903.405 13934.64 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: 12/24/15 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