全国各地区可支配收入与消费性支出异方差检验综合案例分析

1、全国各地区可支配收入与消费性支出异方差检验综合案例分析小组成员：翟丽萍指导老师：毛锦凰张丹 穆小斌 王淏珑 孙琴令 冶贵花2009年全国各地区城镇居民平均每人全年家庭可支配收入与消费性支出数据来源：中经网利用Yi=0+1Xi+i形式的线性模型研究全国各地区城镇居民平均每人全年家庭可支配收入与消费性支出的影响情况，并检验模型的异方差情况。1.线性回归结果󰀀󰀀Dependent Variable: Y Method: Least Squares Date: 10/28/13 Time: 22:37 Sample: 20 31Included observations

2、: 12Variable X CR-squaredCoefficient0.646420 1280.351Std. Error0.067014 1392.994t-Statistic9.646057 0.919136Prob. 0.0000 0.379714419.60 3091.470 16.82441 16.90523 16.79449 1.8421780.902956 Mean dependent var 0.893252 S.D. dependent var 1010.055 Akaike info criterion 10202108 Schwarz criterion -98.94

3、645 Hannan-Quinn criter. 93.04641 Durbin-Watson stat 0.000002Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)根据回归结果可得到下面的估计方程： Y=1280.351+0.646420X (0.919136) (9.646057)R2=0.902956 DW=1.842178 F=93.04641 R2接近于1，表明模型的拟合效果非常好；F检验的相伴概率为0.000000，反映变量间呈

4、高度线性，方程回归效果显著。利用回归方程可以分析各个自变量的边际效应，X变量的系数为0.646420，说明在其他变量保持不变的情况下，每增加一个单位的城镇居民平均每人全年家庭可支配收入，就要增加0.646420个单位的食品性支出。2.Y和X的散点图30,00027,50025,00022,50020,00017,50015,00012,50010,000XY从上图可以看出，消费性支出随着城镇居民平均每人全年家庭可支配收入的增加而增加。但是，值得注意的是随着可支配收入增加，消费性支出的变动幅度也增大了，可能存在异方差。3.E2和X散点图30,00027,50025,00022,50020,000

5、17,50015,00012,50010,000E2X从上图可以看出，残差平方随着的城镇居民平均每人全年家庭可支配收入增加而不规则变化，表明不同的城镇居民平均每人全年家庭可支配收入，消费性支出的方差是不同的，从而模型中随机误差不是常数，存在异方差现象。4.怀特检验结果󰀀󰀀Heteroskedasticity Test: White4.170152 Prob. F(2,28) 7.114674 Prob. Chi-Square(2) 4.350479 Prob. Chi-Square(2)0.0260 0.0285 0.1136F-statisticObs*R-s

6、quared Scaled explained SSTest Equation:Dependent Variable: RESID2 Method: Least SquaresDate: 10/28/13 Time: 22:52 Sample: 1 31Included observations: 31Variable C X X2Coefficient-3677786. 420.3678 -0.009405Std. Error1905234. 207.6375 0.005277t-Statistic-1.930359 2.024527 -1.782297Prob.0.0637 0.0525

7、0.0855502421.5 603751.5 29.35975 29.49852 29.40499 2.983131R-squared0.229506 Mean dependent var 0.174470 S.D. dependent var 548560.5 Akaike info criterion 8.43E+12 Schwarz criterion -452.0761 Hannan-Quinn criter. 4.170152 Durbin-Watson stat 0.025988Adjusted R-squared S.E. of regression Sum squared r

8、esid Log likelihood F-statistic Prob(F-statistic)从表中可以看到N* R²=7.114686，自由度为2的c²分布在5%的显著性水平下对应的临界值为5.99，很显然7.114686>5.99 ，则拒绝原假设，即模型存在异方差。 5.Goldfeld-Quandt检验方法前12个样本的OLS回归结果󰀀󰀀Dependent Variable: Y Method: Least Squares Date: 10/28/13 Time: 22:56 Sample: 1 12Included obse

9、rvations: 12VariableCoefficientStd. Errort-Statistic Prob.X C0.615224 1485.8750.226020 3008.7292.721988 0.4938550.0215 0.63219662.787 733.0866 15.72431 15.80513 15.69439 2.700706R-squared0.425592 Mean dependent var 0.368151 S.D. dependent var 582.7228 Akaike info criterion 3395658. Schwarz criterion

10、 -92.34587 Hannan-Quinn criter. 7.409217 Durbin-Watson stat 0.021487Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)后12个样本的OLS回归结果󰀀󰀀Dependent Variable: Y Method: Least Squares Date: 10/28/13 Time: 22:58 Sample: 20 31Included observa

11、tions: 12Variable X CR-squaredAdjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)Coefficient0.646420 1280.351Std. Error0.067014 1392.994t-Statistic9.646057 0.919136Prob.0.0000 0.379714419.60 3091.470 16.82441 16.90523 16.79449 1.8421780.902956 Mean de

12、pendent var 0.893252 S.D. dependent var 1010.055 Akaike info criterion 10202108 Schwarz criterion -98.94645 Hannan-Quinn criter. 93.04641 Durbin-Watson stat 0.000002进行F检验：F=10202108/3395658=3.004457,F0.05(10,10)=2.97,因此，很明显的可以得到样本存在异方差性的结论。6.加权最小二乘估计结果󰀀󰀀Dependent Variable: Y Method:

13、Least Squares Date: 10/28/13 Time: 23:02 Sample: 1 31Included observations: 31 Weighting series: WIWeight type: Inverse standard deviation (EViews default scaling)Variable X CR-squaredCoefficient0.652320 988.4306Std. Error0.014164 213.6569t-Statistic46.05412 4.62625110822.76 59573.16 4.639305 4.7318

14、20 4.669463 1.688227 10828.2111628.97 2978.791 15730220Prob. 0.0000 0.0001Weighted Statistics0.986512 Mean dependent var 0.986046 S.D. dependent var 2.385822 Akaike info criterion 165.0722 Schwarz criterion -69.90923 Hannan-Quinn criter. 2120.982 Durbin-Watson stat 0.000000 Weighted mean dep. Unweighted Statistics0.940907 Mean dependent var 0.938870 S.D. dependent var 736.4926 Sum squared resid 1.990927Adjusted R-squared S.E. of regression Sum squared re