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1、建立国民总收入Y关于能源消费总量X的回归模型，并进行回归分析年份国民总收入（亿元）能源消费总量（万吨）19783645.2174745714419794062.5791915871819804545.6239736027519814889.4610626345019825330.4509656653219835985.55156869813198410743.7517273191198514340.7365876682198620274.3792281043198726805.6151385895198835036.8230190647198941000.9191194238199046718
2、.3223898703199154826.19941103783199258937.27645109170199366260.02471115993199468108.45644122737199575310.52921131176199676842.49165135192199778060.835135909199883024.27977136184199988479.15475140569200098000.454311455312001108068.22061504062002119095.68931594312003148173.97611837922004183586.7479213
3、4562005225808.5592359972006256522.66982586762007287763.65882805082008306228.82482914482009323464.6903306647资料来源：国家统计年鉴2011解：根据经济理论和对实际情况的分析可发现，国民总收入水平Y与能源消费总量X有关，因此我们设定回归模型为 被解释变量：Y国民总收入水平 解释变量：X能源消费总量应用Eviews的最小二乘法程序，输出的结果如下Dependent Variable: YMethod: Least SquaresDate: 12/15/11 Time: 14:17Sample:
4、 1978 2009Included observations: 32CoefficientStd. Errort-StatisticProb.C-84796.842971.040-28.541130.0000X1.3024520.01943367.023510.0000R-squared0.993366Mean dependent var91560.69Adjusted R-squared0.993145S.D. dependent var94262.20S.E. of regression7804.515Akaike info criterion20.82325Sum squared re
5、sid1.83E+09Schwarz criterion20.91486Log likelihood-331.1721Hannan-Quinn criter.20.85362F-statistic4492.151Durbin-Watson stat0.220564Prob(F-statistic)0.000000散点图由上表得到估计的回归方程为 1. 检验根据R-squared=0.993366接近于1，所以此组数据拟合度较好。2. 回归方程的显著性检验（F检验）提出检验的原假设 H0：=0根据上表的结果可知n=32，k=1F=4492.151对于给定的显著性水平=0.05，从附录4的表3中，
6、查出分子自由度1，分母自由度为30的F分布上侧分位数F0.05（1,30）=4.17。因为F=4492.1514.17，所以否定H0,总体回归方程存在显著的线性关系，即在国民收入水平和能源消费总量之间的线性关系是显著的。3. 解释变量的显著性检验（t检验）首先提出检验的原假设 H0：=0根据上表的计算结果可知 =67.02351对于给定的显著性水平=0.05，从附录4的表1中，查出t分布的自由度为v=30的双侧分位数（30）=2.04。因为II=67.02351（30）=2.04，所以否定H0，显著不等于0，即可认为能源消费总量对国民收入水平有显著的影响。4. 异方差检验对原数据的最小二乘估计
7、进行怀特检验Heteroskedasticity Test: WhiteF-statistic0.172872Prob. F(2,29)0.8421Obs*R-squared0.377015Prob. Chi-Square(2)0.8282Scaled explained SS0.207551Prob. Chi-Square(2)0.9014Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 12/15/11 Time: 14:23Sample: 1978 2009Included observations: 3
8、2CoefficientStd. Errort-StatisticProb.C66267721613174841.0807310.2887X-213.2341840.3359-0.2537490.8015X20.0008430.0023840.3536330.7262R-squared0.011782Mean dependent var57103548Adjusted R-squared-0.056371S.D. dependent var64935804S.E. of regression66740970Akaike info criterion38.95960Sum squared res
9、id1.29E+17Schwarz criterion39.09701Log likelihood-620.3535Hannan-Quinn criter.39.00514F-statistic0.172872Durbin-Watson stat0.473428Prob(F-statistic)0.842106由上表可知：Obs*R-squared=0.37701520.05（2）=5.991因为=0.37701520.05（2）=5.991，所以结论是该回归模型中不存在异方差。5. 自相关检验提出假设H0：=0（不存在自相关）H1:：0（存在一阶自相关）根据上表的结果可知 DW=0.2205
10、64=1.37，=1.50,4-=2.50,4-=2.63DW=0.220564在（0,）之间，拒绝原假设H0=0,认为存在一阶正自相关。克服自相关根据上表可知DW=0.220564=1-=1-=0.889718对原变量做广义差分变换。令，得年份国民总收入（亿元）(GDY)能源消费总量（万吨）(GDX)1979819.36359047875.9546081980931.07414078032.5384761981845.13759169822.247551982980.209447610079.392919831242.95339710618.2820219845418.29874811077
11、.1172719854781.82728911562.6498619867515.16774712817.6443219878767.13499713789.58413198811187.3847314224.6723919899828.02701213587.73245199010239.0666314857.75512199113260.0670615965.16425199210157.4199616832.39681199313822.4689918862.4859419949155.71977619535.94003199514713.2095621974.6818319969837
12、.35822518482.3516319979692.68700715626.24414199813572.1497815263.31634199914610.958619403.64389200019278.957720464.23046200120875.4523520924.44974200222945.4482225612.07449200342212.3976841943.36954200451753.6942149932.94934200562468.1247846081.35459200655616.7303548705.22115200759530.8220350359.30663200850200.3178941874.98326200951007.3927347340.46834以、，（1979-2009）为样本再次回归，得Dependent Variable: YMethod: Least SquaresDate: 12/15/11 Time: 14:29Sample: 1979 2009Included observations: 31CoefficientStd. Errort-StatisticProb.
