粮食产量影响因素的回归分析

第第#页共16页3=0089374,B5=0.091727。这表示当农业机械总动力增加一万千瓦，粮食产量减少0.089374万吨；受灾面积增加一公顷，粮食产量提高0.091727万吨。显然，这是与经济理论相矛盾，不符合实际意义。（二）统计推断检验可决系数R2=0.982669接近1，表明模型在整体上拟合优度很高。下面对各个变量进行t的显著性检验（n=16,k=6,在95%的显著性水平下查表得t的临界值t0.05=2.262）：1、播种面积对粮食产量的影响t=9.396472>t0.05说明粮食播种面积对粮食产量的影响显著2、有效灌溉面积对粮食产量的影响t=0.388566<t0.05说明有效灌溉面积对粮食产量的影响不显著3、农业机械总动力对粮食产量的影响t=-1.163420<t0.05说明农业机械总动力对粮食产量的影响不显著4、化肥施用量对粮食产量的影响t=7.495217>t0.05说明化肥施用量对粮食产量的影响显著5、受灾面积对粮食产量的影响t=1.231436<t0.05说明受灾面积对粮食产量的影响不显著6、成灾面积对粮食产量的影响t=-3.069621<t0.05说明成灾面积对粮食产量的影响不显著（三）计量经济的检验与修正I、多重共线性的检验用EVIEWS软件，得相关系数矩阵表：表3X1X2X3X4X5X6X11.000000-0.665790-0.772475-0.6323230.187816-0.074759X2-0.6657901.0000000.9710440.960485-0.1359010.173937X3-0.7724750.9710441.0000000.947631-0.2688680.048714X4-0.6323230.9604850.9476311.000000-0.1715000.095160X50.187816-0.135901-0.268868-0.1715001.0000000.905112X6-0.0747590.1739370.0487140.0951600.9051121.000000从上表可以看出，解释变量XI与X3、X2与X3、X2与X4、X3与X4、X5与X6之间的相关系数都比较大，可见存在严重的多重共线性。经济意义上，粮食播种面积、有效灌溉面积、农业机械总动力、化肥施用量、受灾面积和成灾面积都与粮食生产密切相关，所以它们之间存在严重的相关性。下面我们利用逐步回归法（变量剔除法）进行修正：表4DependentVariable:YMethod:LeastSquaresDate:06/22/11Time:16:46Sample:19902005Includedobservations:16

VariableCoefficientStd.Errort-StatisticProb.X41.6349990.9579881.7067010.1100C40444.713702.54710.923490.0000R-squared0.172226Meandependentvar46674.03AdjustedR-squared0.113099S.D.dependentvar2642.191S.E.ofregression2488.294Akaikeinfocriterion18.59305Sumsquaredresid86682489Schwarzcriterion18.68962Loglikelihood-146.7444F-statistic2.912827Durbin-Watsonstat0.795863Prob(F-statistic)0.109951根据调整后可决系数最大原则，选择X4为第一个选入的解释变量Y=1.634999461*X4+40444.71441表5DependentVariable:YMethod:LeastSquaresDate:06/22/11Time:16:51Sample:19902005Includedobservations:16VariableCoefficientStd.Errort-StatisticProb.X44.3607820.4662049.3538030.0000X10.6370690.0688999.2464700.0000C-39324.738739.218-4.4998000.0006R-squared0.890748Meandependentvar46674.03AdjustedR-squared0.873939S.D.dependentvar2642.191S.E.ofregression938.1100Akaikeinfocriterion16.69297Sumsquaredresid11440654Schwarzcriterion16.83783Loglikelihood-130.5438F-statistic52.99522Durbin-Watsonstat1.695692Prob(F-statistic)0.000001同理，Y=4.360781918*X4+0.6370685778*X1-39324.73173表6DependentVariable:YMethod:LeastSquaresDate:06/22/11Time:16:55Sample:19902005Includedobservations:16VariableCoefficientStd.Errort-StatisticProb.X44.4478630.26815916.586650.0000X10.6331480.03956116.004310.0000X6-0.1348270.025737-5.2387150.0002C-35740.955063.528-7.0585070.0000

R-squared0.966762Meandependentvar46674.03AdjustedR-squared0.958453S.D.dependentvar2642.191S.E.ofregression538.5602Akaikeinfocriterion15.62799Sumsquaredresid3480565.Schwarzcriterion15.82114Loglikelihood-121.0239F-statistic116.3455Durbin-Watsonstat1.526751Prob(F-statistic)0.000000同理，选取了X6为第三个解释变量，Y=4.447862661*X4+0.6331482891*X1-0.1348266189*X6-35740.94873在后面的逐步回归中调整后的可决系数X5最大，但与上一步的调整后的可决系数相比，拟合优度变化很不显著，则说明新引入的变量与其它变量之间存在共线性关系，逐步回归终止。所以最终的回归模型为Y=4.447862661*X4+0.6331482891*X1-0.1348266189*X6-35740.94873(16.58665)(16.00431)(-5.238715)(-7.058507)R2=0.966762R2=0.958453F-statistic=116.3455DW=1.526751II、异方差性的检验多重共线性检验后原模型还剩下粮食播种面积X1、化肥施用量X4和成灾面积X6,模型形式如下：Y=C+B1X1+B4X4+B6X6+U1、图示检验法既可用Y-X的散点图进行判断，也可用e2-X的散点图进行判断。对前者看是否存在明显的散点扩大、缩小或复杂型趋势(即不存在一个固定的带型域中)(1)^2(1)^2随X1的增大而增大(2)随X4的增大而增大X4X4（3）2随X6的变化呈复杂形式2、Goldfeld-Guandt法将本样本观测值按升序排列，的样本观测值按原来与的对应关系排列，略去中心约1/4即4个样本观测值，将剩下的12个样本观测值分成容量相近的两个子样本，每个子样本观测值个数分别为6，6，将所得结果列表如下：YY1（粮食播种面积）Y4（化肥施用量）Y6（成灾面积）SIG1(199O-1995)1830.62404408851.9701238242280.78788980SIG2(2000-2005)3554.357608541666.145757352566.06321608F2.5768322.9128270.940338经比较，发现Y1,Y4和Y6均存在异方差用加权最小二乘法WLS进行修正。

修正Y(权重w=l/e2)OLS结果：表7：DependentVariable:YMethod:LeastSquaresDate:06/23/11Time:13:15VariableCoefficientStd.Errort-StatisticProb.X10.6331480.03956116.004310.0000X44.4478630.26815916.586650.0000VariableCoefficientStd.Errort-StatisticProb.X10.6331480.03956116.004310.0000X44.4478630.26815916.586650.0000X6-0.1348270.025737-5.2387150.0002C-35740.955063.528-7.0585070.0000R-squared0.966762Meandependentvar46674.03AdjustedR-squared0.958453S.D.dependentvar2642.191Akaikeinfocriterion538.560215.62799Sample:19902005Includedobservations:16S.E.ofregressionSumsquaredresidLoglikelihoodDurbin-Watsonstat3480565.-121.02391.526751SchwarzcriterionF-statisticProb(F-statistic)15.82114116.34550.000000Y=4.447862661*X4+0.6331482891*X1-0.1348266189*X6-35740.94873(16.58665)(16.00431)(-5.238715)(-7.058507)R2=0.966762R2=0.958453F-statistic=116.3455DW=1.526751WLS结果:表8：DependentVariable:YMethod:LeastSquaresDate:06/23/11Time:13:22Sample:19902005Includedobservations:16Weightingseries:WVariableCoefficientStd.Errort-StatisticProb.X10.6336420.00724087.521990.0000X44.5666210.21299321.440250.0000X6-0.1213080.004584-26.462750.0000

C-36627.731780.393-20.572830.0000WeightedStatisticsR-squared1.000000Meandependentvar47630.45AdjustedR-squared1.000000S.D.dependentvar93785.71S.E.ofregression43.55001Akaikeinfocriterion10.59801Sumsquaredresid22759.24Schwarzcriterion10.79116Loglikelihood-80.78412F-statistic40873.93Durbin-Watsonstat2.139284Prob(F-statistic)0.000000UnweightedStatisticsR-squared0.964813Meandependentvar46674.03AdjustedR-squared0.956016S.D.dependentvar2642.191S.E.ofregression554.1276Sumsquaredresid3684689.Durbin-Watsonstat1.842142Y=0.6336415971*X1+4.566621221*X4-0.1213084647*X6-36627.72591(87.52199)(21.44025)(-26.46275)(-20.57283)R2=1.000000R2=1.000000F-statistic=40873.93DW=2.139284可以看出，无论是拟合优度，还是各参数的t统计量的值都有了显著的改进。III、序列相关性的检验1、图示检验法1000-1000500--500-E-1000-5000500100010"由于残差e可以作为u的估计，因此，如果u1000-1000500--500-E-1000-5000500100010"有图形我们很难判断模型是否存在序列相关性2、杜宾-瓦森(Durbin-Watson)检验法

已知:DW=1.526751;又查表得DL=0.86,DU=1.73（n=16,k=4,包含常数项）所以，DL〈DW〈DU，不能确定模型的自相关状态用广义差分法进行修正由DW=1.526751,得到一阶自相关系数得估计值l—DW/2=0.2366245修正结果如下表表9：DependentVariable:DYMethod:LeastSquaresDate:06/23/11Time:14:08Sample(adjusted):19912005Ineludedobservations:15afteradjustingendpointsVariableCoefficientStd.Errort-StatisticProb.R-squared0.963279AdjustedR-squaredR-squared0.963279AdjustedR-squared0.953264S.E.ofregression502.7214Sumsquaredresid2780017.Loglikelihood-112.2585Durbin-Watsonstat2.196799Meandependentvar35793.72S.D.dependentvar2325.429Akaikeinfoeriterion15.50113Sehwarzeriterion15.68994F-statistie96.18567Prob(F-statistic)0.000000DX10.6217650.04490113.84746DX44.1312660.36422711.34256DX6-0.1497090.026196-5.715020C-25056.224557.361-5.4979670.00000.00000.00010.0002在5%的显著性水平下，DW=2.196799，故，DU〈DW〈4-DU,已不存在自相关这时，新方程为：DY=0.6217646959*DX1+4.131265608*DX4-0.1497094008*DX6—(13.84746)(11.34256)(-5.715020)25056.2213(-5.497967)R2=0.963279R2=0.953264F-statistic=96.18567DW=2.196799

1000500-40000-38000-36000-34000-32000-30000-10001000500-40000-38000-36000-34000-32000-30000919293949596979899000102030405ResidualActualFitted六、模型的分析我们进行了一系列检验和修正后的最终结果如下：Y=0.6217646959*X1+4.131265608*X4-0.1497094008*X6-(13.84746)(11.34256)(-5.715020)25056.2213(-5.497967)R2=0.963279R2=0.953264F-statistic=96.18567DW=2.196799从模型中可看出：1、X2、X3、X5不符合经济意义的检验，因为粮食产量是随着有效灌溉面积和机械总动力的投入的增加而提高的，是随着受灾面积的增加而降低的。所以最新模型的剔除了这三个在原模型中的解释变量；2、新的模型表明：粮食播种面积每增加一个单位，粮食产量提高0.6217646959万吨;多投入一万公斤的化肥，粮食增产4.131265608万吨；而成灾面积每增加一公顷，粮食减产0.1497094008万吨。3、可见，化肥使用量是影响粮食产量的显著性因素。但从经济意义上来说，施肥过度反而会导致谷物死亡，粮食减产。4、同时从模型中可以看出，随机扰动项的数值很大，说明模型中未包含的其它随机变量，比如说政府政策，农业劳动力等都会对粮食产量产生很大影响。5、所以我们的模型所反映的经济意义不能包含现实中的每一种情况。七、政策建议我们知道农业是一个国民经济的基础，而粮食则是基础的基