影响粮食产量的相关因素分析.doc

影响粮食产量的相关因素分析 为了研究中国影响粮食产量的各种因素，通过经济理论分析得出粮产量与以下四个因素有关 ，现建模如下：y=+1X1+2X2+3X3+4X4+UX1:农业机械总动力（万千瓦）X2：有效灌溉面积（千公顷）X3：化肥施用量（万吨）X4：农业从业人员（万人）Y:粮食总产量（万吨）数据资料如下：地区X1X2X3X4Y北 京 399.2328.217.969.7144.2 天 津 593.4353.216.679.7124.1 河 北 7000.44482.3270.61665.52551.1 山 西 1701.3110587658.3853.4 内蒙古 1350.32371.774.8524.31241.9 辽 宁 1339.81440.7109.8651.21140.0 吉 林 1015.41315.1112.1516.81638.0 黑龙江 1613.82032121.6744.12545.5 上 海 142.5285.919.384.6174.0 江 苏 2925.33900.9335.51480.23106.6 浙 江 1990.11403.289.71014.91217.7 安 徽 2975.93197.2253.22001.82472.1 福 建 873.3940.2123.3768.7854.7 江 西 902.31903.4106.9983.41614.6 山 东 7025.24824.9423.22462.63837.7 河 南 5780.64725.3419.53558.64101.5 湖 北 1414.02072.5247.11159.12218.5 湖 南 2209.72677.5182.22071.42767.9 广 东 1763.91478.5176.21570.11760.1 广 西 1467.91501.6157.81556.81528.5 海 南 200.9179.826.3177.2199.6 重 庆 586.5624.672921.51106.9 四 川 1679.72469212.62631.13372.0 贵 州 618.6653.471.31372.11161.3 云 南 1301.31403.4112.11674.31467.8 西 藏 114.51572.590.196.2 陕 西 1042.91308131.21002.21089.1 甘 肃 1056.9981.564.5697.5713.5 青 海 256.2211.47.2142.382.7 宁 夏 380.6398.823.6153.1252.7 新 疆 851.23094.379.2314.5783.7第一,进行OLS检验Dependent Variable: YMethod: Least SquaresDate: 05/16/04 Time: 14:53Sample: 1 31Included observations: 31VariableCoefficientStd. Errort-StatisticProb. X1-0.1362880.087494-1.5576810.1314X20.3015940.1348122.2371360.0341X35.5783721.9193772.9063450.0074X40.3595310.1519242.3665260.0257C79.59973119.36160.6668790.5107R-squared0.902706 Mean dependent var1490.890Adjusted R-squared0.887738 S.D. dependent var1141.343S.E. of regression382.4131 Akaike info criterion14.87757Sum squared resid3802234. Schwarz criterion15.10886Log likelihood-225.6023 F-statistic60.30791Durbin-Watson stat1.447710 Prob(F-statistic)0.000000从估计结果可以看出，模型拟合较好，可决系数R2=0.9027,表明模型在整体上拟合非常好。系数显著性检验：对于，T统计量为负，说明1未通过检验，即农业机械总动力对粮产量的影响不显著，初步决定删除X1。第二，从影响粮产量的因素来看，所选的四个解释变量与粮产量都有密切关系，因此它们之间可能具有较强的共线性，现进行多重共线性检验：（1）根据简单相关系数公式，该模型中四个解释变量得相关系数矩阵如图所示：X1X2X3X4X110.8820383578510.8633335592230.714970041093X20.88203835785110.9017697064170.731461937668X30.8633335592230.90176970641710.848157708636X40.7149700410930.7314619376680.8481577086361 由此可知，X2与X3的相关系数较高，说明它们之间可能存在共线性。（2）修正运用OLS方法逐一用Y对X1，X2，X3，X4回归Y 对X1回归 Dependent Variable: YMethod: Least SquaresDate: 05/16/04 Time: 15:00Sample: 1 31Included observations: 31VariableCoefficientStd. Errort-StatisticProb. X10.4964550.0736126.7442290.0000C648.9313180.30593.5990570.0012R-squared0.610658 Mean dependent var1490.890Adjusted R-squared0.597232 S.D. dependent var1141.343S.E. of regression724.3415 Akaike info criterion16.07074Sum squared resid15215448 Schwarz criterion16.16326Log likelihood-247.0965 F-statistic45.48463Durbin-Watson stat1.403900 Prob(F-statistic)0.000000Y 对X2回归Dependent Variable: YMethod: Least SquaresDate: 05/16/04 Time: 15:01Sample: 1 31Included observations: 31VariableCoefficientStd. Errort-StatisticProb. X20.7276330.0746099.7525610.0000C227.6144164.12191.3868620.1761R-squared0.766341 Mean dependent var1490.890Adjusted R-squared0.758284 S.D. dependent var1141.343S.E. of regression561.1372 Akaike info criterion15.56015Sum squared resid9131373. Schwarz criterion15.65266Log likelihood-239.1823 F-statistic95.11244Durbin-Watson stat0.880823 Prob(F-statistic)0.000000Y对 X3回归Dependent Variable: YMethod: Least SquaresDate: 05/16/04 Time: 15:02Sample: 1 31Included observations: 31VariableCoefficientStd. Errort-StatisticProb. X39.3661440.68493013.674600.0000C238.0023119.29351.9950980.0555R-squared0.865737 Mean dependent var1490.890Adjusted R-squared0.861108 S.D. dependent var1141.343S.E. of regression425.3585 Akaike info criterion15.00608Sum squared resid5246965. Schwarz criterion15.09860Log likelihood-230.5943 F-statistic186.9948Durbin-Watson stat1.848900 Prob(F-statistic)0.000000Y对 X4回归Dependent Variable: X4Method: Least SquaresDate: 05/16/04 Time: 15:02Sample: 1 31Included observations: 31VariableCoefficientStd. Errort-StatisticProb. Y0.6594240.0732169.0065220.0000C53.24803136.64990.3896680.6996R-squared0.736645 Mean dependent var1036.377Adjusted R-squared0.727564 S.D. dependent var876.9039S.E. of regression457.7038 Akaike info criterion15.15266Sum squared resid6075291. Schwarz criterion15.24518Log likelihood-232.8663 F-statistic81.11745Durbin-Watson stat1.402526 Prob(F-statistic)0.000000由此，X3的可决系数最高，说明Y对X3的线性关系最强，结合经济意义和统计检验，选出如下线性回归方程：Y=238.0023+9.366x3(1.995) (13.6746)R2=0.866 SE=425.3585 F=18609948以它为基础逐步回归：1,Y=230.705-0.054X1+10.112X3 (1.905) (-0.629) (70372) R2=0.868 SE=429.86 F=91.7492,Y=148.389-0.135X1+0.259X2+8.379X3(1.184) (-1.428) （1.798）（5.125）R2=0.882 SE=413.7 F=67.13,Y=79.599-0.136X1+0.302X2+5.578X3+0.359X4 (0.667) （-1.56）（2.237）（2.906） （2.367） R2=0.903 SE=382.413 F=60.308由此可见，X1对Y影响并不显著，现决定将X1删除，得如下模型：Dependent Variable: YMethod: Least SquaresDate: 05/16/04 Time: 15:19Sample: 1 31Included observations: 31VariableCoefficientStd. Errort-StatisticProb. X20.2026520.1220111.6609270.1083X34.8027461.9019962.5251070.0177X40.3582880.1558832.2984440.0295C125.2837118.71931.0552930.3006R-squared0.893626 Mean dependent var1490.890Adjusted R-squared0.881807 S.D. dependent var1141.343S.E. of regression392.3843 Akaike info criterion14.90227Sum squared resid4157066. Schwarz criterion15.08731Log likelihood-226.9853 F-statistic75.60752Durbin-Watson stat1.440474 Prob(F-statistic)0.000000第三，由于随机扰动项可能包含对粮产量的影响因素，从而使得随机扰动项可能出现自相关，现检验如下：(1)图示从图中可以看出，残差成线性自回归，说明随机扰动项存在自相关。（2） DW检验DW=1.44 DL=1.229 DU=1.650 无法确定是否存在自相关，需进一步检验（3） 修正由DW=1.44，算出=0.28。分别对Y,X2,X3,X4作广义差分得如下模型：Dependent Variable: DYMethod: Least SquaresDate: 05/16/04 Time: 15:56Sample(adjusted): 2 31Included observations: 30 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. DX20.2559810.1131952.2614080.0323DX34.1922081.7272702.4270720.0225DX40.3576790.1546272.3131720.0289C82.65742100.15920.8252600.4167R-squared0.892301 Mean dependent var1111.730Adjusted R-squared0.879874 S.D. dependent var1106.490S.E. of regression383.5008 Akaike info criterion14.86013Sum squared resid3823895. Schwarz criterion15.04695Log likelihood-218.9019 F-statistic71.80427Durbin-Watson stat1.818796 Prob(F-statistic)0.000000这时我们发现DW知在经过广义差分后有所提高，自相关消除。第四,由于样本数据的观测误差和模型设置的不正确性，随机误差项可能随某个解释变量的变化而变化，所以进行异方差检验。（1） 图示有图可知，该模型存在复杂型的异方差（2） 用对数变换法对该模型进行修正，得新模型如下：Dependent Variable: LYMethod: Least SquaresDate: 05/16/04 Time: 16:06Sample: 1 31Included observations: 31VariableCoefficientStd. Errort-StatisticProb. LX20.3721390.1427152.6075680.0147LX30.5200760.1412613.6816730.0010LX40.1373480.0852331.6114330.1187C1.0437000.6277731.6625440.1080R-squared0.933482 Mean dependent var6.857225Adjusted R-squared0.926091 S.D. dependent var1.148277S.E. of regression0.312173 Akaike info criterion0.629398Sum squared resid2.631209 Schwarz criterion0.814428Log likelihood-5.755664 F-statistic126.3013Durbin-Watson stat1.321994 Prob(F-statistic)0.000000经过对数变换后，该模型的可决系数有所提高，异方差消除。 通过上述检验和修正最后得出如下模型：LY=+2LX2+3LX3+4LX4+U令Y*=LY *= 2*=2 3*=3 4*=4 U*=U X2*=LX2 X3*=LX3 X4*=X4即：Y*=*+2*X2*+3*X3*+4*X4*+U*该模型剔除了无关的解释变量X1，并消除了多重共线性，自相关，异方差，从而具有较高的拟合优度，最后得出如下结论：粮产量与如下三个因素有关：有效灌溉面积，化肥施用量，农业从业人数。 学生：康 勤（40104034） 罗 丹（40104035） 田萍萍（40104036） 谢小英（40104037） 韦 蔚（40104033）