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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: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=91.749 2,Y=148.389-0.135X1+0.259X2+8.379X3 (1.184) (-1.428) (1.798) (5.125) R2=0.882 SE=413.7 F=67.1 3,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: Lea
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