多元线性回归模型案例

我国农民收入影响因素的回归 分析 定性数据统计分析pdf销售业绩分析模板建筑结构震害分析销售进度分析表京东商城竞争战略分析 本文力图应用适当的多元线性回归模型,对有关农民收入的历史数据和现状进行分析,探讨影响农民收入的主要因素,并在此基础上对如何增加农民收入提出相应的政策建议。 农民收入水平的度量常采用人均纯收入指标。影响农民收入增长的因素是多方面的，既有结构性矛盾因素，又有体制性障碍因素。但可以归纳为以下几个方面：一是农产品收购价格水平。二是农业剩余劳动力转移水平。三是城市化、工业化水平。四是农业产业结构状况。五是农业投入水平。考虑到复杂性和可行性，所以对农业投入与农民收入，本文暂不作讨论。因此，以全国为例，把农民收入与各影响因素关系进行线性回归分析，并建立数学模型。一、计量经济模型分析(一)、数据搜集根据以上分析，我们在影响农民收入因素中引入7个解释变量。即：-财政用于农业的支出的比重，-第二、三产业从业人数占全社会从业人数的比重，-非农村人口比重，-乡村从业人员占农村人口的比重，-农业总产值占农林牧总产值的比重，-农作物播种面积，—农村用电量。 　 y x2 x3 x4 x5 x6 x7 x8 年份 78年可比价 比重 % % 比重 比重 千公顷 亿千瓦时 1986 133.60 13.43 29.50 17.92 36.01 79.99 150104.07 253.10 1987 137.63 12.20 31.30 19.39 38.62 75.63 146379.53 320.80 1988 147.86 7.66 37.60 23.71 45.90 69.25 143625.87 508.90 1989 196.76 9.42 39.90 26.21 49.23 62.75 146553.93 790.50 1990 220.53 9.98 39.90 26.41 49.93 64.66 148362.27 844.50 1991 223.25 10.26 40.30 26.94 50.92 63.09 149585.80 963.20 1992 233.19 10.05 41.50 27.46 51.53 61.51 149007.10 1106.90 1993 265.67 9.49 43.60 27.99 51.86 60.07 147740.70 1244.90 1994 335.16 9.20 45.70 28.51 52.12 58.22 148240.60 1473.90 1995 411.29 8.43 47.80 29.04 52.41 58.43 149879.30 1655.70 1996 460.68 8.82 49.50 30.48 53.23 60.57 152380.60 1812.70 1997 477.96 8.30 50.10 31.91 54.93 58.23 153969.20 1980.10 1998 474.02 10.69 50.20 33.35 55.84 58.03 155705.70 2042.20 1999 466.80 8.23 49.90 34.78 57.16 57.53 156372.81 2173.45 2000 466.16 7.75 50.00 36.22 59.33 55.68 156299.85 2421.30 2001 469.80 7.71 50.00 37.66 60.62 55.24 155707.86 2610.78 2002 468.95 7.17 50.00 39.09 62.02 54.51 154635.51 2993.40 2003 476.24 7.12 50.90 40.53 63.72 50.08 152414.96 3432.92 2004 499.39 9.67 53.10 41.76 65.64 50.05 153552.55 3933.03 2005 521.20 7.22 55.20 42.99 67.59 49.72 155487.73 4375.70资料来源《中国统计年鉴2006》。(二)、计量经济学模型建立我们设定模型为下面所示的形式：利用Eviews软件进行最小二乘估计，估计结果如下表所示： DependentVariable:Y Method:LeastSquares Sample:19862004 Includedobservations:19 Variable Coefficient Std.Error t-Statistic Prob. C -1102.373 375.8283 -2.933184 0.0136 X1 -6.635393 3.781349 -1.754769 0.1071 X3 18.22942 2.066617 8.820899 0.0000 X4 2.430039 8.370337 0.290316 0.7770 X5 -16.23737 5.894109 -2.754847 0.0187 X6 -2.155208 2.770834 -0.777819 0.4531 X7 0.009962 0.002328 4.278810 0.0013 X8 0.063389 0.021276 2.979348 0.0125 R-squared 0.995823 Meandependentvar 345.5232 AdjustedR-squared 0.993165 S.D.dependentvar 139.7117 S.E.ofregression 11.55028 Akaikeinfocriterion 8.026857 Sumsquaredresid 1467.498 Schwarzcriterion 8.424516 Loglikelihood -68.25514 F-statistic 374.6600 Durbin-Watsonstat 1.993270 Prob(F-statistic) 0.000000表1最小二乘估计结果回归 分析报告 成本分析报告下载顾客满意度调查结果及分析报告员工思想动态分析报告期中考试质量分析报告高一期中考试质量分析报告 为：二、计量经济学检验(一)、多重共线性的检验及修正①、检验多重共线性(a)、直观法从“表1最小二乘估计结果”中可以看出，虽然模型的整体拟合的很好，但是x4x6的t统计量并不显著，所以可能存在多重共线性。(b)、相关系数矩阵 X2 X3 X4 X5 X6 X7 X8 X2 1.000000 -0.717662 -0.695257 -0.731326 0.737028 -0.332435 -0.594699 X3 -0.717662 1.000000 0.922286 0.935992 -0.945701 0.742251 0.883804 X4 -0.695257 0.922286 1.000000 0.986050 -0.937751 0.753928 0.974675 X5 -0.731326 0.935992 0.986050 1.000000 -0.974750 0.687439 0.940436 X6 0.737028 -0.945701 -0.937751 -0.974750 1.000000 -0.603539 -0.887428 X7 -0.332435 0.742251 0.753928 0.687439 -0.603539 1.000000 0.742781 X8 -0.594699 0.883804 0.974675 0.940436 -0.887428 0.742781 1.000000表2相关系数矩阵从“表2相关系数矩阵”中可以看出，个个解释变量之间的相关程度较高，所以应该存在多重共线性。②、多重共线性的修正——逐步迭代法A、一元回归 DependentVariable:Y Method:LeastSquares Sample:19862004 Includedobservations:19 Variable Coefficient Std.Error t-Statistic Prob. C 820.3133 151.8712 5.401374 0.0000 X2 -51.37836 16.18923 -3.173614 0.0056 R-squared 0.372041 Meandependentvar 345.5232 AdjustedR-squared 0.335102 S.D.dependentvar 139.7117 S.E.ofregression 113.9227 Akaikeinfocriterion 12.40822 Sumsquaredresid 220632.4 Schwarzcriterion 12.50763 Loglikelihood -115.8781 F-statistic 10.07183 Durbin-Watsonstat 0.644400 Prob(F-statistic) 0.005554表3y对x2的回归结果 DependentVariable:Y Method:LeastSquares Sample:19862004 Includedobservations:19 Variable Coefficient Std.Error t-Statistic Prob. C -525.8891 64.11333 -8.202492 0.0000 X3 19.46031 1.416043 13.74274 0.0000 R-squared 0.917421 Meandependentvar 345.5232 AdjustedR-squared 0.912563 S.D.dependentvar 139.7117 S.E.ofregression 41.31236 Akaikeinfocriterion 10.37950 Sumsquaredresid 29014.09 Schwarzcriterion 10.47892 Loglikelihood -96.60526 F-statistic 188.8628 Durbin-Watsonstat 0.598139 Prob(F-statistic) 0.000000表4y对x3的回归结果 DependentVariable:Y Method:LeastSquares Sample:19862004 Includedobservations:19 Variable Coefficient Std.Error t-Statistic Prob. C -223.1905 69.92322 -3.191937 0.0053 X4 18.65086 2.242240 8.317956 0.0000 R-squared 0.802758 Meandependentvar 345.5232 AdjustedR-squared 0.791155 S.D.dependentvar 139.7117 S.E.ofregression 63.84760 Akaikeinfocriterion 11.25018 Sumsquaredresid 69300.77 Schwarzcriterion 11.34959 Loglikelihood -104.8767 F-statistic 69.18839 Durbin-Watsonstat 0.282182 Prob(F-statistic) 0.000000表5y对x4的回归结果 DependentVariable:Y Method:LeastSquares Sample:19862004 Includedobservations:19 Variable Coefficient Std.Error t-Statistic Prob. C -494.1440 118.1449 -4.182526 0.0006 X5 15.77978 2.198711 7.176832 0.0000 R-squared 0.751850 Meandependentvar 345.5232 AdjustedR-squared 0.737253 S.D.dependentvar 139.7117 S.E.ofregression 71.61463 Akaikeinfocriterion 11.47978 Sumsquaredresid 87187.14 Schwarzcriterion 11.57919 Loglikelihood -107.0579 F-statistic 51.50691 Durbin-Watsonstat 0.318959 Prob(F-statistic) 0.000002表6y对x5的回归结果 DependentVariable:Y Method:LeastSquares Sample:19862004 Includedobservations:19 Variable Coefficient Std.Error t-Statistic Prob. C 1288.009 143.8088 8.956395 0.0000 X6 -15.52398 2.351180 -6.602635 0.0000 R-squared 0.719448 Meandependentvar 345.5232 AdjustedR-squared 0.702945 S.D.dependentvar 139.7117 S.E.ofregression 76.14674 Akaikeinfocriterion 11.60250 Sumsquaredresid 98571.54 Schwarzcriterion 11.70192 Loglikelihood -108.2238 F-statistic 43.59479 Durbin-Watsonstat 0.395893 Prob(F-statistic) 0.000004表7y对x6的回归结果 DependentVariable:Y Method:LeastSquares Sample:19862004 Includedobservations:19 Variable Coefficient Std.Error t-Statistic Prob. C -4417.766 681.1678 -6.485577 0.0000 X7 0.031528 0.004507 6.994943 0.0000 R-squared 0.742148 Meandependentvar 345.5232 AdjustedR-squared 0.726980 S.D.dependentvar 139.7117 S.E.ofregression 73.00119 Akaikeinfocriterion 11.51813 Sumsquaredresid 90595.96 Schwarzcriterion 11.61754 Loglikelihood -107.4222 F-statistic 48.92923 Durbin-Watsonstat 0.572651 Prob(F-statistic) 0.000002表8y对x7的回归结果 DependentVariable:Y Method:LeastSquares Sample:19862004 Includedobservations:19 Variable Coefficient Std.Error t-Statistic Prob. C 140.1625 28.96616 4.838835 0.0002 X8 0.119827 0.014543 8.239503 0.0000 R-squared 0.799739 Meandependentvar 345.5232 AdjustedR-squared 0.787959 S.D.dependentvar 139.7117 S.E.ofregression 64.33424 Akaikeinfocriterion 11.26536 Sumsquaredresid 70361.21 Schwarzcriterion 11.36478 Loglikelihood -105.0209 F-statistic 67.88941 Durbin-Watsonstat 0.203711 Prob(F-statistic) 0.000000表9y对x8的回归结果综合比较表3~9的回归结果，发现加入x3的回归结果最好。以x3为基础顺次加入其他解释变量，进行二元回归，具体的回归结果如下表10~15所示： DependentVariable:Y Method:LeastSquares Sample:19862004 Includedobservations:19 Variable Coefficient Std.Error t-Statistic Prob. C -754.4481 149.1701 -5.057637 0.0001 X3 21.78865 1.932689 11.27375 0.0000 X2 13.45070 8.012745 1.678663 0.1126 R-squared 0.929787 Meandependentvar 345.5232 AdjustedR-squared 0.921010 S.D.dependentvar 139.7117 S.E.ofregression 39.26619 Akaikeinfocriterion 10.32254 Sumsquaredresid 24669.34 Schwarzcriterion 10.47167 Loglikelihood -95.06417 F-statistic 105.9385 Durbin-Watsonstat 0.595954 Prob(F-statistic) 0.000000表10加入x2的回归结果 DependentVariable:Y Method:LeastSquares Sample:19862004 Includedobservations:19 Variable Coefficient Std.Error t-Statistic Prob. C -508.6781 75.73220 -6.716802 0.0000 X3 17.88200 3.752121 4.765837 0.0002 X4 1.753351 3.844305 0.456090 0.6545 R-squared 0.918481 Meandependentvar 345.5232 AdjustedR-squared 0.908291 S.D.dependentvar 139.7117 S.E.ofregression 42.30965 Akaikeinfocriterion 10.47185 Sumsquaredresid 28641.71 Schwarzcriterion 10.62097 Loglikelihood -96.48254 F-statistic 90.13613 Durbin-Watsonstat 0.596359 Prob(F-statistic) 0.000000表11加入x4的回归结果 DependentVariable:Y Method:LeastSquares Sample:19862004 Includedobservations:19 Variable Coefficient Std.Error t-Statistic Prob. C -498.1550 67.21844 -7.410986 0.0000 X3 23.97516 3.967183 6.043370 0.0000 X5 -4.320566 3.553466 -1.215874 0.2417 R-squared 0.924405 Meandependentvar 345.5232 AdjustedR-squared 0.914956 S.D.dependentvar 139.7117 S.E.ofregression 40.74312 Akaikeinfocriterion 10.39639 Sumsquaredresid 26560.02 Schwarzcriterion 10.54551 Loglikelihood -95.76570 F-statistic 97.82772 Durbin-Watsonstat 0.607882 Prob(F-statistic) 0.000000表12加入x5的回归结果 DependentVariable:Y Method:LeastSquares Sample:19862004 Includedobservations:19 Variable Coefficient Std.Error t-Statistic Prob. C -1600.965 346.9265 -4.614709 0.0003 X3 29.93768 3.534753 8.469528 0.0000 X6 9.980135 3.184176 3.134291 0.0064 R-squared 0.948835 Meandependentvar 345.5232 AdjustedR-squared 0.942440 S.D.dependentvar 139.7117 S.E.ofregression 33.51927 Akaikeinfocriterion 10.00606 Sumsquaredresid 17976.66 Schwarzcriterion 10.15518 Loglikelihood -92.05754 F-statistic 148.3576 Durbin-Watsonstat 1.125188 Prob(F-statistic) 0.000000表13加入x6的回归结果 DependentVariable:Y Method:LeastSquares Sample:19862004 Includedobservations:19 Variable Coefficient Std.Error t-Statistic Prob. C -2153.028 327.1248 -6.581673 0.0000 X3 14.40497 1.358355 10.60472 0.0000 X7 0.012268 0.002447 5.014015 0.0001 R-squared 0.967884 Meandependentvar 345.5232 AdjustedR-squared 0.963869 S.D.dependentvar 139.7117 S.E.ofregression 26.55648 Akaikeinfocriterion 9.540364 Sumsquaredresid 11283.94 Schwarzcriterion 9.689485 Loglikelihood -87.63345 F-statistic 241.0961 Durbin-Watsonstat 0.690413 Prob(F-statistic) 0.000000表14加入x7的回归结果 DependentVariable:Y Method:LeastSquares Sample:19862004 Includedobservations:19 Variable Coefficient Std.Error t-Statistic Prob. C -400.5635 103.0301 -3.887832 0.0013 X3 15.54271 2.916358 5.329493 0.0001 X8 0.029233 0.019233 1.519929 0.1480 R-squared 0.927840 Meandependentvar 345.5232 AdjustedR-squared 0.918820 S.D.dependentvar 139.7117 S.E.ofregression 39.80687 Akaikeinfocriterion 10.34990 Sumsquaredresid 25353.40 Schwarzcriterion 10.49902 Loglikelihood -95.32401 F-statistic 102.8643 Durbin-Watsonstat 0.559772 Prob(F-statistic) 0.000000表15加入x8的回归结果综合表10~15所示，加入x7的模型的R最大,以x3、x7为基础顺次加入其他解释变量，进行三元回归，具体回归结果如下表16~20所示： DependentVariable:Y Method:LeastSquares Sample:19862004 Includedobservations:19 Variable Coefficient Std.Error t-Statistic Prob. C -2133.921 340.6965 -6.263406 0.0000 X3 14.96023 2.094645 7.142134 0.0000 X7 0.011843 0.002786 4.250908 0.0007 X2 2.195243 6.170403 0.355770 0.7270 R-squared 0.968153 Meandependentvar 345.5232 AdjustedR-squared 0.961783 S.D.dependentvar 139.7117 S.E.ofregression 27.31242 Akaikeinfocriterion 9.637224 Sumsquaredresid 11189.52 Schwarzcriterion 9.836053 Loglikelihood -87.55363 F-statistic 151.9988 Durbin-Watsonstat 0.712258 Prob(F-statistic) 0.000000表16加入x2的回归结果 DependentVariable:Y Method:LeastSquares Sample:19862004 Includedobservations:19 Variable Coefficient Std.Error t-Statistic Prob. C -2226.420 353.4425 -6.299243 0.0000 X3 15.66729 2.443113 6.412839 0.0000 X7 0.012703 0.002589 4.906373 0.0002 X4 -1.601362 2.553294 -0.627175 0.5400 R-squared 0.968705 Meandependentvar 345.5232 AdjustedR-squared 0.962445 S.D.dependentvar 139.7117 S.E.ofregression 27.07472 Akaikeinfocriterion 9.619741 Sumsquaredresid 10995.60 Schwarzcriterion 9.818571 Loglikelihood -87.38754 F-statistic 154.7677 Durbin-Watsonstat 0.704178 Prob(F-statistic) 0.000000表17加入x4的回归结果 DependentVariable:Y Method:LeastSquares Sample:19862004 Includedobservations:19 Variable Coefficient Std.Error t-Statistic Prob. C -2110.381 306.2690 -6.890613 0.0000 X3 18.60156 2.617381 7.106937 0.0000 X7 0.012139 0.002285 5.311665 0.0001 X5 -3.964878 2.163262 -1.832823 0.0868 R-squared 0.973760 Meandependentvar 345.5232 AdjustedR-squared 0.968512 S.D.dependentvar 139.7117 S.E.ofregression 24.79152 Akaikeinfocriterion 9.443544 Sumsquaredresid 9219.289 Schwarzcriterion 9.642373 Loglikelihood -85.71367 F-statistic 185.5507 Durbin-Watsonstat 0.733972 Prob(F-statistic) 0.000000表18加入x5的回归结果 DependentVariable:Y Method:LeastSquares Sample:19862004 Includedobservations:19 Variable Coefficient Std.Error t-Statistic Prob. C -2418.859 323.7240 -7.471979 0.0000 X3 20.99887 3.397120 6.181374 0.0000 X7 0.009920 0.002495 3.976660 0.0012 X6 5.359184 2.571950 2.083705 0.0547 R-squared 0.975093 Meandependentvar 345.5232 AdjustedR-squared 0.970112 S.D.dependentvar 139.7117 S.E.ofregression 24.15359 Akaikeinfocriterion 9.391407 Sumsquaredresid 8750.940 Schwarzcriterion 9.590236 Loglikelihood -85.21837 F-statistic 195.7489 Durbin-Watsonstat 1.084023 Prob(F-statistic) 0.000000表19加入x6的回归结果 DependentVariable:Y Method:LeastSquares Sample:19862004 Includedobservations:19 Variable Coefficient Std.Error t-Statistic Prob. C -2013.355 361.8657 -5.563818 0.0001 X3 13.01578 2.032420 6.404078 0.0000 X7 0.011615 0.002558 4.540322 0.0004 X8 0.012375 0.013416 0.922401 0.3709 R-squared 0.969608 Meandependentvar 345.5232 AdjustedR-squared 0.963529 S.D.dependentvar 139.7117 S.E.ofregression 26.68115 Akaikeinfocriterion 9.590455 Sumsquaredresid 10678.26 Schwarzcriterion 9.789285 Loglikelihood -87.10933 F-statistic 159.5158 Durbin-Watsonstat 0.672264 Prob(F-statistic) 0.000000表20加入x8的回归结果综合上述表16~20的回归结果所示，其中加入x6的回归结果最好，以x3x6x7为基础一次加入其他解释变量，作四元回归估计，估计结果如表21~24所示： DependentVariable:Y Method:LeastSquares Sample:19862004 Includedobservations:19 Variable Coefficient Std.Error t-Statistic Prob. C -2405.108 339.7396 -7.079269 0.0000 X3 21.26850 3.699787 5.748573 0.0001 X6 5.310543 2.665569 1.992273 0.0662 X7 0.009689 0.002766 3.503386 0.0035 X2 1.302605 5.655390 0.230330 0.8212 R-squared 0.975187 Meandependentvar 345.5232 AdjustedR-squared 0.968098 S.D.dependentvar 139.7117 S.E.ofregression 24.95411 Akaikeinfocriterion 9.492888 Sumsquaredresid 8717.904 Schwarzcriterion 9.741424 Loglikelihood -85.18244 F-statistic 137.5567 Durbin-Watsonstat 1.082771 Prob(F-statistic) 0.000000表21加入x2的回归结果 DependentVariable:Y Method:LeastSquares Sample:19862004 Includedobservations:19 Variable Coefficient Std.Error t-Statistic Prob. C -2401.402 316.2980 -7.592215 0.0000 X3 22.10570 3.420783 6.462174 0.0000 X6 9.089033 3.781330 2.403660 0.0307 X7 0.007086 0.003247 2.182005 0.0466 X4 4.417678 3.348889 1.319147 0.2083 R-squared 0.977847 Meandependentvar 345.5232 AdjustedR-squared 0.971517 S.D.dependentvar 139.7117 S.E.ofregression 23.57887 Akaikeinfocriterion 9.379513 Sumsquaredresid 7783.481 Schwarzcriterion 9.628049 Loglikelihood -84.10537 F-statistic 154.4909 Durbin-Watsonstat 1.580301 Prob(F-statistic) 0.000000表22加入x4的回归结果 DependentVariable:Y Method:LeastSquares Sample:19862004 Includedobservations:19 Variable Coefficient Std.Error t-Statistic Prob. C -2375.188 430.7065 -5.514631 0.0001 X3 20.83493 3.657414 5.696629 0.0001 X6 4.629196 5.252860 0.881272 0.3930 X7 0.010217 0.003171 3.221953 0.0061 X5 -0.693692 4.304485 -0.161156 0.8743 R-squared 0.975139 Meandependentvar 345.5232 AdjustedR-squared 0.968036 S.D.dependentvar 139.7117 S.E.ofregression 24.97818 Akaikeinfocriterion 9.494817 Sumsquaredresid 8734.736 Schwarzcriterion 9.743353 Loglikelihood -85.20076 F-statistic 137.2849 Durbin-Watsonstat 1.023211 Prob(F-statistic) 0.000000表23加入x5的回归结果 DependentVariable:Y Method:LeastSquares Sample:19862004 Includedobservations:19 Variable Coefficient Std.Error t-Statistic Prob. C -2212.242 259.5324 -8.523951 0.0000 X3 22.06629 2.662231 8.288647 0.0000 X6 9.595653 2.380088 4.031638 0.0012 X7 0.006115 0.002260 2.705978 0.0171 X8 0.036923 0.011239 3.285354 0.0054 R-squared 0.985936 Meandependentvar 345.5232 AdjustedR-squared 0.981918 S.D.dependentvar 139.7117 S.E.ofregression 18.78702 Akaikeinfocriterion 8.925144 Sumsquaredresid 4941.332 Schwarzcriterion 9.173681 Loglikelihood -79.78887 F-statistic 245.3639 Durbin-Watsonstat 2.186293 Prob(F-statistic) 0.000000表24加入x8的回归结果综合表21~24所示的回归结果，其中加入x8的回归结果最好，以x3x6x7x8为基础顺次加入其他的解释变量，其回归结果如表25~27所示： DependentVariable:Y Method:LeastSquares Sample:19862004 Includedobservations:19 Variable Coefficient Std.Error t-Statistic Prob. C -2207.020 272.6061 -8.096005 0.0000 X3 22.17495 2.903190 7.638133 0.0000 X6 9.566731 2.480057 3.857464 0.0020 X7 0.006028 0.002451 2.458949 0.0287 X8 0.036846 0.011674 3.156195 0.0076 X2 0.535811 4.422645 0.121152 0.9054 R-squared 0.985952 Meandependentvar 345.5232 AdjustedR-squared 0.980549 S.D.dependentvar 139.7117 S.E.ofregression 19.48522 Akaikeinfocriterion 9.029279 Sumsquaredresid 4935.759 Schwarzcriterion 9.327523 Loglikelihood -79.77815 F-statistic 182.4791 Durbin-Watsonstat 2.180501 Prob(F-statistic) 0.000000表25加入x2的回归结果 DependentVariable:Y Method:LeastSquares Sample:19862004 Includedobservations:19 Variable Coefficient Std.Error t-Statistic Prob. C -1373.136 279.4825 -4.913137 0.0003 X3 20.09330 1.928486 10.41921 0.0000 X6 0.480401 2.845972 0.168800 0.8686 X7 0.008497 0.001692 5.021410 0.0002 X8 0.060502 0.009873 6.128146 0.0000 X5 -11.23292 2.844094 -3.949560 0.0017 R-squared 0.993607 Meandependentvar 345.5232 AdjustedR-squared 0.991148 S.D.dependentvar 139.7117 S.E.ofregression 13.14457 Akaikeinfocriterion 8.241984 Sumsquaredresid 2246.136 Schwarzcriterion 8.540228 Loglikelihood -72.29885 F-statistic 404.1009 Durbin-Watsonstat 1.704834 Prob(F-statistic) 0.000000表26加入x5的回归结果 DependentVariable:Y Method:LeastSquares Sample:19862004 Includedobservations:19 Variable Coefficient Std.Error t-Statistic Prob. C -2056.366 236.8112 -8.683569 0.0000 X3 20.60220 2.413096 8.537661 0.0000 X6 5.264834 2.804292 1.877420 0.0831 X7 0.008853 0.002306 3.839446 0.0020 X8 0.071742 0.018026 3.980036 0.0016 X4 -9.861231 4.279624 -2.304228 0.0384 R-squared 0.990014 Meandependentvar 345.5232 AdjustedR-squared 0.986174 S.D.dependentvar 139.7117 S.E.ofregression 16.42798 Akaikeinfocriterion 8.687938 Sumsquaredresid 3508.420 Schwarzcriterion 8.986182 Loglikelihood -76.53541 F-statistic 257.7752 Durbin-Watsonstat 1.965748 Prob(F-statistic) 0.000000表27加入x4的回归结果据表25~27所示，分别加入x2x4x5后R均有所增加，但是参数的T检验均不显著，所以最终的计量模型如下表所示： DependentVariable:Y Method:LeastSquares Sample:19862004 Includedobservations:19 Variable Coefficient Std.Error t-Statistic Prob. C -2212.242 259.5324 -8.523951 0.0000 X3 22.06629 2.662231 8.288647 0.0000 X6 9.595653 2.380088 4.031638 0.0012 X7 0.006115 0.002260 2.705978 0.0171 X8 0.036923 0.011239 3.285354 0.0054 R-squared 0.985936 Meandependentvar 345.5232 AdjustedR-squared 0.981918 S.D.dependentvar 139.7117 S.E.ofregression 18.78702 Akaikeinfocriterion 8.925144 Sumsquaredresid 4941.332 Schwarzcriterion 9.173681 Loglikelihood -79.78887 F-statistic 245.3639 Durbin-Watsonstat 2.186293 Prob(F-statistic) 0.000000表28多重共线性修正后的最终模型回归分析报告为：(二)、异方差的检验A、相关图形分析图1图2图3图4从图1~4可以看出y并不随着x的增大而变得更离散，表明模型可能不存在异方差。B、残差分析图图5图6图7图8从图5~8看出，e2并不随x的增大而变化，表明模型可能不存在异方差。C、ARCH检验 ARCHTest: F-statistic 0.558635 Probability 0.652331 Obs*R-squared 1.960709 Probability 0.580602 TestEquation: DependentVariable:RESID^2 Method:LeastSquares Sample(adjusted):19892004 Includedobservations:16afteradjustingendpoints Variable Coefficient Std.Error t-Statistic Prob. C 279.7407 120.1889 2.327509 0.0382 RESID^2(-1) 0.051971 0.251414 0.206717 0.8397 RESID^2(-2) -0.223409 0.241815 -0.923887 0.3737 RESID^2(-3) -0.157992 0.249154 -0.634115 0.5379 R-squared 0.122544 Meandependentvar 204.2351 AdjustedR-squared -0.096820 S.D.dependentvar 286.6884 S.E.ofregression 300.2464 Akaikeinfocriterion 14.45940 Sumsquaredresid 1081774. Schwarzcriterion 14.65255 Loglikelihood -111.6752 F-statistic 0.558635 Durbin-Watsonstat 1.767931 Prob(F-statistic) 0.652331表29ARCH检验D、White检验 WhiteHeteroskedasticityTest: F-statistic 5.378778 Probability 0.058152 Obs*R-squared 18.04165 Probability 0.204891 TestEquation: DependentVariable:RESID^2 Method:LeastSquares Sample:19862004 Includedobservations:19 Variable Coefficient Std.Error t-Statistic Prob. C 83312.19 792151.1 0.105172 0.9213 X3 8939.976 3785.514 2.361628 0.0775 X3^2 92.15690 56.34778 1.635502 0.1773 X3*X6 -23.05086 26.32794 -0.875529 0.4307 X3*X7 -0.094926 0.045467 -2.087801 0.1051 X3*X8 -0.965260 0.775504 -1.244688 0.2812 X6 14984.21 4130.063 3.628083 0.0222 X6^2 -53.86422 41.43287 -1.300036 0.2634 X6*X7 -0.045905 0.033365 -1.375837 0.2409 X6*X8 -0.395631 0.371854 -1.063942 0.3473 X7 -10.35154 12.19311 -0.848966 0.4437 X7^2 5.76E-05 4.21E-05 1.369855 0.2426 X7*X8 -7.38E-06 0.000266 -0.027789 0.9792 X8 62.90965 32.25761 1.950226 0.1229 X8^2 0.001515 0.002697 0.561479 0.6044 R-squared 0.949560 Meandependentvar 260.0701 AdjustedR-squared 0.773022 S.D.dependentvar 337.4753 S.E.ofregression 160.7806 Akaikeinfocriterion 13.01876 Sumsquaredresid 103401.7 Schwarzcriterion 13.76437 Loglikelihood -108.6782 F-statistic 5.378778 Durbin-Watsonstat 3.254288 Prob(F-statistic) 0.058152表30White检验综合上述4种方法得出的结论，说明模型中不存在异方差。(三)、自相关检验及修正①自相关的检验A、DW检验已知DW=2.18535949259，查表得DL=0.859，DU=1.848，所以4-DU=2.152<DW<4-DL=3.141，因此不能确定是否存在自相关性B、图示法：图9从图中可以看出大部分点落在1、3象限，表明存在正自相关。图10从图中可以看出，随着t的变化逐次变化，并不频繁改变符号，而是正的后面跟着几个负的，表明存在正自相关。综上所述，说明模型存在自相关性。②自相关的修正——德宾两步法 DependentVariable:Y Method:LeastSquares Sample(adjusted):19872003 Includedobservations:17afteradjustingendpoints Variable Coefficient Std.Error t-Statistic Prob. C -2604.551 1325.611 -1.964793 0.0902 X3 7.131100 6.627590 1.075972 0.3176 X6 8.128983 3.462779 2.347532 0.0513 X7 0.019522 0.007068 2.762059 0.0280 X8 -0.006728 0.071817 -0.093687 0.9280 X3(1) 17.36973 3.915884 4.435710 0.0030 X6(-1) 3.379990 3.045985 1.109654 0.3038 X7(-1) -0.012486 0.003263 -3.826887 0.0065 X8(-1) 0.095023 0.114697 0.828466 0.4347 Y(-1) -0.208123 0.495599 -0.419942 0.6871 R-squared 0.997436 Meandependentvar 348.9382 AdjustedR-squared 0.994140 S.D.dependentvar 132.8918 S.E.ofregression 10.17327 Akaikeinfocriterion 7.766572 Sumsquaredresid 724.4683 Schwarzcriterion 8.256698 Loglikelihood -56.01586 F-statistic 302.5781 Durbin-Watsonstat 2.420889 Prob(F-statistic) 0.000000表31广义方程估计结果 DependentVariable:Y+Y(-1)*0.208123 Method:LeastSquares Sample(adjusted):19872004 Includedobservations:18afteradjustingendpoints Variable Coefficient Std.Error t-Statistic Prob. C -2681.442 307.9863 -8.706368 0.0000 X3+X3(-1)*0.208123 23.58766 2.433154 9.694275 0.0000 X6+X6(-1)*0.208123 11.09440 2.238039 4.957199 0.0003 X7+X7(-1)*0.208123 0.005062 0.002144 2.361369 0.0345 X8+X8(-1)*0.208123 0.041248 0.010478 3.936757 0.0017 R-squared 0.989648 Meandependentvar 427.4289 AdjustedR-squared 0.986463 S.D.dependentvar 162.1550 S.E.ofregression 18.86626 Akaikeinfocriterion 8.942761 Sumsquaredresid 4627.166 Schwarzcriterion 9.190086 Loglikelihood -75.48485 F-statistic 310.7127 Durbin-Watsonstat 2.038980 Prob(F-statistic) 0.000000表32广义差分估计结果此时DW=2.03898，查表得DL=0.820，DU=1.872，DU<DW<4-DU=2.138,表明模型不存在异方差(四)、模型的最终结果为：三、经济意义检验模型估计结果表明：在假定其他解释变量不变的情况下，当第二、三产业从业人数占全社会从业人数的比重增长一个百分点，农民人均纯收入就会增加23.5877元；在假定其他解释变量不变的情况下，当农业总产值占农林牧总产值的比重增长一个百分点，农民人均纯收入就会增加11.0944元；在假定其他解释变量不变的情况下，当农作物播种面积增长一千公顷，农民人均纯收入就会增加0.002144元；在假定其他解释变量不变的情况下，当农村用电量增长一亿千瓦时，农民人均纯收入就会增加0.4124元；（四） 、统计检验A、拟合优度检验B、F检验C、t检验(五)、回归预测①、点预测使用Eview软件进行点预测：首先在Workfile窗口点击Range，出现ChangeWorkfileRange窗口，将EndData改为2005；然后在Workfile中点击Sample，将窗口中的19862004改为19862005；使用命令DataX3X6X7X8，在数据表中将2005年的数据输入；在Equation中，点击Forecast，确定后可得到如下图所示的结果，同时在Workfile中生成一新的序列Yf。在Workfile中双击Yf就可以看到其具体的数值。最终得到的点预测的纸如下表33所示： 　 实际值 预测值 1987 137.6259 112.227 1988 147.86166 183.74 1989 196.76153 192.343 1990 220.53342 224.91 1991 223.25142 228.018 1992 233.19453 241.791 1993 265.66734 274.631 1994 335.16333 315.617 1995 411.2878 383.275 1996 460.67926 466.255 1997 477.95564 469.394 1998 474.01886 480.886 1999 466.80042 477.053 2000 466.15639 468.741 2001 469.80345 468.679 2002 468.95245 470.933 2003 476.2441 449.902 2004 499.38776 527.849 2005 521.20096 601.733表33(附：)②、区间预测A、平均值区间预测B、个别值区间预测_1234567897.unknown_1234567901.unknown_1234567905.unknown_1234567907.unknown_1234567909.unknown_1234567910.unknown_1234567911.unknown_1234567908.unknown_1234567906.unknown_1234567903.unknown_1234567904.unknown_1234567902.unknown_1234567899.unknown_1234567900.unknown_1234567898.unknown_1234567893.unknown_1234567895.unknown_1234567896.unknown_1234567894.unknown_1234567891.unknown_1234567892.unknown_1234567890.unknown