多元线性回归模型案例.doc

1、我国农民收入影响因素的回归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

2、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： -2x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3x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4x5 6x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。7x8xy 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 150104.07 253.101987 137.63 12.20 31.30 19.39 3

3、8.62 75.63 146379.53 320.801988 147.86 7.66 37.60 23.71 45.90 69.25 143625.87 508.901989 196.76 9.42 39.90 26.21 49.23 62.75 146553.93 790.501990 220.53 9.98 39.90 26.41 49.93 64.66 148362.27 844.501991 223.25 10.26 40.30 26.94 50.92 63.09 149585.80 963.201992 233.19 10.05 41.50 27.46 51.53 61.51 14

4、9007.10 1106.901993 265.67 9.49 43.60 27.99 51.86 60.07 147740.70 1244.901994 335.16 9.20 45.70 28.51 52.12 58.22 148240.60 1473.901995 411.29 8.43 47.80 29.04 52.41 58.43 149879.30 1655.701996 460.68 8.82 49.50 30.48 53.23 60.57 152380.60 1812.701997 477.96 8.30 50.10 31.91 54.93 58.23 153969.20 19

5、80.101998 474.02 10.69 50.20 33.35 55.84 58.03 155705.70 2042.201999 466.80 8.23 49.90 34.78 57.16 57.53 156372.81 2173.452000 466.16 7.75 50.00 36.22 59.33 55.68 156299.85 2421.302001 469.80 7.71 50.00 37.66 60.62 55.24 155707.86 2610.782002 468.95 7.17 50.00 39.09 62.02 54.51 154635.51 2993.402003

6、 476.24 7.12 50.90 40.53 63.72 50.08 152414.96 3432.922004 499.39 9.67 53.10 41.76 65.64 50.05 153552.55 3933.032005 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： 12345678t tYXXXu利用 Eviews 软件进行最小二乘估计，估计结果如下表所示：Dependent Variable: YMethod: Least Sq

7、uaresSample: 1986 2004Included observations: 19Variable Coefficient Std. Error t-Statistic Prob. C -1102.373 375.8283 -2.933184 0.0136X1 -6.635393 3.781349 -1.754769 0.1071X3 18.22942 2.066617 8.820899 0.0000X4 2.430039 8.370337 0.290316 0.7770X5 -16.23737 5.894109 -2.754847 0.0187X6 -2.155208 2.770

8、834 -0.777819 0.4531X7 0.009962 0.002328 4.278810 0.0013X8 0.063389 0.021276 2.979348 0.0125R-squared 0.995823 Mean dependent var 345.5232Adjusted R-squared 0.993165 S.D. dependent var 139.7117S.E. of regression 11.55028 Akaike info criterion 8.026857Sum squared resid 1467.498 Schwarz criterion 8.42

9、4516Log likelihood -68.25514 F-statistic 374.6600Durbin-Watson stat 1.993270 Prob(F-statistic) 0.000000表 1 最小二乘估计结果回归分析报告为： 23456782 -10.37-654X+8.92.0X-16.37-2.X+0.1.634X8.16898201 .9.4.9iYSEtR2DfWF二、计量经济学检验(一)、多重共线性的检验及修正、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 x4 x6 的 t 统计量并不显著，所以可能存在多

10、重共线性。(b)、相关系数矩阵X2 X3 X4 X5 X6 X7 X8X2 1.000000 -0.717662 -0.695257 -0.731326 0.737028 -0.332435 -0.594699X3 -0.717662 1.000000 0.922286 0.935992 -0.945701 0.742251 0.883804X4 -0.695257 0.922286 1.000000 0.986050 -0.937751 0.753928 0.974675X5 -0.731326 0.935992 0.986050 1.000000 -0.974750 0.687439 0.

11、940436X6 0.737028 -0.945701 -0.937751 -0.974750 1.000000 -0.603539 -0.887428X7 -0.332435 0.742251 0.753928 0.687439 -0.603539 1.000000 0.742781X8 -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。、多重共线性的修正逐步迭代法A、 一元回归Dependent Va

12、riable: YMethod: Least SquaresSample: 1986 2004Included observations: 19Variable Coefficient Std. Error t-Statistic Prob. C 820.3133 151.8712 5.401374 0.0000X2 -51.37836 16.18923 -3.173614 0.0056R-squared 0.372041 Mean dependent var 345.5232Adjusted R-squared 0.335102 S.D. dependent var 139.7117S.E.

13、 of regression 113.9227 Akaike info criterion 12.40822Sum squared resid 220632.4 Schwarz criterion 12.50763Log likelihood -115.8781 F-statistic 10.07183Durbin-Watson stat 0.644400 Prob(F-statistic) 0.005554表 3 y 对 x2 的回归结果Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observatio

14、ns: 19Variable Coefficient Std. Error t-Statistic Prob. C -525.8891 64.11333 -8.202492 0.0000X3 19.46031 1.416043 13.74274 0.0000R-squared 0.917421 Mean dependent var 345.5232Adjusted R-squared 0.912563 S.D. dependent var 139.7117S.E. of regression 41.31236 Akaike info criterion 10.37950Sum squared

15、resid 29014.09 Schwarz criterion 10.47892Log likelihood -96.60526 F-statistic 188.8628Durbin-Watson stat 0.598139 Prob(F-statistic) 0.000000表 4 y 对 x3 的回归结果Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19Variable Coefficient Std. Error t-Statistic Prob. C -223.190

16、5 69.92322 -3.191937 0.0053X4 18.65086 2.242240 8.317956 0.0000R-squared 0.802758 Mean dependent var 345.5232Adjusted R-squared 0.791155 S.D. dependent var 139.7117S.E. of regression 63.84760 Akaike info criterion 11.25018Sum squared resid 69300.77 Schwarz criterion 11.34959Log likelihood -104.8767

17、F-statistic 69.18839Durbin-Watson stat 0.282182 Prob(F-statistic) 0.000000表 5 y 对 x4 的回归结果Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19Variable Coefficient Std. Error t-Statistic Prob. C -494.1440 118.1449 -4.182526 0.0006X5 15.77978 2.198711 7.176832 0.0000R-s

18、quared 0.751850 Mean dependent var 345.5232Adjusted R-squared 0.737253 S.D. dependent var 139.7117S.E. of regression 71.61463 Akaike info criterion 11.47978Sum squared resid 87187.14 Schwarz criterion 11.57919Log likelihood -107.0579 F-statistic 51.50691Durbin-Watson stat 0.318959 Prob(F-statistic)

19、0.000002表 6 y 对 x5 的回归结果Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19Variable Coefficient Std. Error t-Statistic Prob. C 1288.009 143.8088 8.956395 0.0000X6 -15.52398 2.351180 -6.602635 0.0000R-squared 0.719448 Mean dependent var 345.5232Adjusted R-squared 0.70

20、2945 S.D. dependent var 139.7117S.E. of regression 76.14674 Akaike info criterion 11.60250Sum squared resid 98571.54 Schwarz criterion 11.70192Log likelihood -108.2238 F-statistic 43.59479Durbin-Watson stat 0.395893 Prob(F-statistic) 0.000004表 7 y 对 x6 的回归结果Dependent Variable: YMethod: Least Squares

21、Sample: 1986 2004Included observations: 19Variable Coefficient Std. Error t-Statistic Prob. C -4417.766 681.1678 -6.485577 0.0000X7 0.031528 0.004507 6.994943 0.0000R-squared 0.742148 Mean dependent var 345.5232Adjusted R-squared 0.726980 S.D. dependent var 139.7117S.E. of regression 73.00119 Akaike

22、 info criterion 11.51813Sum squared resid 90595.96 Schwarz criterion 11.61754Log likelihood -107.4222 F-statistic 48.92923Durbin-Watson stat 0.572651 Prob(F-statistic) 0.000002表 8 y 对 x7 的回归结果Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19Variable Coefficient Std

23、. Error t-Statistic Prob. C 140.1625 28.96616 4.838835 0.0002X8 0.119827 0.014543 8.239503 0.0000R-squared 0.799739 Mean dependent var 345.5232Adjusted R-squared 0.787959 S.D. dependent var 139.7117S.E. of regression 64.33424 Akaike info criterion 11.26536Sum squared resid 70361.21 Schwarz criterion

24、 11.36478Log likelihood -105.0209 F-statistic 67.88941Durbin-Watson stat 0.203711 Prob(F-statistic) 0.000000表 9 y 对 x8 的回归结果综合比较表 39 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 1015 所示：Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19Variable Coeffic

25、ient Std. Error t-Statistic Prob. C -754.4481 149.1701 -5.057637 0.0001X3 21.78865 1.932689 11.27375 0.0000X2 13.45070 8.012745 1.678663 0.1126R-squared 0.929787 Mean dependent var 345.5232Adjusted R-squared 0.921010 S.D. dependent var 139.7117S.E. of regression 39.26619 Akaike info criterion 10.322

26、54Sum squared resid 24669.34 Schwarz criterion 10.47167Log likelihood -95.06417 F-statistic 105.9385Durbin-Watson stat 0.595954 Prob(F-statistic) 0.000000表 10 加入 x2 的回归结果Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19Variable Coefficient Std. Error t-Statistic Pr

27、ob. C -508.6781 75.73220 -6.716802 0.0000X3 17.88200 3.752121 4.765837 0.0002X4 1.753351 3.844305 0.456090 0.6545R-squared 0.918481 Mean dependent var 345.5232Adjusted R-squared 0.908291 S.D. dependent var 139.7117S.E. of regression 42.30965 Akaike info criterion 10.47185Sum squared resid 28641.71 S

28、chwarz criterion 10.62097Log likelihood -96.48254 F-statistic 90.13613Durbin-Watson stat 0.596359 Prob(F-statistic) 0.000000表 11 加入 x4 的回归结果Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19Variable Coefficient Std. Error t-Statistic Prob. C -498.1550 67.21844 -7.41

29、0986 0.0000X3 23.97516 3.967183 6.043370 0.0000X5 -4.320566 3.553466 -1.215874 0.2417R-squared 0.924405 Mean dependent var 345.5232Adjusted R-squared 0.914956 S.D. dependent var 139.7117S.E. of regression 40.74312 Akaike info criterion 10.39639Sum squared resid 26560.02 Schwarz criterion 10.54551Log

30、 likelihood -95.76570 F-statistic 97.82772Durbin-Watson stat 0.607882 Prob(F-statistic) 0.000000表 12 加入 x5 的回归结果Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19Variable Coefficient Std. Error t-Statistic Prob. C -1600.965 346.9265 -4.614709 0.0003X3 29.93768 3.534

31、753 8.469528 0.0000X6 9.980135 3.184176 3.134291 0.0064R-squared 0.948835 Mean dependent var 345.5232Adjusted R-squared 0.942440 S.D. dependent var 139.7117S.E. of regression 33.51927 Akaike info criterion 10.00606Sum squared resid 17976.66 Schwarz criterion 10.15518Log likelihood -92.05754 F-statis

32、tic 148.3576Durbin-Watson stat 1.125188 Prob(F-statistic) 0.000000表 13 加入 x6 的回归结果Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19Variable Coefficient Std. Error t-Statistic Prob. C -2153.028 327.1248 -6.581673 0.0000X3 14.40497 1.358355 10.60472 0.0000X7 0.012268

33、 0.002447 5.014015 0.0001R-squared 0.967884 Mean dependent var 345.5232Adjusted R-squared 0.963869 S.D. dependent var 139.7117S.E. of regression 26.55648 Akaike info criterion 9.540364Sum squared resid 11283.94 Schwarz criterion 9.689485Log likelihood -87.63345 F-statistic 241.0961Durbin-Watson stat

34、 0.690413 Prob(F-statistic) 0.000000表 14 加入 x7 的回归结果Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19Variable Coefficient Std. Error t-Statistic Prob. C -400.5635 103.0301 -3.887832 0.0013X3 15.54271 2.916358 5.329493 0.0001X8 0.029233 0.019233 1.519929 0.1480R-squ

35、ared 0.927840 Mean dependent var 345.5232Adjusted R-squared 0.918820 S.D. dependent var 139.7117S.E. of regression 39.80687 Akaike info criterion 10.34990Sum squared resid 25353.40 Schwarz criterion 10.49902Log likelihood -95.32401 F-statistic 102.8643Durbin-Watson stat 0.559772 Prob(F-statistic) 0.

36、000000表 15 加入 x8 的回归结果综合表 1015 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 1620 所示：Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19Variable Coefficient Std. Error t-Statistic Prob. C -2133.921 340.6965 -6.263406 0.0000X3 14.96023 2.094645 7.142134 0.

37、0000X7 0.011843 0.002786 4.250908 0.0007X2 2.195243 6.170403 0.355770 0.7270R-squared 0.968153 Mean dependent var 345.5232Adjusted R-squared 0.961783 S.D. dependent var 139.7117S.E. of regression 27.31242 Akaike info criterion 9.637224Sum squared resid 11189.52 Schwarz criterion 9.836053Log likeliho

38、od -87.55363 F-statistic 151.9988Durbin-Watson stat 0.712258 Prob(F-statistic) 0.000000表 16 加入 x2 的回归结果Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19Variable Coefficient Std. Error t-Statistic Prob. C -2226.420 353.4425 -6.299243 0.0000X3 15.66729 2.443113 6.412

39、839 0.0000X7 0.012703 0.002589 4.906373 0.0002X4 -1.601362 2.553294 -0.627175 0.5400R-squared 0.968705 Mean dependent var 345.5232Adjusted R-squared 0.962445 S.D. dependent var 139.7117S.E. of regression 27.07472 Akaike info criterion 9.619741Sum squared resid 10995.60 Schwarz criterion 9.818571Log

40、likelihood -87.38754 F-statistic 154.7677Durbin-Watson stat 0.704178 Prob(F-statistic) 0.000000表 17 加入 x4 的回归结果Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19Variable Coefficient Std. Error t-Statistic Prob. C -2110.381 306.2690 -6.890613 0.0000X3 18.60156 2.6173

41、81 7.106937 0.0000X7 0.012139 0.002285 5.311665 0.0001X5 -3.964878 2.163262 -1.832823 0.0868R-squared 0.973760 Mean dependent var 345.5232Adjusted R-squared 0.968512 S.D. dependent var 139.7117S.E. of regression 24.79152 Akaike info criterion 9.443544Sum squared resid 9219.289 Schwarz criterion 9.64

42、2373Log likelihood -85.71367 F-statistic 185.5507Durbin-Watson stat 0.733972 Prob(F-statistic) 0.000000表 18 加入 x5 的回归结果Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19Variable Coefficient Std. Error t-Statistic Prob. C -2418.859 323.7240 -7.471979 0.0000X3 20.9988

43、7 3.397120 6.181374 0.0000X7 0.009920 0.002495 3.976660 0.0012X6 5.359184 2.571950 2.083705 0.0547R-squared 0.975093 Mean dependent var 345.5232Adjusted R-squared 0.970112 S.D. dependent var 139.7117S.E. of regression 24.15359 Akaike info criterion 9.391407Sum squared resid 8750.940 Schwarz criterio

44、n 9.590236Log likelihood -85.21837 F-statistic 195.7489Durbin-Watson stat 1.084023 Prob(F-statistic) 0.000000表 19 加入 x6 的回归结果Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19Variable Coefficient Std. Error t-Statistic Prob. C -2013.355 361.8657 -5.563818 0.0001X3 1

45、3.01578 2.032420 6.404078 0.0000X7 0.011615 0.002558 4.540322 0.0004X8 0.012375 0.013416 0.922401 0.3709R-squared 0.969608 Mean dependent var 345.5232Adjusted R-squared 0.963529 S.D. dependent var 139.7117S.E. of regression 26.68115 Akaike info criterion 9.590455Sum squared resid 10678.26 Schwarz cr

46、iterion 9.789285Log likelihood -87.10933 F-statistic 159.5158Durbin-Watson stat 0.672264 Prob(F-statistic) 0.000000表 20 加入 x8 的回归结果综合上述表 1620 的回归结果所示，其中加入 x6 的回归结果最好，以 x3 x6 x7 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 2124 所示：Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19Va

47、riable Coefficient Std. Error t-Statistic Prob. C -2405.108 339.7396 -7.079269 0.0000X3 21.26850 3.699787 5.748573 0.0001X6 5.310543 2.665569 1.992273 0.0662X7 0.009689 0.002766 3.503386 0.0035X2 1.302605 5.655390 0.230330 0.8212R-squared 0.975187 Mean dependent var 345.5232Adjusted R-squared 0.9680

48、98 S.D. dependent var 139.7117S.E. of regression 24.95411 Akaike info criterion 9.492888Sum squared resid 8717.904 Schwarz criterion 9.741424Log likelihood -85.18244 F-statistic 137.5567Durbin-Watson stat 1.082771 Prob(F-statistic) 0.000000表 21 加入 x2 的回归结果Dependent Variable: YMethod: Least SquaresSample