多元线性回归模型案例[行稳书苑]

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、计量经济模型分

2、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 x2x3x4x5x6x7x8年份78年可比价比重%比重比重千公顷亿千瓦时1986133.6013.4329.5017.9236.0179.99150104.07253.101987137.6312.2031.3019.3938.6275.63146379.53320.801988147.867.6637.6023.7

3、145.9069.25143625.87508.901989196.769.4239.9026.2149.2362.75146553.93790.501990220.539.9839.9026.4149.9364.66148362.27844.501991223.2510.2640.3026.9450.9263.09149585.80963.201992233.1910.0541.5027.4651.5361.51149007.101106.901993265.679.4943.6027.9951.8660.07147740.701244.901994335.169.2045.7028.515

4、2.1258.22148240.601473.901995411.298.4347.8029.0452.4158.43149879.301655.701996460.688.8249.5030.4853.2360.57152380.601812.701997477.968.3050.1031.9154.9358.23153969.201980.101998474.0210.6950.2033.3555.8458.03155705.702042.201999466.808.2349.9034.7857.1657.53156372.812173.452000466.167.7550.0036.22

5、59.3355.68156299.852421.302001469.807.7150.0037.6660.6255.24155707.862610.782002468.957.1750.0039.0962.0254.51154635.512993.402003476.247.1250.9040.5363.7250.08152414.963432.922004499.399.6753.1041.7665.6450.05153552.553933.032005521.207.2255.2042.9967.5949.72155487.734375.70资料来源中国统计年鉴2006。(二)、计量经济学

6、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：Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19VariableCoefficientStd. Errort-StatisticProb. C-1102.373375.8283-2.9331840.0136X1-6.6353933.781349-1.7547690.1071X318.229422.0666178.8208990.0000X42.4300398.3703370.290

7、3160.7770X5-16.237375.894109-2.7548470.0187X6-2.1552082.770834-0.7778190.4531X70.0099620.0023284.2788100.0013X80.0633890.0212762.9793480.0125R-squared0.995823 Mean dependent var345.5232Adjusted R-squared0.993165 S.D. dependent var139.7117S.E. of regression11.55028 Akaike info criterion8.026857Sum sq

8、uared resid1467.498 Schwarz criterion8.424516Log likelihood-68.25514 F-statistic374.6600Durbin-Watson stat1.993270 Prob(F-statistic)0.000000表1 最小二乘估计结果回归分析报告为：二、计量经济学检验(一)、多重共线性的检验及修正、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，所以可能存在多重共线性。(b)、相关系数矩阵X2X3X4X5X6X7X8X2 1.000000-0.71

9、7662-0.695257-0.731326 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 0.940436X6 0.737028-0.945701-0.937751-0.974750 1.000000-0.603539

10、-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 Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19V

11、ariableCoefficientStd. Errort-StatisticProb. C820.3133151.87125.4013740.0000X2-51.3783616.18923-3.1736140.0056R-squared0.372041 Mean dependent var345.5232Adjusted R-squared0.335102 S.D. dependent var139.7117S.E. of regression113.9227 Akaike info criterion12.40822Sum squared resid220632.4 Schwarz cri

12、terion12.50763Log likelihood-115.8781 F-statistic10.07183Durbin-Watson stat0.644400 Prob(F-statistic)0.005554表3 y对x2的回归结果Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19VariableCoefficientStd. Errort-StatisticProb. C-525.889164.11333-8.2024920.0000X319.460311.4160

13、4313.742740.0000R-squared0.917421 Mean dependent var345.5232Adjusted R-squared0.912563 S.D. dependent var139.7117S.E. of regression41.31236 Akaike info criterion10.37950Sum squared resid29014.09 Schwarz criterion10.47892Log likelihood-96.60526 F-statistic188.8628Durbin-Watson stat0.598139 Prob(F-sta

14、tistic)0.000000表4 y对x3的回归结果Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19VariableCoefficientStd. Errort-StatisticProb. C-223.190569.92322-3.1919370.0053X418.650862.2422408.3179560.0000R-squared0.802758 Mean dependent var345.5232Adjusted R-squared0.791155 S.D. de

15、pendent var139.7117S.E. of regression63.84760 Akaike info criterion11.25018Sum squared resid69300.77 Schwarz criterion11.34959Log likelihood-104.8767 F-statistic69.18839Durbin-Watson stat0.282182 Prob(F-statistic)0.000000表5 y对x4的回归结果Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included

16、 observations: 19VariableCoefficientStd. Errort-StatisticProb. C-494.1440118.1449-4.1825260.0006X515.779782.1987117.1768320.0000R-squared0.751850 Mean dependent var345.5232Adjusted R-squared0.737253 S.D. dependent var139.7117S.E. of regression71.61463 Akaike info criterion11.47978Sum squared resid87

17、187.14 Schwarz criterion11.57919Log likelihood-107.0579 F-statistic51.50691Durbin-Watson stat0.318959 Prob(F-statistic)0.000002表6 y对x5的回归结果Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19VariableCoefficientStd. Errort-StatisticProb. C1288.009143.80888.9563950.0000

18、X6-15.523982.351180-6.6026350.0000R-squared0.719448 Mean dependent var345.5232Adjusted R-squared0.702945 S.D. dependent var139.7117S.E. of regression76.14674 Akaike info criterion11.60250Sum squared resid98571.54 Schwarz criterion11.70192Log likelihood-108.2238 F-statistic43.59479Durbin-Watson stat0

19、.395893 Prob(F-statistic)0.000004表7 y对x6的回归结果Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19VariableCoefficientStd. Errort-StatisticProb. C-4417.766681.1678-6.4855770.0000X70.0315280.0045076.9949430.0000R-squared0.742148 Mean dependent var345.5232Adjusted R-squar

20、ed0.726980 S.D. dependent var139.7117S.E. of regression73.00119 Akaike info criterion11.51813Sum squared resid90595.96 Schwarz criterion11.61754Log likelihood-107.4222 F-statistic48.92923Durbin-Watson stat0.572651 Prob(F-statistic)0.000002表8 y对x7的回归结果Dependent Variable: YMethod: Least SquaresSample:

21、 1986 2004Included observations: 19VariableCoefficientStd. Errort-StatisticProb. C140.162528.966164.8388350.0002X80.1198270.0145438.2395030.0000R-squared0.799739 Mean dependent var345.5232Adjusted R-squared0.787959 S.D. dependent var139.7117S.E. of regression64.33424 Akaike info criterion11.26536Sum

22、 squared resid70361.21 Schwarz criterion11.36478Log likelihood-105.0209 F-statistic67.88941Durbin-Watson stat0.203711 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 observati

23、ons: 19VariableCoefficientStd. Errort-StatisticProb. C-754.4481149.1701-5.0576370.0001X321.788651.93268911.273750.0000X213.450708.0127451.6786630.1126R-squared0.929787 Mean dependent var345.5232Adjusted R-squared0.921010 S.D. dependent var139.7117S.E. of regression39.26619 Akaike info criterion10.32

24、254Sum squared resid24669.34 Schwarz criterion10.47167Log likelihood-95.06417 F-statistic105.9385Durbin-Watson stat0.595954 Prob(F-statistic)0.000000表10 加入x2的回归结果Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19VariableCoefficientStd. Errort-StatisticProb. C-508.67

25、8175.73220-6.7168020.0000X317.882003.7521214.7658370.0002X41.7533513.8443050.4560900.6545R-squared0.918481 Mean dependent var345.5232Adjusted R-squared0.908291 S.D. dependent var139.7117S.E. of regression42.30965 Akaike info criterion10.47185Sum squared resid28641.71 Schwarz criterion10.62097Log lik

26、elihood-96.48254 F-statistic90.13613Durbin-Watson stat0.596359 Prob(F-statistic)0.000000表11 加入x4的回归结果Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19VariableCoefficientStd. Errort-StatisticProb. C-498.155067.21844-7.4109860.0000X323.975163.9671836.0433700.0000X5-4

27、.3205663.553466-1.2158740.2417R-squared0.924405 Mean dependent var345.5232Adjusted R-squared0.914956 S.D. dependent var139.7117S.E. of regression40.74312 Akaike info criterion10.39639Sum squared resid26560.02 Schwarz criterion10.54551Log likelihood-95.76570 F-statistic97.82772Durbin-Watson stat0.607

28、882 Prob(F-statistic)0.000000表12 加入x5的回归结果Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19VariableCoefficientStd. Errort-StatisticProb. C-1600.965346.9265-4.6147090.0003X329.937683.5347538.4695280.0000X69.9801353.1841763.1342910.0064R-squared0.948835 Mean dependen

29、t var345.5232Adjusted R-squared0.942440 S.D. dependent var139.7117S.E. of regression33.51927 Akaike info criterion10.00606Sum squared resid17976.66 Schwarz criterion10.15518Log likelihood-92.05754 F-statistic148.3576Durbin-Watson stat1.125188 Prob(F-statistic)0.000000表13 加入x6的回归结果Dependent Variable:

30、 YMethod: Least SquaresSample: 1986 2004Included observations: 19VariableCoefficientStd. Errort-StatisticProb. C-2153.028327.1248-6.5816730.0000X314.404971.35835510.604720.0000X70.0122680.0024475.0140150.0001R-squared0.967884 Mean dependent var345.5232Adjusted R-squared0.963869 S.D. dependent var139

31、.7117S.E. of regression26.55648 Akaike info criterion9.540364Sum squared resid11283.94 Schwarz criterion9.689485Log likelihood-87.63345 F-statistic241.0961Durbin-Watson stat0.690413 Prob(F-statistic)0.000000表14 加入x7的回归结果Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations

32、: 19VariableCoefficientStd. Errort-StatisticProb. C-400.5635103.0301-3.8878320.0013X315.542712.9163585.3294930.0001X80.0292330.0192331.5199290.1480R-squared0.927840 Mean dependent var345.5232Adjusted R-squared0.918820 S.D. dependent var139.7117S.E. of regression39.80687 Akaike info criterion10.34990

33、Sum squared resid25353.40 Schwarz criterion10.49902Log likelihood-95.32401 F-statistic102.8643Durbin-Watson stat0.559772 Prob(F-statistic)0.000000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 observat

34、ions: 19VariableCoefficientStd. Errort-StatisticProb. C-2133.921340.6965-6.2634060.0000X314.960232.0946457.1421340.0000X70.0118430.0027864.2509080.0007X22.1952436.1704030.3557700.7270R-squared0.968153 Mean dependent var345.5232Adjusted R-squared0.961783 S.D. dependent var139.7117S.E. of regression27

35、.31242 Akaike info criterion9.637224Sum squared resid11189.52 Schwarz criterion9.836053Log likelihood-87.55363 F-statistic151.9988Durbin-Watson stat0.712258 Prob(F-statistic)0.000000表16 加入x2的回归结果Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19VariableCoefficientSt

36、d. Errort-StatisticProb. C-2226.420353.4425-6.2992430.0000X315.667292.4431136.4128390.0000X70.0127030.0025894.9063730.0002X4-1.6013622.553294-0.6271750.5400R-squared0.968705 Mean dependent var345.5232Adjusted R-squared0.962445 S.D. dependent var139.7117S.E. of regression27.07472 Akaike info criterio

37、n9.619741Sum squared resid10995.60 Schwarz criterion9.818571Log likelihood-87.38754 F-statistic154.7677Durbin-Watson stat0.704178 Prob(F-statistic)0.000000表17 加入x4的回归结果Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19VariableCoefficientStd. Errort-StatisticProb. C-

38、2110.381306.2690-6.8906130.0000X318.601562.6173817.1069370.0000X70.0121390.0022855.3116650.0001X5-3.9648782.163262-1.8328230.0868R-squared0.973760 Mean dependent var345.5232Adjusted R-squared0.968512 S.D. dependent var139.7117S.E. of regression24.79152 Akaike info criterion9.443544Sum squared resid9

39、219.289 Schwarz criterion9.642373Log likelihood-85.71367 F-statistic185.5507Durbin-Watson stat0.733972 Prob(F-statistic)0.000000表18 加入x5的回归结果Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19VariableCoefficientStd. Errort-StatisticProb. C-2418.859323.7240-7.4719790.

40、0000X320.998873.3971206.1813740.0000X70.0099200.0024953.9766600.0012X65.3591842.5719502.0837050.0547R-squared0.975093 Mean dependent var345.5232Adjusted R-squared0.970112 S.D. dependent var139.7117S.E. of regression24.15359 Akaike info criterion9.391407Sum squared resid8750.940 Schwarz criterion9.59

41、0236Log likelihood-85.21837 F-statistic195.7489Durbin-Watson stat1.084023 Prob(F-statistic)0.000000表19 加入x6的回归结果Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19VariableCoefficientStd. Errort-StatisticProb. C-2013.355361.8657-5.5638180.0001X313.015782.0324206.40407

42、80.0000X70.0116150.0025584.5403220.0004X80.0123750.0134160.9224010.3709R-squared0.969608 Mean dependent var345.5232Adjusted R-squared0.963529 S.D. dependent var139.7117S.E. of regression26.68115 Akaike info criterion9.590455Sum squared resid10678.26 Schwarz criterion9.789285Log likelihood-87.10933 F

43、-statistic159.5158Durbin-Watson stat0.672264 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: 19VariableCoefficientStd. Errort-StatisticProb. C-2405.10833

44、9.7396-7.0792690.0000X321.268503.6997875.7485730.0001X65.3105432.6655691.9922730.0662X70.0096890.0027663.5033860.0035X21.3026055.6553900.2303300.8212R-squared0.975187 Mean dependent var345.5232Adjusted R-squared0.968098 S.D. dependent var139.7117S.E. of regression24.95411 Akaike info criterion9.4928

45、88Sum squared resid8717.904 Schwarz criterion9.741424Log likelihood-85.18244 F-statistic137.5567Durbin-Watson stat1.082771 Prob(F-statistic)0.000000表21 加入x2的回归结果Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19VariableCoefficientStd. Errort-StatisticProb. C-2401.40

46、2316.2980-7.5922150.0000X322.105703.4207836.4621740.0000X69.0890333.7813302.4036600.0307X70.0070860.0032472.1820050.0466X44.4176783.3488891.3191470.2083R-squared0.977847 Mean dependent var345.5232Adjusted R-squared0.971517 S.D. dependent var139.7117S.E. of regression23.57887 Akaike info criterion9.3

47、79513Sum squared resid7783.481 Schwarz criterion9.628049Log likelihood-84.10537 F-statistic154.4909Durbin-Watson stat1.580301 Prob(F-statistic)0.000000表22 加入x4的回归结果Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19VariableCoefficientStd. Errort-StatisticProb. C-2375

48、.188430.7065-5.5146310.0001X320.834933.6574145.6966290.0001X64.6291965.2528600.8812720.3930X70.0102170.0031713.2219530.0061X5-0.6936924.304485-0.1611560.8743R-squared0.975139 Mean dependent var345.5232Adjusted R-squared0.968036 S.D. dependent var139.7117S.E. of regression24.97818 Akaike info criterion9.494817Sum squared resid8734.736 Schwarz criterion9.743353Log likelihood-85.20076 F-statistic137.2849Durbin-Watson stat1.023211 Prob(F-statistic)0.000000表23 加入x5的回归结果Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19VariableCoefficientStd. Errort-Statistic