多元线性回归模型案例

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

2、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：x2 - 财政用于农业的支出的比重， x3 - 第二、三产业从业人数占全社会从业人数的比重，x4 - 非农村人口比重，x5 - 乡村从业人员占农村人口的比重，x6 - 农业总产值占农林牧总产值的比重，x7 - 农作物播种面积，x8 农村用电量。yx2x3x4x5x6x7x8年份78 年可比价比重%比重比重千公顷亿千瓦时1986133.6013.4329.5017.9236.0179.99150104.07253.101987137.6312.2031.3019.3938.6275.631

3、46379.53320.801988147.867.6637.6023.7145.9069.25143625.87508.901989196.769.4239.9026.2149.2362.75146553.93790.501990220.539.9839.9026.4149.9364.66148362.27844.501991223.2510.2640.3026.9450.9263.09149585.80963.201992233.1910.0541.5027.4651.5361.51149007.101106.901993265.679.4943.6027.9951.8660.071477

4、40.701244.901994335.169.2045.7028.5152.1258.22148240.601473.901995411.298.4347.8029.0452.4158.43149879.301655.701996460.688.8249.5030.4853.2360.57152380.601812.701997477.968.3050.1031.9154.9358.23153969.201980.101998474.0210.6950.2033.3555.8458.03155705.702042.201999466.808.2349.9034.7857.1657.53156

5、372.812173.452000466.167.7550.0036.2259.3355.68156299.852421.302001469.807.7150.0037.6660.6255.24155707.862610.782002468.957.1750.0039.0962.0254.51154635.512993.402003476.247.1250.9040.5363.7250.08152414.963432.922004499.399.6753.1041.7665.6450.05153552.553933.032005521.207.2255.2042.9967.5949.72155

6、487.734375.70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：Yt12 X 23 X 34 X45 X56 X 67 X78 X8ut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.

7、781349-1.7547690.1071X318.229422.0666178.8208990.0000X42.4300398.3703370.2903160.7770X5-16.237375.894109-2.7548470.0187X6-2.1552082.770834-0.7778190.4531X70.0099620.0023284.2788100.0013X80.0633890.0212762.9793480.0125R-squared0.995823Mean dependent var345.5232Adjusted R-squared0.993165S.D. dependent

8、 var139.7117S.E. of regression11.55028Akaike info criterion8.026857Sum squared resid1467.498Schwarz criterion8.424516Log likelihood-68.25514F-statistic374.6600Durbin-Watson stat1.993270Prob(F-statistic)0.000000表 1 最小二乘估计结果回归分析报告为：?-1102.373-6.6354X 2 +18.2294X3 +2.4300X4 -16.2374X5 -2.1552X 6 +0.010

9、0X 7 +0.0634X 8YiSE375.833.78132.066618.370345.89412.77080.002330.02128t-2.9331.7558.820900.203162.7550.7784.278812.9793R20.995823R20.993165 Df19 DW1.99327F 374.66二、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X2X3X4X5X6X7X8X21.00

10、0000-0.717662-0.695257-0.7313260.737028-0.332435-0.594699X3-0.7176621.0000000.9222860.935992-0.9457010.7422510.883804X4-0.6952570.9222861.0000000.986050-0.9377510.7539280.974675X5-0.7313260.9359920.9860501.000000-0.9747500.6874390.940436X60.737028-0.945701-0.937751-0.9747501.000000-0.603539-0.887428

11、X7-0.3324350.7422510.7539280.687439-0.6035391.0000000.742781X8-0.5946990.8838040.9746750.940436-0.8874280.7427811.000000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: 19VariableCoefficient

12、Std. Errort-StatisticProb.C820.3133151.87125.4013740.0000X2-51.3783616.18923-3.1736140.0056R-squared0.372041Mean dependent var345.5232Adjusted R-squared0.335102S.D. dependent var139.7117S.E. of regression113.9227Akaike info criterion12.40822Sum squared resid220632.4Schwarz criterion12.50763Log likel

13、ihood-115.8781F-statistic10.07183Durbin-Watson stat0.644400Prob(F-statistic)0.005554表 3y 对 x2的回归结果Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19VariableCoefficientStd. Errort-StatisticProb.C-525.889164.11333-8.2024920.0000X319.460311.41604313.742740.0000R-square

14、d0.917421Mean dependent var345.5232Adjusted R-squared0.912563S.D. dependent var139.7117S.E. of regression41.31236Akaike info criterion10.37950Sum squared resid29014.09Schwarz criterion10.47892Log likelihood-96.60526F-statistic188.8628Durbin-Watson stat0.598139Prob(F-statistic)0.000000表 4y 对 x3的回归结果D

15、ependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19VariableCoefficientStd. Errort-StatisticProb.C-223.190569.92322-3.1919370.0053X418.650862.2422408.3179560.0000R-squared0.802758Mean dependent var345.5232Adjusted R-squared0.791155S.D. dependent var139.7117S.E. of regr

16、ession63.84760Akaike info criterion11.25018Sum squared resid69300.77Schwarz criterion11.34959Log likelihood-104.8767F-statistic69.18839Durbin-Watson stat0.282182Prob(F-statistic)0.000000表 5y 对 x4的回归结果Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19VariableCoeffici

17、entStd. Errort-StatisticProb.C-494.1440118.1449-4.1825260.0006X515.779782.1987117.1768320.0000R-squared0.751850Mean dependent var345.5232Adjusted R-squared0.737253S.D. dependent var139.7117S.E. of regression71.61463Akaike info criterion11.47978Sum squared resid87187.14Schwarz criterion11.57919Log li

18、kelihood-107.0579F-statistic51.50691Durbin-Watson stat0.318959Prob(F-statistic)0.000002表6y 对x5的回归结果Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19VariableCoefficientStd. Errort-StatisticProb.C1288.009143.80888.9563950.0000X6-15.523982.351180-6.6026350.0000R-squar

19、ed0.719448Mean dependent var345.5232Adjusted R-squared0.702945S.D. dependent var139.7117S.E. of regression76.14674Akaike info criterion11.60250Sum squared resid98571.54Schwarz criterion11.70192Log likelihood-108.2238F-statistic43.59479Durbin-Watson stat0.395893Prob(F-statistic)0.000004表 7y 对 x6的回归结果

20、Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19VariableCoefficientStd. Errort-StatisticProb.C-4417.766681.1678-6.4855770.0000X70.0315280.0045076.9949430.0000R-squared0.742148Mean dependent var345.5232Adjusted R-squared0.726980S.D. dependent var139.7117S.E. of reg

21、ression73.00119Akaike info criterion11.51813Sum squared resid90595.96Schwarz criterion11.61754Log likelihood-107.4222F-statistic48.92923Durbin-Watson stat0.572651Prob(F-statistic)0.000002表 8y 对 x7的回归结果Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19VariableCoeffic

22、ientStd. Errort-StatisticProb.C140.162528.966164.8388350.0002X80.1198270.0145438.2395030.0000R-squared0.799739Mean dependent var345.5232Adjusted R-squared0.787959S.D. dependent var139.7117S.E. of regression64.33424Akaike info criterion11.26536Sum squared resid70361.21Schwarz criterion11.36478Log lik

23、elihood-105.0209F-statistic67.88941Durbin-Watson stat0.203711Prob(F-statistic)0.000000表 9y 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: 19VariableCoefficientStd. Errort-Statistic

24、Prob.C-754.4481149.1701-5.0576370.0001X321.788651.93268911.273750.0000X213.450708.0127451.6786630.1126R-squared0.929787Mean dependent var345.5232Adjusted R-squared0.921010S.D. dependent var139.7117S.E. of regression39.26619Akaike info criterion10.32254Sum squared resid24669.34Schwarz criterion10.471

25、67Log likelihood-95.06417F-statistic105.9385Durbin-Watson stat0.595954Prob(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-508.678175.73220-6.7168020.0000X317.882003.7521214.7658370.

26、0002X41.7533513.8443050.4560900.6545R-squared0.918481Mean dependent var345.5232Adjusted R-squared0.908291S.D. dependent var139.7117S.E. of regression42.30965Akaike info criterion10.47185Sum squared resid28641.71Schwarz criterion10.62097Log likelihood-96.48254F-statistic90.13613Durbin-Watson stat0.59

27、6359Prob(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-498.155067.21844-7.4109860.0000X323.975163.9671836.0433700.0000X5-4.3205663.553466-1.2158740.2417R-squared0.924405Mean depend

28、ent var345.5232Adjusted R-squared0.914956S.D. dependent var139.7117S.E. of regression40.74312Akaike info criterion10.39639Sum squared resid26560.02Schwarz criterion10.54551Log likelihood-95.76570F-statistic97.82772Durbin-Watson stat0.607882Prob(F-statistic)0.000000表 12加入 x5 的回归结果Dependent Variable:

29、YMethod: Least SquaresSample: 1986 2004Included observations: 19VariableCoefficientStd. Errort-StatisticProb.C-1600.965346.9265-4.6147090.0003X329.937683.5347538.4695280.0000X69.9801353.1841763.1342910.0064R-squared0.948835Mean dependent var345.5232Adjusted R-squared0.942440S.D. dependent var139.711

30、7S.E. of regression33.51927Akaike info criterion10.00606Sum squared resid17976.66Schwarz criterion10.15518Log likelihood-92.05754F-statistic148.3576Durbin-Watson stat1.125188Prob(F-statistic)0.000000表 13加入 x6 的回归结果Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19Va

31、riableCoefficientStd. Errort-StatisticProb.C-2153.028327.1248-6.5816730.0000X314.404971.35835510.604720.0000X70.0122680.0024475.0140150.0001R-squared0.967884Mean dependent var345.5232Adjusted R-squared0.963869S.D. dependent var139.7117S.E. of regression26.55648Akaike info criterion9.540364Sum square

32、d resid11283.94Schwarz criterion9.689485Log likelihood-87.63345F-statistic241.0961Durbin-Watson stat0.690413Prob(F-statistic)0.000000表 14加入 x7 的回归结果Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19VariableCoefficientStd. Errort-StatisticProb.C-400.5635103.0301-3.88

33、78320.0013X315.542712.9163585.3294930.0001X80.0292330.0192331.5199290.1480R-squared0.927840Mean dependent var345.5232Adjusted R-squared0.918820S.D. dependent var139.7117S.E. of regression39.80687Akaike info criterion10.34990Sum squared resid25353.40Schwarz criterion10.49902Log likelihood-95.32401F-s

34、tatistic102.8643Durbin-Watson stat0.559772Prob(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 observations: 19VariableCoefficientStd. Errort-StatisticProb.C-2133.921340

35、.6965-6.2634060.0000X314.960232.0946457.1421340.0000X70.0118430.0027864.2509080.0007X22.1952436.1704030.3557700.7270R-squared0.968153Mean dependent var345.5232Adjusted R-squared0.961783S.D. dependent var139.7117S.E. of regression27.31242Akaike info criterion9.637224Sum squared resid11189.52Schwarz c

36、riterion9.836053Log likelihood-87.55363F-statistic151.9988Durbin-Watson stat0.712258Prob(F-statistic)0.000000表 16加入 x2 的回归结果Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19VariableCoefficientStd. Errort-StatisticProb.C-2226.420353.4425-6.2992430.0000X315.667292.44

37、31136.4128390.0000X70.0127030.0025894.9063730.0002X4-1.6013622.553294-0.6271750.5400R-squared0.968705Mean dependent var345.5232Adjusted R-squared0.962445S.D. dependent var139.7117S.E. of regression27.07472Akaike info criterion9.619741Sum squared resid10995.60Schwarz criterion9.818571Log likelihood-8

38、7.38754F-statistic154.7677Durbin-Watson stat0.704178Prob(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-2110.381306.2690-6.8906130.0000X318.601562.6173817.1069370.0000X70.0121390.00

39、22855.3116650.0001X5-3.9648782.163262-1.8328230.0868R-squared0.973760Mean dependent var345.5232Adjusted R-squared0.968512S.D. dependent var139.7117S.E. of regression24.79152Akaike info criterion9.443544Sum squared resid9219.289Schwarz criterion9.642373Log likelihood-85.71367F-statistic185.5507Durbin

40、-Watson stat0.733972Prob(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-2418.859323.7240-7.4719790.0000X320.998873.3971206.1813740.0000X70.0099200.0024953.9766600.0012X65.3591842.57

41、19502.0837050.0547R-squared0.975093Mean dependent var345.5232Adjusted R-squared0.970112S.D. dependent var139.7117S.E. of regression24.15359Akaike info criterion9.391407Sum squared resid8750.940Schwarz criterion9.590236Log likelihood-85.21837F-statistic195.7489Durbin-Watson stat1.084023Prob(F-statist

42、ic)0.000000表 19加入 x6 的回归结果Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19VariableCoefficientStd. Errort-StatisticProb.C-2013.355361.8657-5.5638180.0001X313.015782.0324206.4040780.0000X70.0116150.0025584.5403220.0004X80.0123750.0134160.9224010.3709R-squared0.96960

43、8Mean dependent var345.5232Adjusted R-squared0.963529S.D. dependent var139.7117S.E. of regression26.68115Akaike info criterion9.590455Sum squared resid10678.26Schwarz criterion9.789285Log likelihood-87.10933F-statistic159.5158Durbin-Watson stat0.672264Prob(F-statistic)0.000000表 20加入 x8 的回归结果综合上述表 16

44、20 的回归结果所示， 其中加入 x6 的回归结果最好， 以 x3 x6x7 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-2405.108339.7396-7.0792690.0000X321.268503.6997875.7485730.0001X65.3105432.6655691.9922730.066

45、2X70.0096890.0027663.5033860.0035X21.3026055.6553900.2303300.8212R-squared0.975187Mean dependent var345.5232Adjusted R-squared0.968098S.D. dependent var139.7117S.E. of regression24.95411Akaike info criterion9.492888Sum squared resid8717.904Schwarz criterion9.741424Log likelihood-85.18244F-statistic137.5567Durbin-Watson stat1.082771Prob(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-2401.402316.2980-7.5922150.0000X322.105703.4207836.4621740.0000X69.0890333.7813302.403660