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1、Good is good, but better carries it.精益求精，善益求善。复习：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自改革开放以来,虽然中国经济平均增长速度为9.5%,但二元经济结构给经济发展带来的问题仍然很突出。农村人口占了中国总人口的70%多,农业产业结构不合理,经济不发达,以及农民收入增长缓慢等问题势必成为我国经济持续稳定增长的障碍。正确有效地解决好“三农”问题是中国经济走出困境,实现长期稳定增长的关键。其中,农民收入增长是核心,也是解决“三农”问题的关键。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,寻找其根源,探讨影响农
2、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，通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。目前农业收入仍是中西部地区农民收入的主要来源。二是农业剩余劳动力转移水平。中国的农业目前仍以农户分散经营为主，农业比较效益低，尽快地把农业剩余劳动力转移出去是有效改善农民收入状况的重要因素。三是城市化、工业化水平。中国多数地区城市化、工业化水平落后于世界平均水平，这种状况极大地影响了农民收入的增长。四是农业产业结构状况。农林牧渔业对农民收入增长贡献率是不同的。随
3、着我国“入世”后农产品市场的开放和人民生活水平的提高、农产品需求市场的改变，农业结构状况直接影响着农民收入的增长。五是农业投入水平。农民收入与财政农业支出、农村集体投入、农户个人投入以及信贷投入都有显著的正相关关系。农业投入是农民收入增长的重要保证。但考虑到农业投入主体的多元性，既有国家、集体和农户的投入，又有银行、企业和外资的投入，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
4、，-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。yx2x3x4x5x6x7x8年份78年可比价比重%比重比重千公顷亿千瓦时1986133.6013.4329.5017.9236.0179.99150104.07253.101987137.6312.2031.3019.3938.6275.63146379.53320.801988147.867.6637.6023.7145.9069.25143625.87508.901989196.769.4239.9026.2149.2362.7
5、5146553.93790.501990220.539.9839.9026.4149.9364.66148362.27844.501991223.2510.2640.3026.9450.9263.09149585.80963.201992233.1910.0541.5027.4651.5361.51149007.101106.901993265.679.4943.6027.9951.8660.07147740.701244.901994335.169.2045.7028.5152.1258.22148240.601473.901995411.298.4347.8029.0452.4158.43
6、149879.301655.701996460.688.8249.5030.4853.2360.57152380.601812.701997477.968.3050.1031.9154.9358.23153969.201980.101998474.0210.6950.2033.3555.8458.03155705.702042.201999466.808.2349.9034.7857.1657.53156372.812173.452000466.167.7550.0036.2259.3355.68156299.852421.302001469.807.7150.0037.6660.6255.2
7、4155707.862610.782002468.957.1750.0039.0962.0254.51154635.512993.402003476.247.1250.9040.5363.7250.08152414.963432.922004499.399.6753.1041.7665.6450.05153552.553933.032005521.207.2255.2042.9967.5949.72155487.734375.70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：DependentVa
8、riable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.C-1102.373375.8283-2.9331840.0136X1-6.6353933.781349-1.7547690.1071X318.229422.0666178.8208990.0000X42.4300398.3703370.2903160.7770X5-16.237375.894109-2.7548470.0187X6-2.1552082.770834-0.7778
9、190.4531X70.0099620.0023284.2788100.0013X80.0633890.0212762.9793480.0125R-squared0.995823Meandependentvar345.5232AdjustedR-squared0.993165S.D.dependentvar139.7117S.E.ofregression11.55028Akaikeinfocriterion8.026857Sumsquaredresid1467.498Schwarzcriterion8.424516Loglikelihood-68.25514F-statistic374.660
10、0Durbin-Watsonstat1.993270Prob(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X2X3X4X5X6X7X8X21.000000-0.717662-0.695257-0.7313260.737028-0.332435-0.594699X3-0.7176621.0000000.9222860.935992-0.9457010
11、.7422510.883804X4-0.6952570.9222861.0000000.986050-0.9377510.7539280.974675X5-0.7313260.9359920.9860501.000000-0.9747500.6874390.940436X60.737028-0.945701-0.937751-0.9747501.000000-0.603539-0.887428X7-0.3324350.7422510.7539280.687439-0.6035391.0000000.742781X8-0.5946990.8838040.9746750.940436-0.8874
12、280.7427811.000000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DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.C820.3133151.87125.4013740.0000X2-51.3783616.18923-3.1736140.0056R-squared0.372041Meande
13、pendentvar345.5232AdjustedR-squared0.335102S.D.dependentvar139.7117S.E.ofregression113.9227Akaikeinfocriterion12.40822Sumsquaredresid220632.4Schwarzcriterion12.50763Loglikelihood-115.8781F-statistic10.07183Durbin-Watsonstat0.644400Prob(F-statistic)0.005554表3y对x2的回归结果DependentVariable:YMethod:LeastSq
14、uaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.C-525.889164.11333-8.2024920.0000X319.460311.41604313.742740.0000R-squared0.917421Meandependentvar345.5232AdjustedR-squared0.912563S.D.dependentvar139.7117S.E.ofregression41.31236Akaikeinfocriterion10.37950Sumsqua
15、redresid29014.09Schwarzcriterion10.47892Loglikelihood-96.60526F-statistic188.8628Durbin-Watsonstat0.598139Prob(F-statistic)0.000000表4y对x3的回归结果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.C-223.190569.92322-3.1919370.0053X418.
16、650862.2422408.3179560.0000R-squared0.802758Meandependentvar345.5232AdjustedR-squared0.791155S.D.dependentvar139.7117S.E.ofregression63.84760Akaikeinfocriterion11.25018Sumsquaredresid69300.77Schwarzcriterion11.34959Loglikelihood-104.8767F-statistic69.18839Durbin-Watsonstat0.282182Prob(F-statistic)0.
17、000000表5y对x4的回归结果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.C-494.1440118.1449-4.1825260.0006X515.779782.1987117.1768320.0000R-squared0.751850Meandependentvar345.5232AdjustedR-squared0.737253S.D.dependentvar139.7117S.E.ofre
18、gression71.61463Akaikeinfocriterion11.47978Sumsquaredresid87187.14Schwarzcriterion11.57919Loglikelihood-107.0579F-statistic51.50691Durbin-Watsonstat0.318959Prob(F-statistic)0.000002表6y对x5的回归结果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-St
19、atisticProb.C1288.009143.80888.9563950.0000X6-15.523982.351180-6.6026350.0000R-squared0.719448Meandependentvar345.5232AdjustedR-squared0.702945S.D.dependentvar139.7117S.E.ofregression76.14674Akaikeinfocriterion11.60250Sumsquaredresid98571.54Schwarzcriterion11.70192Loglikelihood-108.2238F-statistic43
20、.59479Durbin-Watsonstat0.395893Prob(F-statistic)0.000004表7y对x6的回归结果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.C-4417.766681.1678-6.4855770.0000X70.0315280.0045076.9949430.0000R-squared0.742148Meandependentvar345.5232Adjuste
21、dR-squared0.726980S.D.dependentvar139.7117S.E.ofregression73.00119Akaikeinfocriterion11.51813Sumsquaredresid90595.96Schwarzcriterion11.61754Loglikelihood-107.4222F-statistic48.92923Durbin-Watsonstat0.572651Prob(F-statistic)0.000002表8y对x7的回归结果DependentVariable:YMethod:LeastSquaresSample:19862004Inclu
22、dedobservations:19VariableCoefficientStd.Errort-StatisticProb.C140.162528.966164.8388350.0002X80.1198270.0145438.2395030.0000R-squared0.799739Meandependentvar345.5232AdjustedR-squared0.787959S.D.dependentvar139.7117S.E.ofregression64.33424Akaikeinfocriterion11.26536Sumsquaredresid70361.21Schwarzcrit
23、erion11.36478Loglikelihood-105.0209F-statistic67.88941Durbin-Watsonstat0.203711Prob(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：DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-StatisticPr
24、ob.C-754.4481149.1701-5.0576370.0001X321.788651.93268911.273750.0000X213.450708.0127451.6786630.1126R-squared0.929787Meandependentvar345.5232AdjustedR-squared0.921010S.D.dependentvar139.7117S.E.ofregression39.26619Akaikeinfocriterion10.32254Sumsquaredresid24669.34Schwarzcriterion10.47167Loglikelihoo
25、d-95.06417F-statistic105.9385Durbin-Watsonstat0.595954Prob(F-statistic)0.000000表10加入x2的回归结果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.C-508.678175.73220-6.7168020.0000X317.882003.7521214.7658370.0002X41.7533513.8443050.4560
26、900.6545R-squared0.918481Meandependentvar345.5232AdjustedR-squared0.908291S.D.dependentvar139.7117S.E.ofregression42.30965Akaikeinfocriterion10.47185Sumsquaredresid28641.71Schwarzcriterion10.62097Loglikelihood-96.48254F-statistic90.13613Durbin-Watsonstat0.596359Prob(F-statistic)0.000000表11加入x4的回归结果D
27、ependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.C-498.155067.21844-7.4109860.0000X323.975163.9671836.0433700.0000X5-4.3205663.553466-1.2158740.2417R-squared0.924405Meandependentvar345.5232AdjustedR-squared0.914956S.D.dependentvar
28、139.7117S.E.ofregression40.74312Akaikeinfocriterion10.39639Sumsquaredresid26560.02Schwarzcriterion10.54551Loglikelihood-95.76570F-statistic97.82772Durbin-Watsonstat0.607882Prob(F-statistic)0.000000表12加入x5的回归结果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoeffic
29、ientStd.Errort-StatisticProb.C-1600.965346.9265-4.6147090.0003X329.937683.5347538.4695280.0000X69.9801353.1841763.1342910.0064R-squared0.948835Meandependentvar345.5232AdjustedR-squared0.942440S.D.dependentvar139.7117S.E.ofregression33.51927Akaikeinfocriterion10.00606Sumsquaredresid17976.66Schwarzcri
30、terion10.15518Loglikelihood-92.05754F-statistic148.3576Durbin-Watsonstat1.125188Prob(F-statistic)0.000000表13加入x6的回归结果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.C-2153.028327.1248-6.5816730.0000X314.404971.35835510.604720.00
31、00X70.0122680.0024475.0140150.0001R-squared0.967884Meandependentvar345.5232AdjustedR-squared0.963869S.D.dependentvar139.7117S.E.ofregression26.55648Akaikeinfocriterion9.540364Sumsquaredresid11283.94Schwarzcriterion9.689485Loglikelihood-87.63345F-statistic241.0961Durbin-Watsonstat0.690413Prob(F-stati
32、stic)0.000000表14加入x7的回归结果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.C-400.5635103.0301-3.8878320.0013X315.542712.9163585.3294930.0001X80.0292330.0192331.5199290.1480R-squared0.927840Meandependentvar345.5232AdjustedR-squared
33、0.918820S.D.dependentvar139.7117S.E.ofregression39.80687Akaikeinfocriterion10.34990Sumsquaredresid25353.40Schwarzcriterion10.49902Loglikelihood-95.32401F-statistic102.8643Durbin-Watsonstat0.559772Prob(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：De
34、pendentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.C-2133.921340.6965-6.2634060.0000X314.960232.0946457.1421340.0000X70.0118430.0027864.2509080.0007X22.1952436.1704030.3557700.7270R-squared0.968153Meandependentvar345.5232AdjustedR-sq
35、uared0.961783S.D.dependentvar139.7117S.E.ofregression27.31242Akaikeinfocriterion9.637224Sumsquaredresid11189.52Schwarzcriterion9.836053Loglikelihood-87.55363F-statistic151.9988Durbin-Watsonstat0.712258Prob(F-statistic)0.000000表16加入x2的回归结果DependentVariable:YMethod:LeastSquaresSample:19862004Includedo
36、bservations:19VariableCoefficientStd.Errort-StatisticProb.C-2226.420353.4425-6.2992430.0000X315.667292.4431136.4128390.0000X70.0127030.0025894.9063730.0002X4-1.6013622.553294-0.6271750.5400R-squared0.968705Meandependentvar345.5232AdjustedR-squared0.962445S.D.dependentvar139.7117S.E.ofregression27.07
37、472Akaikeinfocriterion9.619741Sumsquaredresid10995.60Schwarzcriterion9.818571Loglikelihood-87.38754F-statistic154.7677Durbin-Watsonstat0.704178Prob(F-statistic)0.000000表17加入x4的回归结果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.
38、C-2110.381306.2690-6.8906130.0000X318.601562.6173817.1069370.0000X70.0121390.0022855.3116650.0001X5-3.9648782.163262-1.8328230.0868R-squared0.973760Meandependentvar345.5232AdjustedR-squared0.968512S.D.dependentvar139.7117S.E.ofregression24.79152Akaikeinfocriterion9.443544Sumsquaredresid9219.289Schwa
39、rzcriterion9.642373Loglikelihood-85.71367F-statistic185.5507Durbin-Watsonstat0.733972Prob(F-statistic)0.000000表18加入x5的回归结果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.C-2418.859323.7240-7.4719790.0000X320.998873.3971206.18137
40、40.0000X70.0099200.0024953.9766600.0012X65.3591842.5719502.0837050.0547R-squared0.975093Meandependentvar345.5232AdjustedR-squared0.970112S.D.dependentvar139.7117S.E.ofregression24.15359Akaikeinfocriterion9.391407Sumsquaredresid8750.940Schwarzcriterion9.590236Loglikelihood-85.21837F-statistic195.7489
41、Durbin-Watsonstat1.084023Prob(F-statistic)0.000000表19加入x6的回归结果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.C-2013.355361.8657-5.5638180.0001X313.015782.0324206.4040780.0000X70.0116150.0025584.5403220.0004X80.0123750.0134160.9224010.3709R-squared0.969608Meandependentvar345.5232AdjustedR-squared0.963529S.D.dependentvar139.7117S.E.ofregression26.68115Akaikeinfocriterion9.590455Sumsquaredresid10678.26Schwarzcri