复习多元线性回归模型案例.docx

1、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

2、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

3、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， -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

4、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1986133.6013.4329.5017.9236.0179.99150104.07253.101987137.6312.2031.3019.3938.6275.63146379.53320.801988147.867.6637.6023.7145.9069.25143625.87508.901989196.769.4239.9026.2149.2362.75146553.93790.501990220.539.9839.9026.

5、4149.9364.66148362.27844.501991223.2510.2640.3026.9450.9263.09149585.80963.201992233.1910.0541.5027.4651.5361.51149007.101106.901993265.679.4943.6027.9951.8660.07147740.701244.901994335.169.2045.7028.5152.1258.22148240.601473.901995411.298.4347.8029.0452.4158.43149879.301655.701996460.688.8249.5030.

6、4853.2360.57152380.601812.701997477.968.3050.1031.9154.9358.23153969.201980.101998474.0210.6950.2033.3555.8458.03155705.702042.201999466.808.2349.9034.7857.1657.53156372.812173.452000466.167.7550.0036.2259.3355.68156299.852421.302001469.807.7150.0037.6660.6255.24155707.862610.782002468.957.1750.0039

7、.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：Dependent Variable: YMethod: Least SquaresSample:

8、 1986 2004Included observations: 19VariableCoefficientStd. Errort-StatisticProb. C-1102.373375.8283-2.9331840.0136X2-6.6353933.781349-1.7547690.1071X318.229422.0666178.8208990.0000X42.4300398.3703370.2903160.7770X5-16.237375.894109-2.7548470.0187X6-2.1552082.770834-0.7778190.4531X70.0099620.0023284.

9、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 squared resid1467.498 Schwarz criterion8.424516Log likelihood-68.25514 F-statistic374.6600Durbin-Wa

10、tson 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 1.000000-0.717662-0.695257-0.731326 0.737028-0.332435-0.594699X3-0.717662 1.000000 0.922286 0.935992-0.945701

11、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 1.000000-0.603539-0.887428X7-0.332435 0.742251 0.753928 0.687439-0.603539 1.000000 0.742781X8-0.594699 0.883804 0.

12、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: 19VariableCoefficientStd. Errort-StatisticProb. C820.3133151.87125.4013740.0000X2-51.3783616.18923-3

13、.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 criterion12.50763Log likelihood-115.8781 F-statistic10.07183Durbin-Watson stat0.644400 Prob(F-statis

14、tic)0.005554表3 y对x2的回归结果Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included observations: 19VariableCoefficientStd. Errort-StatisticProb. C-525.889164.11333-8.2024920.0000X319.460311.41604313.742740.0000R-squared0.917421 Mean dependent var345.5232Adjusted R-squared0.912563 S.D. depen

15、dent 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-statistic)0.000000表4 y对x3的回归结果Dependent Variable: YMethod: Least SquaresSample: 1986 2004Included ob

16、servations: 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. dependent var139.7117S.E. of regression63.84760 Akaike info criterion11.25018Sum squared resid69300

17、.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 observations: 19VariableCoefficientStd. Errort-StatisticProb. C-494.1440118.1449-4.1825260.0006X

18、515.779782.1987117.1768320.0000R-squared0.751850 Mean dependent var345.5232Adjusted R-squared0.737253 S.D. dependent var139.7117S.E. of regression71.61463 Akaike info criterion11.47978Sum squared resid87187.14 Schwarz criterion11.57919Log likelihood-107.0579 F-statistic51.50691Durbin-Watson stat0.31

19、8959 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. C1288.009143.80888.9563950.0000X6-15.523982.351180-6.6026350.0000R-squared0.719448 Mean dependent var345.5232Adjusted R-squared0

20、.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 stat0.395893 Prob(F-statistic)0.000004表7 y对x6的回归结果Dependent Variable: YMethod: Least SquaresSample: 19

21、86 2004Included observations: 19VariableCoefficientStd. Errort-StatisticProb. C-4417.766681.1678-6.4855770.0000X70.0315280.0045076.9949430.0000R-squared0.742148 Mean dependent var345.5232Adjusted R-squared0.726980 S.D. dependent var139.7117S.E. of regression73.00119 Akaike info criterion11.51813Sum

22、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: 1986 2004Included observations: 19VariableCoefficientStd. Errort-StatisticProb. C140.162528.9661

23、64.8388350.0002X80.1198270.0145438.2395030.0000R-squared0.799739 Mean dependent var345.5232Adjusted R-squared0.787959 S.D. dependent var139.7117S.E. of regression64.33424 Akaike info criterion11.26536Sum squared resid70361.21 Schwarz criterion11.36478Log likelihood-105.0209 F-statistic67.88941Durbin

24、-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 observations: 19VariableCoefficientStd. Errort-StatisticProb. C-754.4481149.1701-5.0576370.0001X321.788651

25、.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 criterion10.32254Sum squared resid24669.34 Schwarz criterion10.47167Log likelihood-95.06417 F-statistic105.9385

26、Durbin-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-508.678175.73220-6.7168020.0000X317.882003.7521214.7658370.0002X41.7533513.8443050.4560900.6545R-square

27、d0.918481 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 likelihood-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-498.155067.21844-7.4109860.0000X32