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 数学模型。

2、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19861987198819891990199119921993199419951996199719981999200020012002200320042005资料来源中国统计年鉴2006（二）、

3、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：Depe ndent Variable: YMethod: Least SquaresSample: 1986 2004In cluded observati ons: 19VariableCoefficie ntStd. Errort-StatisticProb.CX1X3X4X5X6X7X8R-squaredAdjusted R-squared .of regressi onSum squared resid Log likelihoodMean depe ndent var .dep

4、endent var Akaike info criteri on Schwarz criteri on F-statisticProb(F-statistic)Durbi n- Watson stat表1最小二乘估计结果回归分析报告为:SER2-1102.373-6.6354X375.83-2.9330.9958233.78131.7552+18.2294X2.066618.82090_2R 0.993165 Df3+2.4300X 4-16.2374X 5-2.1552X 6+0.0100X 7+0.0634X 88.370340.2031619 DW5.89412.7551.993272

5、.77080.002330.7784.27881374.660.021282.9793、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统计量并不显着，所以可能存在多重共线性。(b)、相关系数矩阵X2X3X4X5X6X7X8X2X3X4X5X6X7X8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。、多重共线性的修正一一逐步迭代法A、一元回归Depe ndent Variable: YMethod: Least Squares

6、Sample: 1986 2004In cluded observati ons: 19VariableCoefficie ntStd. Errort-StatisticProb.CX2R-squaredAdjusted R-squared .of regressi onSum squared resid Log likelihoodDurbi n- Watson statMean depe ndent var .dependent var Akaike info criteri on Schwarz criteri on F-statistic Prob(F-statistic)表3 y对x

7、2的回归结果Depe ndent Variable: YMethod: Least SquaresSample: 1986 2004In cluded observati ons: 19VariableCoefficie ntStd. Errort-StatisticProb.CX3R-squaredMean depe ndent varAdjusted R-squared.dependent var.of regressi onAkaike info criteri onSum squared residSchwarz criteri onLog likelihoodF-statisticD

8、urbi n- Watson statProb(F-statistic)表4 y对x3的回归结果Depe ndent Variable: YMethod: Least SquaresSample: 1986 2004In cluded observati ons: 19VariableCoefficie ntStd. Errort-StatisticProb.CX4R-squaredAdjusted R-squared .of regressi on Sum squared resid Log likelihood Durbi n- Watson statMean depe ndent var

9、 .dependent var Akaike info criteri on Schwarz criteri on F-statistic Prob(F-statistic)表5 y对x4的回归结果Depe ndent Variable: YMethod: Least SquaresSample: 1986 2004In cluded observati ons: 19VariableCoefficie ntStd. Errort-StatisticProb.CX5R-squaredAdjusted R-squared .of regressi onSum squared resid Log

10、likelihoodDurbi n- Watson statMean depe ndent var .dependent var Akaike info criteri on Schwarz criteri on F-statistic Prob(F-statistic)表6 y对x5的回归结果Depe ndent Variable: YMethod: Least SquaresSample: 1986 2004In cluded observati ons: 19VariableCoefficie ntStd. Errort-StatisticProb.CX6R-squaredAdjuste

11、d R-squared .of regressi onSum squared resid Log likelihoodDurbi n- Watson statMean depe ndent var .dependent var Akaike info criteri on Schwarz criteri on F-statistic Prob(F-statistic)表7 y对x6的回归结果Depe ndent Variable: YMethod: Least SquaresSample: 1986 2004In cluded observati ons: 19VariableCoeffici

12、e ntStd. Errort-StatisticProb.CX7R-squaredMean depe ndent varAdjusted R-squared.dependent var.of regressi onAkaike info criteri onSum squared residSchwarz criteri onLog likelihoodF-statisticDurbi n- Watson statProb(F-statistic)表8 y对x7的回归结果Depe ndent Variable: YMethod: Least SquaresSample: 1986 2004I

13、n cluded observati ons: 19VariableCoefficie ntStd. Errort-StatisticProb.CX8R-squaredMean depe ndent varAdjusted R-squared.dependent var.of regressi onAkaike info criteri onSum squared residSchwarz criteri onLog likelihoodF-statisticDurbi n- Watson statProb(F-statistic)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

14、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:Depe ndent Variable: YMethod: Least SquaresSample: 1986 2004In eluded observati ons: 19VariableCoeffieie ntStd. Errort-StatistieProb.CX3X2R-squaredAdjusted R-squared .of regressi onSum squared resid Log likelihoodDurbi n- Watson statMean depe ndent va

15、r .dependent var Akaike info eriteri on Sehwarz eriteri on F-statistie Prob(F-statistie)表10加入x2的回归结果Depe ndent Variable: YMethod: Least SquaresSample: 1986 2004In eluded observati ons: 19VariableCoeffieie ntStd. Errort-StatistieProb.CX3X4R-squaredAdjusted R-squared .of regressi onSum squared resid L

16、og likelihoodDurbi n- Watson statMean depe ndent var .dependent var Akaike info eriteri on Sehwarz eriteri on F-statistie Prob(F-statistie)表11加入x4的回归结果Depe ndent Variable: YMethod: Least SquaresSample: 1986 2004In eluded observati ons: 19VariableCoeffieie ntStd. Errort-StatistieProb.CX3X5R-squaredAd

17、justed R-squared .of regressi on Sum squared resid Log likelihoodMean depe ndent var .dependent var Akaike info eriteri on Sehwarz eriteri on F-statistieDurbi n-Watson statProb(F-statistic)Depe ndent Variable: YMethod: Least SquaresSample: 1986 2004In cluded observati ons: 19表12加入x5的回归结果VariableCoef

18、ficie ntStd. Errort-StatisticProb.CX3X6R-squaredMean depe ndent varAdjusted R-squared.dependent var.of regressi onAkaike info criteri onSum squared residSchwarz criteri onLog likelihoodF-statisticDurbi n- Watson statProb(F-statistic)表13 加入x6的回归结果Depe ndent Variable: YMethod: Least SquaresSample: 198

19、6 2004In cluded observati ons: 19VariableCoefficie ntStd. Errort-StatisticProb.CX3X7R-squaredMean depe ndent varAdjusted R-squared.dependent var.of regressi onAkaike info criteri onSum squared residSchwarz criteri onLog likelihoodF-statisticDurbi n- Watson statProb(F-statistic)表14加入x7的回归结果Depe ndent

20、 Variable: YMethod: Least SquaresSample: 1986 2004In cluded observati ons: 19VariableCoefficie ntStd. Errort-StatisticProb.CX3X8R-squaredMean depe ndent varAdjusted R-squared.dependent var.of regressi onSum squared residAkaike info criteri onSchwarz criteri onLog likelihoodF-statisticDurbi n- Watson

21、 statProb(F-statistic)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：Depe ndent Variable: YMethod: Least SquaresSample: 1986 2004In cluded observati ons: 19VariableCoefficie ntStd. Errort-StatisticProb.CX3X7X2R-squaredMean depe ndent varAdjusted R-squared.dependent va

22、r.of regressi onAkaike info criteri onSum squared residSchwarz criteri onLog likelihoodF-statisticDurbi n- Watson statProb(F-statistic)表16加入x2的回归结果Depe ndent Variable: YMethod: Least SquaresSample: 1986 2004In cluded observati ons: 19VariableCoefficie ntStd. Errort-StatisticProb.CX3X7X4R-squaredMean

23、 depe ndent varAdjusted R-squared.dependent var.of regressi onAkaike info criteri onSum squared residSchwarz criteri onLog likelihoodF-statisticDurbi n- Watson statProb(F-statistic)表17加入x4的回归结果Depe ndent Variable: YMethod: Least SquaresSample: 1986 2004In eluded observati ons: 19VariableCoeffieie nt

24、Std. Errort-StatistieProb.CX3X7X5R-squaredAdjusted R-squared .of regressi onSum squared resid Log likelihoodDurbi n- Watson statMean depe ndent var .dependent var Akaike info eriteri on Sehwarz eriteri on F-statistie Prob(F-statistie)表18加入x5的回归结果Depe ndent Variable: YMethod: Least SquaresSample: 198

25、6 2004In eluded observati ons: 19VariableCoeffieie ntStd. Errort-StatistieProb.CX3X7X6R-squaredAdjusted R-squared .of regressi onSum squared resid Log likelihoodDurbi n- Watson statMean depe ndent var .dependent var Akaike info eriteri on Sehwarz eriteri on F-statistie Prob(F-statistie)表19加入x6的回归结果D

26、epe ndent Variable: YMethod: Least SquaresSample: 1986 2004In eluded observati ons: 19VariableCoeffieie ntStd. Errort-StatistieProb.CX3X7X8R-squaredAdjusted R-squared.of regressi onMean depe ndent var.dependent varAkaike info eriteri onSum squared residLog likelihoodDurbi n- Watson statSchwarz crite

27、ri onF-statisticProb(F-statistic)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:Depe ndent Variable: YMethod: Least SquaresSample: 1986 2004In cluded observati ons: 19VariableCoefficie ntStd. Errort-StatisticProb.CX3X6X7X2R-squaredMean depe ndent varAdjusted

28、R-squared.dependent var.of regressi onAkaike info criteri onSum squared residSchwarz criteri onLog likelihoodF-statisticDurbi n- Watson statProb(F-statistic)表21加入x2的回归结果Depe ndent Variable: YMethod: Least SquaresSample: 1986 2004In cluded observati ons: 19VariableCoefficie ntStd. Errort-StatisticPro

29、b.CX3X6X7X4R-squaredMean depe ndent varAdjusted R-squared.dependent var.of regressi onAkaike info criteri onSum squared residSchwarz criteri onLog likelihoodF-statisticDurbi n- Watson statProb(F-statistic)表22 加入x4的回归结果Depe ndent Variable: YMethod: Least SquaresSample: 1986 2004In cluded observati on

30、s: 19VariableCoefficie ntStd. Errort-StatisticProb.CX3X6X7X5R-squaredMean depe ndent varAdjusted R-squared.dependent var.of regressi onAkaike info criteri onSum squared residSchwarz criteri onLog likelihoodF-statisticDurbi n- Watson statProb(F-statistic)表23加入x5的回归结果Depe ndent Variable: YMethod: Leas

31、t SquaresSample: 1986 2004In cluded observati ons: 19VariableCoefficie ntStd. Errort-StatisticProb.CX3X6X7X8R-squaredMean depe ndent varAdjusted R-squared.dependent var.of regressi onAkaike info criteri onSum squared residSchwarz criteri onLog likelihoodF-statisticDurbi n- Watson statProb(F-statisti

32、c)表24加入x8的回归结果综合表2124所示的回归结果，其中加入x8的回归结果最好，以x3 x6 x7x8为基础顺次加入其他的解释变量，其回归结果如表2527所示：Depe ndent Variable: YMethod: Least SquaresSample: 1986 2004In cluded observati ons: 19VariableCoefficie ntStd. Errort-StatisticProb.CX3X6X7X8X2R-squaredMean depe ndent varAdjusted R-squared.dependent var.of regressi

33、onAkaike info criteri onSum squared residSchwarz criteri onLog likelihoodF-statisticDurbi n- Watson statProb(F-statistic)表25加入x2的回归结果Depe ndent Variable: YMethod: Least SquaresSample: 1986 2004In cluded observati ons: 19VariableCoefficie ntStd. Errort-StatisticProb.CX3X6X7X8X5R-squaredMean depe nden

34、t varAdjusted R-squared.dependent var.of regressi onAkaike info criteri onSum squared residSchwarz criteri onLog likelihoodF-statisticDurbi n- Watson statProb(F-statistic)表26 加入x5的回归结果Depe ndent Variable: YMethod: Least SquaresSample: 1986 2004In cluded observati ons: 19VariableCoefficie ntStd. Erro

35、rt-StatisticProb.X3X6X7X8X4R-squaredAdjusted R-squared .of regressi onSum squared resid Log likelihoodDurbi n- Watson statMean depe ndent var .dependent var Akaike info criteri on Schwarz criteri on F-statistic Prob(F-statistic)表27 加入x4的回归结果据表2527所示，分别加入x2 x4 x5后R均有所增加，但是参数的T检验均不显着，所以最终的计量模型如下表所示:De

36、pe ndent Variable: YMethod: Least SquaresSample: 1986 2004In cluded observati ons: 19VariableCoefficie ntStd. Errort-StatisticProb.CX3X6X7X8R-squaredMean depe ndent varAdjusted R-squared.dependent var.of regressi onAkaike info criteri onSum squared residSchwarz criteri onLog likelihoodF-statisticDur

37、bi n- Watson statProb(F-statistic)表28多重共线性修正后的最终模型回归分析报告为：（二）、异方差的检验A、相关图形分析图1图2图3图4从图14可以看出y并不随着x的增大而变得更离散，表明模型可能不存 在异方差。B、残差分析图从图58看出，e2并不随x的增大而变化，表明模型可能不存在异方差。C、ARCH检验ARCH Test:F-statisticProbabilityObs*R-squaredProbabilityTest Equati on:Depe ndent Variable: RESIDEMethod: Least SquaresSample(adju

38、sted): 1989 2004In eluded observati ons: 16 after adjusti ng en dpo intsVariableCoefficie ntStd. Errort-StatisticProb.CRESIDA2(-1)RESIDA2(-2)RESIDA2(-3)R-squaredMean depe ndent varAdjusted R-squared.dependent var.of regressi onAkaike info criteri onSum squared resid1081774.Schwarz criteri onLog like

39、lihoodF-statisticDurbi n- Watson statProb(F-statistic)表29 ARCH检验D White检验White Heteroskedasticity Test:F-statisticObs*R-squaredProbabilityProbabilityTest Equati on:Depe ndent Variable: RESIDA2Method: Least SquaresSample: 1986 2004In cluded observati ons: 19VariableCoefficie ntStd. Errort-StatisticPr

40、ob.CX3X3A2X3*X6X3*X7X3*X8X6X6A2X6*X7X6*X8X7X7A2X7*X8X8X8A2R-squaredMean depe ndent varAdjusted R-squared.dependent var.of regressi onAkaike info criteri onSum squared residSchwarz criteri onLog likelihoodF-statisticDurbi n- Watson statProb(F-statistic)表30 White 检验综合上述4种方法得出的结论，说明模型中不存在异方差。（三）、自相关检验及

41、修正自相关的检验A DW检验已知，查表得DL= ，DU=所以4-DU=DW4-DL=因此不能确定是否存在 自相关性B、图示法:从图中可以看出大部分点落在1、3象限，表明存在正自相关。图10从图中可以看出， 随着t的变化逐次变化，并不频繁改变符号，而是正的 后面跟着几个负的，表明存在正自相关。综上所述，说明模型存在自相关性。自相关的修正一一德宾两步法Depe ndent Variable: YMethod: Least SquaresSample(adjusted): 1987 2003Included observations: 17 after adjusting endpointsVariableCoefficie ntStd. Errort-StatisticProb.C