多元線性回歸模型案例

1、我國農(nóng)民收入影響因素的回歸分析本文力圖應(yīng)用適當(dāng)?shù)亩嘣€性回歸模型，對有關(guān)農(nóng)民收入的歷史數(shù)據(jù)和現(xiàn)狀進(jìn)行分析，探討影響農(nóng)民收入的主要因素，并在此基礎(chǔ)上對如何增加農(nóng)民收入提出相應(yīng)的政策建議。？農(nóng)民收入水平的度量常采用人均純收入指標(biāo)。影響農(nóng)民收入增長的因素是多方面的，既有結(jié)構(gòu)性矛盾因素，又有體制性障礙因素。但可以歸納為以下幾個方面：一是農(nóng)產(chǎn)品收購價格水平。二是農(nóng)業(yè)剩余勞動力轉(zhuǎn)移水平。三是城市化、工業(yè)化水平。四是農(nóng)業(yè)產(chǎn)業(yè)結(jié)構(gòu)狀況。五是農(nóng)業(yè)投入水平?？紤]到復(fù)雜性和可行性，所以對農(nóng)業(yè)投入與農(nóng)民收入，本文暫不作討論。因此，以全國為例，把農(nóng)民收入與各影響因素關(guān)系進(jìn)行線性回歸分析，并建立數(shù)學(xué)模型。一、計量經(jīng)濟(jì)模型

2、分析（一）、數(shù)據(jù)搜集根據(jù)以上分析，我們在影響農(nóng)民收入因素中引入7個解釋變量。即：X2-財政用于農(nóng)業(yè)的支出的比重，X3-第二、三產(chǎn)業(yè)從業(yè)人數(shù)占全社會從業(yè)人數(shù)的比重，X4-非農(nóng)村人口比重，X鄉(xiāng)村從業(yè)人員占農(nóng)村人口的比重，X6-農(nóng)業(yè)總產(chǎn)值占農(nóng)林牧總產(chǎn)值的比重，X7農(nóng)作物播種面積，X8-農(nóng)村用電量。yx2X3x4x5x6x7x8年份78年可比價比重%比重比重千公頃億千瓦時19861987198819891990199119921993199419951996199719981999200020012002200320042005資料來源中國統(tǒng)計年鑒2006。(二卜計量經(jīng)濟(jì)學(xué)模型建立我們設(shè)定模型為下面所

3、示的形式：利用Eviews軟件進(jìn)行最小二乘估計，估計結(jié)果如下表所示:DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.CX1X3X4X5X6X7X8R-squaredAdjustedR-squared.ofregressionSumsquaredresidLoglikelihoodDurbin-WatsonstatMeandependentvar.dependentvarAkaikeinfocriterio

4、nSchwarzcriterionF-statisticProb(F-statistic)表1最小二乘估計結(jié)果回歸分析報告為：Y?-1102.373-6.6354X2+18.2294XSE375.833.78132.06661t-2.9331.7558.8209022R20.995823R20.993165Df3+2.4300X4-16.2374X5-2.1552X6+0.0100X7+0.0634X88.370345.89412.77080.002330.021280.203162.7550.7784.278812.979319DW1.99327F374.66二、計量經(jīng)濟(jì)學(xué)檢驗(yàn)(一卜多重共線

5、性的檢驗(yàn)及修正、檢驗(yàn)多重共線性(a)、直觀法從“表1最小二乘估計結(jié)果”中可以看出，雖然模型的整體擬合的很好，但是x4x6的t統(tǒng)計量并不顯著，所以可能存在多重共線性。(b)、相關(guān)系數(shù)矩陣X2X3X4X5X6X7X8X2X3X4X5X6X7X8表2相關(guān)系數(shù)矩陣從“表2相關(guān)系數(shù)矩陣”中可以看出，個個解釋變量之間的相關(guān)程度較高，所以應(yīng)該存在多重共線性。、多重共線性的修正一一逐步迭代法A、一元回歸DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort

6、-StatisticProb.CX2R-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodF-statisticDurbin-WatsonstatProb(F-statistic)表3y對x2的回歸結(jié)果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficient

7、Std.Errort-StatisticProb.CX3R-squaredMeandependentvar.of regressionSum squared residAkaike info criterionSchwarz criterionLog likelihoodDurbin-Watson statF-statisticProb(F-statistic)表4y對x3的回歸結(jié)果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-S

8、tatisticProb.CX4R-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodF-statisticDurbin-WatsonstatProb(F-statistic)表5y對x4的回歸結(jié)果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientSt

9、d.Errort-StatisticProb.CX5R-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodF-statisticDurbin-WatsonstatProb(F-statistic)表6y對x5的回歸結(jié)果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoe

10、fficientStd.Errort-StatisticProb.CX6R-squaredMean dependent varAdjustedR-squared.ofregressionSumsquaredresidLoglikelihoodDurbin-Watsonstat.dependentvarAkaikeinfocriterionSchwarzcriterionF-statisticProb(F-statistic)表7y對x6的回歸結(jié)果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:1

11、9VariableCoefficientStd.Errort-StatisticProb.CX7R-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodF-statisticDurbin-WatsonstatProb(F-statistic)表8y對x7的回歸結(jié)果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobse

12、rvations:19VariableCoefficientStd.Errort-StatisticProb.CX8R-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodF-statisticDurbin-WatsonstatProb(F-statistic)表9y對x8的回歸結(jié)果綜合比較表39的回歸結(jié)果，發(fā)現(xiàn)加入x3的回歸結(jié)果最好。以x3為基礎(chǔ)順次加入其他解釋變量，進(jìn)行二元回歸，具體的回

13、歸結(jié)果如下表1015所示:DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.CX3X2R-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodF-statisticDurbin-WatsonstatPro

14、b(F-statistic)表10加入x2的回歸結(jié)果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.CX3X4R-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodF-statisticDurbin-

15、WatsonstatProb(F-statistic)表11加入x4的回歸結(jié)果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.CX3X5R-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodF-sta

16、tisticDurbin-WatsonstatProb(F-statistic)表12加入x5的回歸結(jié)果Method:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.CX3X6R-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodF-statistic

17、Durbin-WatsonstatProb(F-statistic)表13加入x6的回歸結(jié)果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.CX3X7R-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikeliho

18、odF-statisticDurbin-WatsonstatProb(F-statistic)表14加入x7的回歸結(jié)果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.CX3X8R-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriteri

19、onLoglikelihoodF-statistic表15加入x8綜合表1015所示，加入x7的模型的R最大，以x3、x7為基礎(chǔ)順次加入其他解釋變量，進(jìn)行三元回歸，具體回歸結(jié)果如下表1620所示：DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.CX3X7X2R-squaredAdjustedR-squared.ofregressionSumsquaredresidLoglikelihoodDurbin-W

20、atsonstatMeandependentvar.dependentvarAkaikeinfocriterionSchwarzcriterionF-statisticProb(F-statistic)表16加入x2的回歸結(jié)果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.CX3X7X4R-squaredAdjustedR-squared.ofregressionSumsquaredresidLoglik

21、elihoodDurbin-WatsonstatMeandependentvar.dependentvarAkaikeinfocriterionSchwarzcriterionF-statisticProb(F-statistic)表17加入x4的回歸結(jié)果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.Durbin-WatsonstatProb(F-statistic)CX3X7X5R-squaredMe

22、andependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodF-statisticDurbin-WatsonstatProb(F-statistic)表18加入x5的回歸結(jié)果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.CX3

23、X7X6R-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodF-statisticDurbin-WatsonstatProb(F-statistic)表19加入x6的回歸結(jié)果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-St

24、atisticProb.CX3X7X8R-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodF-statisticDurbin-WatsonstatProb(F-statistic)表20加入x8的回歸結(jié)果綜合上述表1620的回歸結(jié)果所示，其中加入x6的回歸結(jié)果最好，以x3x6x7為基礎(chǔ)一次加入其他解釋變量，作四元回歸估計，估計結(jié)果如表2124所示：DependentVariable:YM

25、ethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.CX3X6X7X2R-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodF-statisticDurbin-WatsonstatProb(F-statistic)表21加入x2的回歸結(jié)果Dep

26、endentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.CX3X6X7X4R-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodF-statisticDurbin-WatsonstatProb(F-statisti

27、c)表22加入x4的回歸結(jié)果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19CX3X6X7X5R-squaredAdjustedR-squared.ofregressionSumsquaredresidLoglikelihoodDurbin-WatsonstatMeandependentvar.dependentvarAkaikeinfocriterionSchwarzcriterionF-statisticProb(F-statistic)表23加入x5的回歸結(jié)果DependentVari

28、able:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.CX3X6X7X8R-squaredAdjustedR-squared.ofregressionSumsquaredresidLoglikelihoodDurbin-WatsonstatMeandependentvar.dependentvarAkaikeinfocriterionSchwarzcriterionF-statisticProb(F-statistic)表24加入x8的

29、回歸結(jié)果綜合表2124所示的回歸結(jié)果，其中加入x8的回歸結(jié)果最好，以x3x6x7x8為基礎(chǔ)順次加入其他的解釋變量，其回歸結(jié)果如表2527所示：DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.VariableCoefficientStd.Errort-StatisticProb.CX3X6X7X8X2R-squaredMeandependentvarAdjustedR-squared.dependentva

30、r.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodF-statisticDurbin-WatsonstatProb(F-statistic)表25加入x2的回歸結(jié)果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.CX3X6X7X8X5R-squaredMeandependentvarAdjustedR-

31、squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodF-statisticDurbin-WatsonstatProb(F-statistic)表26加入x5的回歸結(jié)果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.CX3X6X7X8X4R-squaredMeandep

32、endentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionF-statisticProb(F-statistic)LoglikelihoodDurbin-Watsonstat表27加入x4的回歸結(jié)果據(jù)表2527所示，分別加入x2x4x5后R均有所增加，但是參數(shù)的T檢驗(yàn)均不顯著，所以最終的計量模型如下表所示：DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations

33、:19VariableCoefficientStd.Errort-StatisticProb.CX3X6X7X8R-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodF-statisticDurbin-WatsonstatProb(F-statistic)表28多重共線性修正后的最終模型回歸分析報告為：（二卜異方差的檢驗(yàn)A、相關(guān)圖形分析圖1圖2圖3圖4從圖14可以看出y并不隨著x的增大而變

34、得更離散，表明模型可能不存在異方差。B、殘差分析圖圖5圖6圖8從圖58看出，e2并不隨x的增大而變化，表明模型可能不存在異方差。C、ARCH檢驗(yàn)ARCHTest:F-statisticProbabilityObs*R-squaredProbabilityTestEquation:DependentVariable:RESIDA2Method:LeastSquaresSample(adjusted):19892004Includedobservations:16afteradjustingendpointsVariableCoefficientStd.Errort-StatisticProb.C

35、RESIDA2(-1)RESIDA2(-2)RESIDA2(-3)R-squaredAdjustedR-squared.ofregressionSumsquaredresid1081774.LoglikelihoodDurbin-WatsonstatMeandependentvar.dependentvarAkaikeinfocriterionSchwarzcriterionF-statisticProb(F-statistic)表29ARCH檢驗(yàn)D、White檢驗(yàn)WhiteHeteroskedasticityTest:F-statisticProbabilityObs*R-squaredPr

36、obabilityTestEquation:DependentVariable:RESIDA2Method:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.CX3X3A2X3*X6X3*X7X3*X8X6X6A2X6*X7X6*X8X7X7A2X7*X8X8X8A2R-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquared

37、residSchwarzcriterionLoglikelihoodF-statisticDurbin-WatsonstatProb(F-statistic)表30White檢驗(yàn)綜合上述4種方法得出的結(jié)論，說明模型中不存在異方差。（三卜自相關(guān)檢驗(yàn)及修正自相關(guān)的檢驗(yàn)A、DW檢驗(yàn)已知，查表得DL=,DU=,所以4-DU=<DW<4-DL=,因此不能確定是否存在自相關(guān)性B、圖示法：圖9從圖中可以看出大部分點(diǎn)落在1、3象限，表明存在正自相關(guān)。圖10從圖中可以看出，隨著t的變化逐次變化，并不頻繁改變符號，而是正的后面跟著幾個負(fù)的，表明存在正自相關(guān)。綜上所述，說明模型存在自相關(guān)性。自相關(guān)的修正德賓兩步法DependentVariable:YMethod:LeastSquaresSample(adjusted):19872003Includedobservations:17afteradjustingendpointsVariableCoefficientStd.Errort-StatisticProb.CX3X6X7X8X3(1)X6(-1)X7(-1)X8(-1)Y(-1)R-squaredMea