spss多元回归分析案例

1、企业治理对居民消费率影响因素的探究-以湖北省为例改革开放以来,我国经济始终保持着高速增长的趋势 ,三十多年间综合国力得 到显著增强,但我国居民消费率一宜偏低,甚至一宜有下降的趋势.居民消费率的偏低必然会导致我国内需的不足,进而会影响我国经济的长期健康开展.本模型以湖北省1995年-2021年数据为例,探究各因素对居民消费率的影响及多元关系.注：计算我国居民的消费率,用居民的人均消费除以人均 GDP,得到居民的消费率.通常来说,影响居民消费率的因素是多方面的,如 ：居民 总收入,人均GDP,人口结构状况1 儿童抚养系数, 老年抚养系数,居民消 费价格指数增长率等因素.总消费C亿元总GDP 亿元消

2、费率19951095.972109.3851.9619971438.122856.4750.3520001594.083545.3944.9620011767.383880.5345.5420021951.544212.8246.3220032188.054757.4545.991.人口年龄结构一种比拟精准的描述是：儿童抚养系数0-14岁人口与15-64岁人口的比值、老年抚养系数65岁及以上人口与15-64岁人口的比值或总抚养系数儿童和老年抚养系数之和.0-14岁人口比例与65岁及以上人口比例可由?湖北省统计年鉴?查得.20042452.625633.2443.5420052785.42659

3、0.1942.2720063124.377617.4741.0220073709.699333.439.7520214225.3811328.9237.3020214456.3112961.134.3820215136.7815806.0932.50注：数据来自 湖北省统计年鉴?、计量经济模型分析一、数据搜集根据以上分析,本模型在影响居民消费率因素中引入6个解释变X1居民总收入亿元,X2:人口增长率.,X3:居民消费价格指数增长率,X4:少儿抚养系数,X5:老年抚养系数,X6:居民消费占收入比重.X2:人口Y:消费率X1:总收入增长率%亿元c/ C199551.961590.759.27199

4、750.352033.688.12200044.962247.253.7率(%)17.145.39.4268.92.841.19.4470.720.4399.5770.93X3:居民消费价格X6:居民X4:少儿X5:老年指数增长消费比重抚养系数 抚养系数200145.542139.712.440.737.839.7282.6200246.322406.552.21-0.436.189.8181.09200345.992594.612.322.234.439.8784.33200443.542660.112.44.932.699.892.2200542.273172.413.052.931.09

5、9.7387.8200641.023538.43.131.630.179.988.3200739.754168.523.234.829.4610.0488.99202137.34852.582.716.328.6210.187.07202134.385335.543.48-0.428.0510.2583.52202132.56248.754.342.927.8310.4182.2二、计愤经济学模型建立假定各个影响因素与Y的关系是线性的,那么多元线性回归模型为yt=0X12X23X34X45X56X6利用SPSS统计分析软件输出分析结果如下:Descriptive StatisticsMeanS

6、td. DeviationNY42.76005.7457413X13.3068E31436.4549013Variables Entered/RemovedbModelVariablesEnteredVariablesRemovedMethod1X4, X3, X2, X6,X1, X5 aEntera. All requested variables entered.b. Dependent Variable: YX23.8769表 2A53813X33.52314.5718613X682.20387.5374413X56.8638.4378513X423.52542.9375213这局部被

7、结果说明在对模型进行回归分析时所采用的方法是全部引入法Enter.CorrelationsYX1X2X3X6X5X4Pearson CorrelationY1.000-.965.480.354-.566-.960.927X1-.9651.000-.288-.215.451.932-.877X2.480-.2881.000.656-.767-.577.623X3.354-.215.6561.000-.293-.365.392X6-.566.451-.767-.2931.000.722-.795X5-.960.932-.577-.365.7221.000-.982X4.927-.877.623.3

8、92-.795-.9821.000Sig. (1-tailed)Y.000.049.118.022.000.000X1.000.170.240.061.000.000X2.049.170.007.001.020.011X3.118.240.007.166.110.093X6.022.061.001.166.003.001X5.000.000.020.110.003.000X4.000.000.011.093.001.000N13131313131313X113131313131313X213131313131313X313131313131313X613131313131313X5131313

9、13131313X413131313131313这局部列出了各变M之间的相关性,从表格可以看出Y与xi的相关性最大.且 自变M之间也存在相关性,如X1与X5, X1与X4,相关系数分别为0.932和0.877 ,说明他们之间也存在相关性Model Summary bModelRR SquareAdjusted RSquareStd. Error of theEstimateDurbin-Watson1.991 a.982.9641.091502.710a. Predictors: (Constant), X4, X3, X2, X6, X1, X5b. Dependent Variable:Y

10、这局部结果得到的是常用统计M,相关系数R=0.991 ,判定系数,=0.982 ,调 整的判定系数 沪=0.964,回归估计的标准误差 S=1.09150.说明样本的回归效果比拟好ANOVA bModelSum of SquaresdfMean SquareFSig.1Regression389.015664.83654.421.000aResidual7.14861.191Total1396.16312a. Predictors: (Constant), X4, X3, X2, X6, X1, X5b. Dependent Variable: Y该表格是方差分析表,从这局部结果看出：统计M

11、F=54.421,显著性水平的值P值为0,说明因变M与自变M的线性关系明显.Sum of Squares 一栏中分别代表回归平方和为389.015,、残差平方和7.148、总平方和为396.163.Coefficients aModelUnstandardized CoefficientsStandardizedCoefficientstSig.BStd. ErrorBeta1(Constant)-33.36466.059-.505.632X1-.006.002-1.475-2.663.037X2.861.391.3352.201.070X3.036.121.029.301.774X6-.09

12、1.198-.120-.460.662X512.7159.581.9691.327.233X4.527.818.269.644.543aDepend lent Variable: Y该表格为回归系数分析,其中Unstandardized Coefficients为非标准化系数,Standardized Coefficients 为标准化系数,t为回归系数检验统计Sig.为相伴概率值.从表格中可以看出该多元线性回归方程：Y=-33.364-0.006X 1+O.86IX 2+0.036X 3+0.527X 4+12.715X 5-0.091X6+&、计量经济学检验一、多重共线性的检验及修

13、正、检验多重共线性从表3相关系数矩阵中可以看出,个个解释变M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运用spss软件中的剔除变M法,选择 stepwise逐步回归 输出表7：进入与剔除变M表Variables Entered/RemovedaModelVariablesEnteredVariablesRemovedMethod1X1Stepwise (Criteria: Probability-of-F-to-enter <= .050, Probability-of-F-to-remove >= .100).2X2Stepwise (Criteri

14、a: Probability-of-F-to-enter <= .050, Probability-of-F-to-remove >= .100).a. Dependent Variable: Y可以看到进入变M为X1与X2.表8:Model Summary cModelRR SquareAdjusted RSquareStd. Error of theEstimateDurbin-Watson1.965a.932.9251.570162.988b.976.971.976731.983a. Predictors: (Constant), X1ModelRR SquareAdjust

15、ed RSquareStd. Error of theEstimateDurbin-Watson1.965 a.932.9251.570162.988b.976.971.976731.983a. Predictors: (Constant), X1b. Predictors: (Constant), X1, X2c. Dependent Variable: YModel Summaryc表8是模型的概况,我们看到下列图中标出来的五个参数,分别是负相关系数、决 定系数、校正决定系数、随机误差的估计值和 D-W值,这些值除了随机误差 的估计值,D-W越接近2越好都是越大说明模型的效果越好,根据比拟

16、,第 二个模型应该是最好的.表9：方差分析表ANOVA cModelSum of SquaresdfMean SquareFSig.1Regression369.0431369.043149.689.000 aResidual27.119112.465Total396.163122Regression386.6232193.311202.632.000 bResidual9.54010.954Total396.16312a. Predictors: (Constant), X1b. Predictors: (Constant), X1, X2c. Dependent Variable: Y方差

17、分析表,四个模型都给出了方差分析的结果,这个表格可以检验是否所有偏回归系数全为0, sig值小于0.05可以证实模型的偏回归系数至少有一个不为零.表10:参数检验Coefficients aStandardizedModelUnstandardized CoefficientsCoefficientstSig.BStd. ErrorBeta1(Constant)55.5261.13149.109.000X1-.004.000-.965-12.235.0002(Constant)52.497.99652.686.000X1-.004.000-.902-17.599.000X2.565.132.2

18、204.293.001a. Dependent Variable: Y参数的检验,这个表格给出了对偏回归系数和标准偏回归系数的检验,偏回归系数用于不同模型的比拟,标准偏回归系数用于同一个模型的不同系数的检验,具值越大说明对因变M的影响越大.综上可得：模型2为最优模型.得出回归方程Y=52.497-0.004X1+0.056X2+&二、异方差的检验输出残差图：如图1ScatterplotDependent variable: Yoo-Regression Standardized Predicted Value从图1看出,e2并不随x的增大而变化,说明模型不存在异方差三、自相关检验-用D-W检验由输出结果表 8得：DW= 1.983 ,查表得DL=0.861 , DU=1.562 ,4-DU=2.438所以DU<DW<4-DU=2.438,因此误差项之间不存在自相关性.四、统计检验1. 拟合优度检验：由表 8相关系数R=0.988,判定系数,=0.976,调整的判定系数 护=0.971,回归估计的标准误差 S=0O 9673.说明样本的回归效果比拟好2. F值检验：由表9F= 202,632 0查表得,置信度为95%,自由度为1,12的F临界值为4.474, F值远远大于临