资源预览内容
亲,该文档总共2页全部预览完了,如果喜欢就下载吧!
资源描述
多重共线性分析案例多重共线性分析案例例 用 1974-1987 年数据建立天津市粮食需求模型如下:表 1 变量 y,x1,x2,x3,x4,x5的数据年yx1x2x3x4x5 197498.45560.2153.206.531.231.89 1975100.70603.11190.009.121.302.03 1976102.80668.05240.308.101.802.71 1977133.95715.47301.1210.102.093.00 1978140.13724.27361.0010.932.393.291979143.11736.13420.0011.853.905.24 1980146.15748.91491.7612.285.136.83 1981144.60760.32501.0013.505.478.36 1982148.94774.92529.2015.296.0910.07 1983158.55785.30552.7218.107.9712.571984169.68795.50771.1619.6110.1815.12 1985162.14804.80811.8017.2211.7918.25 1986170.09814.94988.4318.6011.5420.59 1987178.69828.731094.6523.5311.6823.37资料来源:天津统计年鉴1988.设回归模型:Y01X12X23X34X45X5+ 利用 spss 统计软件进行线性回归(点选 Statistics 选项框中 Collinearity 共线性诊断选项), 设显著性水平 0.05,输出结果如下:ANOVAb8592.68651718.53752.531.000a 261.718832.715 8854.40413Regression Residual TotalModel 1Sum of SquaresdfMean SquareFSig.Predictors: (Constant), X5, X1, X3, X4, X2a. Dependent Variable: Yb. 从回归方程的 P 检验结果看出 Sig0,整体通过显著性检验。Coefficientsa-3.49730.007-.117.910 .125.059.3802.119.067.1158.716 .074.038.8231.945.088.02148.411 2.6781.257.5082.130.066.06515.418 3.4532.451.5371.409.196.02539.281 -4.4912.215-1.263-2.028.077.010105.035(Constant) X1 X2 X3 X4 X5Model 1BStd. ErrorUnstandardized Coefficients BetaStandardized Coefficients tSig.ToleranceVIFCollinearity StatisticsDependent Variable: Ya. 从输出结果看,在 0.05 的显著性水平下,i的 t 统计量单独对因变量 y 都无显著性影响 (P 值都大于 0.05)。其中方差扩大因子 VIF5105.035,VIF248.411,VIF4 39.281 远大于 10(VIFj1/(1R2j),R2j表示了自变量表示了自变量 xj与其余与其余 p1 个自变量的线性相关的程度,个自变量的线性相关的程度, R2j越接近越接近 1,VIFj也就越大,一般大于也就越大,一般大于 10 时,就说明时,就说明 xj就与其余自变量存在共线性就与其余自变量存在共线性), 因此 X2,X4,X5存在多重共线性。为了建立正确的回归模型,现在采用逐步回归的方法 进行线性回归分析,取显著性水平 进0.05,出0.1。输出结果为:Model Summary.962a.925.9197.44696 .977b.954.9466.08867Model 1 2RR SquareAdjusted R SquareStd. Error of the EstimatePredictors: (Constant), X1a. Predictors: (Constant), X1, X3b. 新模型2剔除了存在多重共线性的X2,X4,X5,得到回归方程为:39.7950.212X11.909X3标准化回归方程为: *0.642X10.362X3ANOVAc8188.91718188.917147.662.000a 665.4871255.457 8854.40413 8446.61324223.307113.922.000b 407.7911137.072 8854.40413Regression Residual Total Regression Residual TotalModel 12Sum of SquaresdfMean SquareFSig.Predictors: (Constant), X1a. Predictors: (Constant), X1, X3b. Dependent Variable: Yc. 样本决定系数为R20.977,调整样本决定系数Ra20.954,拟合优度仍然很高。Coefficientsa-90.92119.329-4.704.001 .317.026.96212.152.0001.0001.000 -39.79525.016-1.591.140 .212.045.6424.670.001.2224.513 1.909.724.3622.637.023.2224.513(Constant) X1 (Constant) X1 X3Model 12BStd. ErrorUnstandardized Coefficients BetaStandardized Coefficients tSig.ToleranceVIFCollinearity StatisticsDependent Variable: Ya. 再看上表,自变量X1,X3的方差扩大因子都是4.513,小于10,认为回归方程已经不存 在多重共线性。
网站客服QQ:2055934822
金锄头文库版权所有
经营许可证:蜀ICP备13022795号 | 川公网安备 51140202000112号