再剔除方差扩大因子最大的x1，重新做回归，结果如下，发现此时多重共线性问题应
经消除。但是继续观察如下结果，自变量x6的P值为0.801，说明x6对于财政收入的回归方程作用是不显著的。
Coefficients Unstandardized Standardized Coefficients Std. Model 1 (Constant) x3 x4 x6 B Error Beta t Sig. -2296.322 1.870E3 1.359 .031 .004 .097 .019 .014 Coefficients Collinearity Statistics Tolerance VIF -1.228 .236 .889 14.036 .000 .111 .010 1.649 .117 .256 .801 a.249 4.018 .222 4.509 .673 1.485 a. Dependent Variable: y
剔除不显著的x6，仅保留x3和x4两个自变量，进行回归分析。
Coefficients Unstandardized Coefficients Standardized Coefficients Collinearity Statistics ToleraModel 1 (Constant) x3 x4 B Std. Error Beta t Sig. nce VIF -2306.802 1820.091 1.359 .033 .094 .018 -1.267 .221 a.889 14.415 .000 .249 4.018 .116 1.886 .076 .249 4.018 a. Dependent Variable: y
???2306.8?1.359x3?0.033x4，但是发现x4的P值为0.076>0.05，表回归方程为y35
示x4对于y只有较弱的显著性。
用逐步回归法所得的选元结果如下，从中可以看出逐步回归法所保留的变量为
x5,x1,x2，而这三个变量正是方差扩大因子法所剔除的，所以按照共线性提出变量与常规的
逐步回归法按照t值显著性提出变量会有较大差别。 Coefficients Unstandardized Coefficients Std. Model 1 (Constant) x5 2 (Constant) x5 x1 3 (Constant) x5 x1 x2
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aStandardized Coefficients Collinearity Statistics B 710.370 .180 Error 90.891 .004 Beta t 7.816 Sig. Tolerance .000 .000 .000 .000 .015 .000 .000 .000 .001 1.000 VIF .994 40.736 7.392 1.000 1011.913 136.899 .311 -.414 .049 .154 1.718 -.726 6.374 -2.694 8.184 .006 162.146 .006 162.146 .001 989.833 .005 192.871 .002 541.459 874.600 106.866 .637 -.611 -.353 .089 .124 .088 3.516 -1.073 -1.454 7.143 -4.936 -3.994 a. Dependent Variable: y
7.7一家大型商业银行有多家分行，近年来，该银行的贷款额平稳增长，但不良贷款额也有较大比例的提高。为了弄清不良贷款形成的原因，希望利用银行业务的有关数据做些定量分析，以便找出控制不良贷款的方法。下表是该银行所属25家分行2002年的有关业务数据。
初始数据：
x1 x2 x3 x4 分行编号 y
1 0.9 67.3 6.8 5 51.9 2 1.1 111.3 19.8 16 90.9 3 4.8 173 7.7 17 73.7 4 3.2 80.8 7.2 10 14.5 5 7.8 199.7 16.5 19 63.2 6 2.7 16.2 2.2 1 2.2 7 1.6 107.4 10.7 17 20.2 8 12.5 185.4 27.1 18 43.8 9 1 96.1 1.7 10 55.9 10 2.6 72.8 9.1 14 64.3 11 0.3 64.2 2.1 11 42.7 12 4 132.2 11.2 23 76.7 13 0.8 58.6 6 14 22.8 14 3.5 174.6 12.7 26 117.1 15 10.2 263.5 15.6 34 146.7 16 3 79.3 8.9 15 29.9 17 0.2 14.8 0.6 2 42.1 18 0.4 73.5 5.9 11 25.3 19 1 24.7 5 4 13.4 20 6.8 139.4 7.2 28 64.3
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21 22 23 24 25
11.6 1.6 1.2 7.2 3.2
368.2 95.7 109.6 196.2 102.2
16.8 3.8 10.3 15.8 12
32 10 14 16 10
163.9 44.5 67.9 39.7 97.1
（1） 建立y与其余四个变量的简单相关系数
Correlations Pearson Correlation y x1 x2 x3 x4 Sig. (1-tailed) y x1 x2 x3 x4 N y x1 x2 x3 x4
从相关阵看出，y与x1,x2,x3的相关系数都在0.7以上，说明所选的自变量与y具有一定的相关性，但并不高度显著。
（2） 建立不良贷款y与4个变量的线性回归方程，所得回归系数是否合理？
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y 1.000 .844 .732 .700 .519 . .000 .000 .000 .004 25 25 25 25 25 x1 .844 1.000 .679 .848 .780 .000 . .000 .000 .000 25 25 25 25 25 x2 .732 .679 1.000 .586 .472 .000 .000 . .001 .009 25 25 25 25 25 x3 .700 .848 .586 1.000 .747 .000 .000 .001 . .000 25 25 25 25 25 x4 .519 .780 .472 .747 1.000 .004 .000 .009 .000 . 25 25 25 25 25
Model Summary Adjusted R Std. Error of Model 1 R .893 abR Square .798 Square .757 the Estimate Durbin-Watson 1.7788 2.626 a. Predictors: (Constant), x4, x2, x3, x1 b. Dependent Variable: y
ANOVA Model 1 Regression Residual Total Sum of Squares 249.371 63.279 312.650 df 4 20 24 b Mean Square 62.343 3.164 aF 19.704 Sig. .000 aa. Predictors: (Constant), x4, x2, x3, x1 b. Dependent Variable: y Coefficients Unstandardized Standardized Coefficients Std. Model 1 (Constant) x1 x2 x3 x4 B -1.022 .040 .148 .015 -.029 Error .782 .010 .079 .083 .015 .891 .260 .034 Beta t -1.306 3.837 1.879 .175 Coefficients 95% Confidence Interval for B Lower Sig. Bound Upper Bound .610 .062 .312 .188 .002 .206 -2.654 .001 .018 .075 -.016 .863 -.159 .067 -.061 -.325 -1.937 a. Dependent Variable: y 回归方程为
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