应用回归分析(第四版)习题7.6答案.doc

1、7.6（1）首先计算 y与其余 4个变量的简单相关系数程序：data a;input y x1-x4;cards;0.9 67.3 6.8 5 51.91.1 111.3 19.8 16 90.94.8 173.0 7.7 17 73.73.2 80.8 7.2 10 14.57.8 199.7 16.5 19 63.22.7 16.2 2.2 1 2.21.6 107.4 10.7 17 20.212.5 185.4 27.1 18 43.81.0 96.1 1.7 10 55.92.6 72.8 9.1 14 64.30.3 64.2 2.1 11 42.74.0 132.2 11.2 2

2、3 76.70.8 58.6 6.0 14 22.83.5 174.6 12.7 26 117.110.2 263.5 15.6 34 146.73.0 79.3 8.9 15 29.90.2 14.8 0.6 2 42.10.4 73.5 5.9 11 25.31.0 24.7 5.0 4 13.46.8 139.4 7.2 28 64.311.6 368.2 16.8 32 163.91.6 95.7 3.8 10 44.51.2 109.6 10.3 14 67.97.2 196.2 15.8 16 39.73.2 102.2 12.0 10 97.1;run;proc corr dat

3、a=a noprob ;label y=“不不不不“ x1=“不不不不不不“ x2=“不不不不不不不不“ x3=“不不不不不不“ x4=“不不不不不不不不不“;var y x1-x4;run;Pearson 相关系数, N = 25y x1 x2 x3 x4y 1.00000 0.84357 0.73151 0.70028 0.51852Pearson 相关系数, N = 25y x1 x2 x3 x4不良贷款x1各项贷款余额0.84357 1.00000 0.67877 0.84842 0.77970x2本年累计应收贷款0.73151 0.67877 1.00000 0.58583 0.47

4、243x3贷款项目个数0.70028 0.84842 0.58583 1.00000 0.74665x4本年固定资产投资额0.51852 0.77970 0.47243 0.74665 1.00000由 Y与四个自变量之相关系数为 0.84357,0.73151,0.70028,0.51852，且都通过显著性检验，说明 Y与四个变量是显著线性相关的，变量之间也存在一定的线性相关性。（2）建立不良贷款 y对 4个自变量的线性回归方程，所得的回归系数是否合理?程序：proc reg data=a;model y=x1-x4;run;参数估计值变量 自由度 参数估计值标准误差t 值 Pr |t|In

5、tercept 1 -1.02164 0.78237 -1.31 0.2064x1 1 0.04004 0.01043 3.84 0.0010x2 1 0.14803 0.07879 1.88 0.0749x3 1 0.01453 0.08303 0.17 0.8629x4 1 -0.02919 0.01507 -1.94 0.0670由结果得自变量 x2，x3，x4 没有通过 t检验，说明回归方程不显著，由实际意义出发，x4 的系数不能是负的。所以所得的回归系数不合理（3）分析回归模型的共线性。程序：proc reg data=a;model y=x1-x4/collin vif ;run;

6、参数估计值变量 标签 自由度参数估计值标准误差t 值 Pr |t| 方差膨胀Intercept Intercept 1 -1.02164 0.78237 -1.31 0.2064 0x1 各项贷款余额1 0.04004 0.01043 3.84 0.0010 5.33081x2 本年累计应收贷款1 0.14803 0.07879 1.88 0.0749 1.88986x3 贷款项目个数1 0.01453 0.08303 0.17 0.8629 3.83482x4 本年固定资产投资额1 -0.02919 0.01507 -1.94 0.0670 2.78122共线性诊断偏差比例个数 特征值 条件

7、指数 Intercept x1 x2 x3 x41 4.53829 1.00000 0.00848 0.00259 0.00659 0.00286 0.004882 0.20263 4.73256 0.68053 0.03353 0.01506 0.00772 0.091333 0.15691 5.37793 0.15815 0.00251 0.65595 0.00596 0.132304 0.06609 8.28687 0.00115 0.08807 0.20045 0.35650 0.716875 0.03608 11.21475 0.15169 0.87330 0.12196 0.626

8、96 0.05462由所有 VIF |t| 方差膨胀Intercept Intercept 1 -0.97160 0.71124 -1.37 0.1864 0x1 各项贷款余额1 0.04104 0.00853 4.81 |t| 方差膨胀Intercept Intercept 1 -0.97160 0.71124 -1.37 0.1864 0x1 各项贷款余 1 0.04104 0.00853 4.81 |t| 方差膨胀额x2 本年累计应收贷款1 0.14886 0.07682 1.94 0.0662 1.88311x4 本年固定资产投资额1 -0.02850 0.01421 -2.01 0.

9、0579 2.59014共线性诊断偏差比例个数 特征值 条件指数 Intercept x1 x2 x41 3.59663 1.00000 0.01577 0.00584 0.01067 0.008332 0.19800 4.26201 0.79074 0.06064 0.00164 0.115613 0.15469 4.82185 0.14958 0.00056777 0.62798 0.208744 0.05067 8.42475 0.04392 0.93295 0.35971 0.66732逐步回归法所得回归方程： Y=-0.97160+0.04104x1+0.14886x2-0.0285

10、0x4,方差扩大因子 VIF=0.4，岭迹曲线趋于稳定，说明 K=0.4即可以满足岭回归参数估计的均方误差较小的要求，对应的岭回归估计的回归方程：Y=-0.78981+0.01712x1+0.15734x2+0.07014x3-0.00214x4X4的系数仍为负值，不合理。Obs_MODEL_TYPE_DEPVAR_RIDGE_PCOMIT_RMSE_Interceptx1 x2 x3 x4 y1 MODEL1PARMSy . . 1.77875-1.021640.040040.148030.01453-0.02919-12 MODEL1RIDGEVIFy 0.0 . . . 5.330811

11、.889863.834822.78122-13 MODEL1RIDGEy 0.0 . 1.77875-1.021640.040040.148030.01453-0.02919-14 MODEL1RIDGEVIFy 0.1 . . . 1.808651.198441.651641.46562-15 MODEL1RIDGEy 0.1 . 1.85428-1.0870.027400.168590.05344-0.01-1Obs_MODEL_TYPE_DEPVAR_RIDGE_PCOMIT_RMSE_Interceptx1 x2 x3 x4 y06 5646 MODEL1RIDGEVIFy 0.2 .

12、 . . 0.931110.867880.959370.94043-17 MODEL1RIDGEy 0.2 . 1.93863-1.012640.022100.168430.06457-0.00892-18 MODEL1RIDGEVIFy 0.3 . . . 0.582530.667930.642260.66858-19 MODEL1RIDGEy 0.3 . 2.00683-0.905400.019100.163470.06867-0.00485-110MODEL1RIDGEVIFy 0.4 . . . 0.408100.534190.468120.50677-111MODEL1RIDGEy

13、0.4 . 2.06377-0.789810.017120.157340.07014-0.00214-112MODEL1RIDGEVIFy 0.5 . . . 0.307650.439200.361160.40141-113MODEL1RIDGEy 0.5 . 2.11323-0.673860.015690.151110.07039-0.00022-114MODEL1RIDGEVIFy 0.6 . . . 0.244000.368850.290190.32835-115MODEL1RIDGEy 0.6 . 2.15754-0.560600.014590.145150.070020.00118-

14、116MODEL1RIDGEVIFy 0.7 . . . 0.200790.315050.240350.27526-117MODEL1RIDGEy 0.7 . 2.19809-0.451280.013700.139580.069290.00223-118MODEL1RIDGEVIFy 0.8 . . . 0.169850.272870.203780.23524-1Obs_MODEL_TYPE_DEPVAR_RIDGE_PCOMIT_RMSE_Interceptx1 x2 x3 x4 y19MODEL1RIDGEy 0.8 . 2.23577-0.346340.012960.134400.068

15、370.00304-120MODEL1RIDGEVIFy 0.9 . . . 0.146770.239110.176000.20419-121MODEL1RIDGEy 0.9 . 2.27118-0.245870.012340.129610.067330.00367-122MODEL1RIDGEVIFy 1.0 . . . 0.128970.211600.154300.17952-123MODEL1RIDGEy 1.0 . 2.30470-0.149800.011790.125170.066230.00417-1（6）剔出 后再做岭回归。3x程序：proc reg data=a graphic

16、s outest=out1 outvif;model y=x1 x2 x4/ridge=0 to 1 by 0.1;plot/ridgeplot;run;proc print data=out1;run;由岭迹图，当 K=0.4后，岭迹曲线趋于稳定，说明 K=0.4即可以满足岭回归参数估计的均方误差较小的的要求，对应的岭回归估计的回归方程: y=-0.44738+0.02002x1+0.17052x2+0.00190x4.X4的回归系数变为正值,合理。Obs_MODEL_TYPE_DEPVAR_RIDGE_PCOMIT_RMSE_Interceptx1 x2 x4 Y1 MODEL1PARMS

17、 Y . . 1.73721-0.971600.041040.14886-0.02850-12 MODEL1RIDGEVIFY 0.0 . . . 3.731051.883112.59014-13 MODEL1RIDGE Y 0.0 . 1.73721-0.971600.041040.14886-0.02850-14 MODEL1RIDGEVIFY 0.1 . . . 1.570851.167601.32188-15 MODEL1RIDGE Y 0.1 . 1.80898-0.885710.030380.17545-0.01260-1Obs_MODEL_TYPE_DEPVAR_RIDGE_PC

18、OMIT_RMSE_Interceptx1 x2 x4 Y6 MODEL1RIDGEVIFY 0.2 . . . 0.899360.838900.86203-17 MODEL1RIDGE Y 0.2 . 1.89761-0.745030.025260.17883-0.00511-18 MODEL1RIDGEVIFY 0.3 . . . 0.602460.645480.62902-19 MODEL1RIDGE Y 0.3 . 1.97268-0.594980.022160.17573-0.00082-110 MODEL1RIDGEVIFY 0.4 . . . 0.443250.517900.48

19、934-111 MODEL1RIDGE Y 0.4 . 2.03698-0.447380.020020.170520.00190-112 MODEL1RIDGEVIFY 0.5 . . . 0.346680.427850.39679-113 MODEL1RIDGE Y 0.5 . 2.09383-0.305990.018420.164700.00373-114 MODEL1RIDGEVIFY 0.6 . . . 0.282840.361260.33126-115 MODEL1RIDGE Y 0.6 . 2.14535-0.171960.017150.158830.00500-116 MODEL1RIDGEVIFY 0.7 . . . 0.237890.310310.28260-117 MODEL1RIDGE y 0.7 . 2.19285-0.045440.016110.153140.00591-118 MODEL1RIDGEVIFY 0.8 . . . 0.204680.270250.24516-119 MODEL1RIDGE Y 0.8 . 2.237150.073820.015240.147740.00657-1