应用回归分析实验报告
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1、实 验 报 告实验课程 应用回归分析 第 6 次实验 实验日期2012.11.22 指导教师 王振羽 班级 基地班 学号 1007402072 姓名 张艺璇 成绩 一、实验目的掌握利用统计软件SAS的REG过程中各种最优准则，选取最好的线性回归方程的方法. 掌握SPSS中用前进法、后退法、逐步回归法选择自变量二、实验内容1在教材习题5.9的问题中，使用直到2004年的数据。(数据在“回归人大数据12-学生.xls：ex5_9-07年”中 )，利用统计软件(1) 写出修正的复决定系数AdjRSQ最好的三个回归方程，及相应的Cp值、AIC值。(2) 写出Cp准则最好的三个回归方程，及相应的AdjR
2、SQ值、AIC值。(3) 写出用向前法 (a进 = 0.05，0.10) 得到的两个回归方程；(4) 写出用后退法 (a退 = 0.10，0.15) 得到的两个回归方程；(5) 写出用逐步回归法 (a进,a退 = 0.05,0.10; 0.10, 0.15; 0.15, 0.20) 得到的三个回归方程；(6) 在你看来，上面写出的回归方程中，哪个最好？(写出理由) 本次实验结果随作业交上来。三、实验结果与分析（包括运行结果及其数据分析、解释等）(1) 写出修正的复决定系数AdjRSQ最好的三个回归方程，及相应的Cp值、AIC值。用SAS寻找最优子集程序如下：proc reg;model y=x
3、1-x6/selection=adjrsq;run;输出部分结果如下：系数a模型非标准化系数标准系数tSig.B标准 误差试用版1(常量)-1.138.325-3.503.002x1-1.487.136-1.313-10.966.000x21.171.1883.0776.237.000x3-2.4671.258-1.009-1.962.063x4.155.035.2404.445.000x6-.058.018-.057-3.151.005a. 因变量: y系数a模型非标准化系数标准系数tSig.B标准 误差试用版1(常量)-1.226.345-3.556.002x1-1.455.142-1.2
4、85-10.228.000x21.235.2053.2466.027.000x3-2.4751.268-1.012-1.952.065x4.162.036.2514.477.000x5-.061.075-.206-.818.423x6-.053.019-.053-2.761.012a. 因变量: y系数a模型非标准化系数标准系数tSig.B标准 误差试用版1(常量)-1.199.344-3.491.002x1-1.567.138-1.384-11.394.000x2.808.0352.12423.165.000x4.165.037.2554.498.000x6-.058.019-.057-2.
5、979.007a. 因变量: y故修正的复决定系数AdjRSQ最好的三个回归方程为：y=-1.138-1.487x1+1.171x2-2.467x3+0.155x4-0.058x6 (cp=5.6693,AIC=-153.1970)y=-1.226-1.455x1+1.235x2-2.475x3+0.162x4-0.061x5-0.053x6 (cp=7.0000,AIC=-153.0858)y=-1.199-1.567x1+0.808x2+0.165x4-0.058x6 (cp=7.4571,AIC=-150.6537)(2) 写出Cp准则最好的三个回归方程，及相应的AdjRSQ值、AIC值
6、。用SAS寻找最优子集程序如下：proc reg;model y=x1-x6/selection=cp;run;输出部分结果如下：故Cp准则最好的三个回归方程为：y=-1.138-1.487x1+1.171x2-2.467x3+0.155x4-0.058x6 (AdjRSQ=0.9943,AIC=-153.1970)y=-1.226-1.455x1+1.235x2-2.475x3+0.162x4-0.061x5-0.053x6 (AdjRSQ=0.9942,AIC=-153.0858)y=-1.199-1.567x1+0.808x2+0.165x4-0.058x6 (AdjRSQ=0.9935
7、,AIC=-150.6537)(3) 写出用向前法 (a进 = 0.05，0.10) 得到的两个回归方程；a进 = 0.05：模型汇总模型RR 方调整 R 方标准 估计的误差1.974a.949.947.162617462.994b.989.988.076818283.996c.992.991.065515374.997d.995.994.05654776a. 预测变量: (常量), x2。b. 预测变量: (常量), x2, x1。c. 预测变量: (常量), x2, x1, x4。d. 预测变量: (常量), x2, x1, x4, x6。Anovae模型平方和df均方FSig.1回归12
8、.223112.223462.225.000a残差.66125.026总计12.884262回归12.74326.3711079.703.000b残差.14224.006总计12.884263回归12.78634.262992.923.000c残差.09923.004总计12.884264回归12.81443.2041001.833.000d残差.07022.003总计12.88426a. 预测变量: (常量), x2。b. 预测变量: (常量), x2, x1。c. 预测变量: (常量), x2, x1, x4。d. 预测变量: (常量), x2, x1, x4, x6。e. 因变量: y系
9、数a模型非标准化系数标准系数tSig.B标准 误差试用版1(常量)-.015.045-.332.743x2.371.017.97421.499.0002(常量).202.0316.474.000x2.760.0421.99717.970.000x1-1.181.126-1.043-9.383.0003(常量)-1.037.393-2.639.015x2.817.0402.14620.275.000x1-1.553.159-1.371-9.751.000x4.125.039.1933.162.0044(常量)-1.199.344-3.491.002x2.808.0352.12423.165.00
10、0x1-1.567.138-1.384-11.394.000x4.165.037.2554.498.000x6-.058.019-.057-2.979.007a. 因变量: y故得到的回归方程为：y=-1.199-1.567x1+0.808x2+0.165x4-0.058x6a进 = 0.10:模型汇总模型RR 方调整 R 方标准 估计的误差1.974a.949.947.162617462.994b.989.988.076818283.996c.992.991.065515374.997d.995.994.056547765.998e.995.994.05320788a. 预测变量: (常量)
11、, x2。b. 预测变量: (常量), x2, x1。c. 预测变量: (常量), x2, x1, x4。d. 预测变量: (常量), x2, x1, x4, x6。e. 预测变量: (常量), x2, x1, x4, x6, x3。Anovaf模型平方和df均方FSig.1回归12.223112.223462.225.000a残差.66125.026总计12.884262回归12.74326.3711079.703.000b残差.14224.006总计12.884263回归12.78634.262992.923.000c残差.09923.004总计12.884264回归12.81443.20
12、41001.833.000d残差.07022.003总计12.884265回归12.82552.565906.011.000e残差.05921.003总计12.88426a. 预测变量: (常量), x2。b. 预测变量: (常量), x2, x1。c. 预测变量: (常量), x2, x1, x4。d. 预测变量: (常量), x2, x1, x4, x6。e. 预测变量: (常量), x2, x1, x4, x6, x3。f. 因变量: y系数a模型非标准化系数标准系数tSig.B标准 误差试用版1(常量)-.015.045-.332.743x2.371.017.97421.499.000
13、2(常量).202.0316.474.000x2.760.0421.99717.970.000x1-1.181.126-1.043-9.383.0003(常量)-1.037.393-2.639.015x2.817.0402.14620.275.000x1-1.553.159-1.371-9.751.000x4.125.039.1933.162.0044(常量)-1.199.344-3.491.002x2.808.0352.12423.165.000x1-1.567.138-1.384-11.394.000x4.165.037.2554.498.000x6-.058.019-.057-2.979
14、.0075(常量)-1.138.325-3.503.002x21.171.1883.0776.237.000x1-1.487.136-1.313-10.966.000x4.155.035.2404.445.000x6-.058.018-.057-3.151.005x3-2.4671.258-1.009-1.962.063a. 因变量: y故得到的回归方程为：y=-1.138-1.487x1+1.171x2-2.467x3+0.155x4-0.058x6 (4) 写出用后退法 (a退 = 0.10，0.15) 得到的两个回归方程；a退 = 0.15:模型汇总模型RR 方调整 R 方标准 估计的误
15、差1.998a.996.994.053632152.998b.995.994.05320788a. 预测变量: (常量), x6, x2, x4, x1, x5, x3。b. 预测变量: (常量), x6, x2, x4, x1, x3。Anovac模型平方和df均方FSig.1回归12.82762.138743.222.000a残差.05820.003总计12.884262回归12.82552.565906.011.000b残差.05921.003总计12.88426a. 预测变量: (常量), x6, x2, x4, x1, x5, x3。b. 预测变量: (常量), x6, x2, x4
16、, x1, x3。c. 因变量: y系数a模型非标准化系数标准系数tSig.B标准 误差试用版1(常量)-1.226.345-3.556.002x1-1.455.142-1.285-10.228.000x21.235.2053.2466.027.000x3-2.4751.268-1.012-1.952.065x4.162.036.2514.477.000x5-.061.075-.206-.818.423x6-.053.019-.053-2.761.0122(常量)-1.138.325-3.503.002x1-1.487.136-1.313-10.966.000x21.171.1883.0776
17、.237.000x3-2.4671.258-1.009-1.962.063x4.155.035.2404.445.000x6-.058.018-.057-3.151.005a. 因变量: y故得到的回归方程为：y=-1.138-1.487x1+1.171x2-2.467x3+0.155x4-0.058x6a退 = 0.10:系数a模型非标准化系数标准系数tSig.B标准 误差试用版1(常量)-1.226.345-3.556.002x1-1.455.142-1.285-10.228.000x21.235.2053.2466.027.000x3-2.4751.268-1.012-1.952.065
18、x4.162.036.2514.477.000x5-.061.075-.206-.818.423x6-.053.019-.053-2.761.0122(常量)-1.138.325-3.503.002x1-1.487.136-1.313-10.966.000x21.171.1883.0776.237.000x3-2.4671.258-1.009-1.962.063x4.155.035.2404.445.000x6-.058.018-.057-3.151.005a. 因变量: y故得到的回归方程为：y=-1.138-1.487x1+1.171x2-2.467x3+0.155x4-0.058x6(5
19、) 写出用逐步回归法 (a进,a退 = 0.05,0.10; 0.10, 0.15; 0.15, 0.20) 得到的三个回归方程；a进,a退 = 0.05,0.10:模型汇总模型RR 方调整 R 方标准 估计的误差1.974a.949.947.162617462.994b.989.988.076818283.996c.992.991.065515374.997d.995.994.05654776a. 预测变量: (常量), x2。b. 预测变量: (常量), x2, x1。c. 预测变量: (常量), x2, x1, x4。d. 预测变量: (常量), x2, x1, x4, x6。Anova
20、e模型平方和df均方FSig.1回归12.223112.223462.225.000a残差.66125.026总计12.884262回归12.74326.3711079.703.000b残差.14224.006总计12.884263回归12.78634.262992.923.000c残差.09923.004总计12.884264回归12.81443.2041001.833.000d残差.07022.003总计12.88426系数a模型非标准化系数标准系数tSig.B标准 误差试用版1(常量)-.015.045-.332.743x2.371.017.97421.499.0002(常量).202.
21、0316.474.000x2.760.0421.99717.970.000x1-1.181.126-1.043-9.383.0003(常量)-1.037.393-2.639.015x2.817.0402.14620.275.000x1-1.553.159-1.371-9.751.000x4.125.039.1933.162.0044(常量)-1.199.344-3.491.002x2.808.0352.12423.165.000x1-1.567.138-1.384-11.394.000x4.165.037.2554.498.000x6-.058.019-.057-2.979.007a. 因变量
22、: y故得到的回归方程为：y=0.202-1.181x1+0.760x2a进,a退 = 0.10, 0.15:模型汇总模型RR 方调整 R 方标准 估计的误差1.974a.949.947.162617462.994b.989.988.076818283.996c.992.991.065515374.997d.995.994.056547765.998e.995.994.05320788a. 预测变量: (常量), x2。b. 预测变量: (常量), x2, x1。c. 预测变量: (常量), x2, x1, x4。d. 预测变量: (常量), x2, x1, x4, x6。e. 预测变量: (
23、常量), x2, x1, x4, x6, x3。Anovaf模型平方和df均方FSig.1回归12.223112.223462.225.000a残差.66125.026总计12.884262回归12.74326.3711079.703.000b残差.14224.006总计12.884263回归12.78634.262992.923.000c残差.09923.004总计12.884264回归12.81443.2041001.833.000d残差.07022.003总计12.884265回归12.82552.565906.011.000e残差.05921.003总计12.88426a. 预测变量:
24、 (常量), x2。b. 预测变量: (常量), x2, x1。c. 预测变量: (常量), x2, x1, x4。d. 预测变量: (常量), x2, x1, x4, x6。e. 预测变量: (常量), x2, x1, x4, x6, x3。f. 因变量: y系数a模型非标准化系数标准系数tSig.B标准 误差试用版1(常量)-.015.045-.332.743x2.371.017.97421.499.0002(常量).202.0316.474.000x2.760.0421.99717.970.000x1-1.181.126-1.043-9.383.0003(常量)-1.037.393-2.
25、639.015x2.817.0402.14620.275.000x1-1.553.159-1.371-9.751.000x4.125.039.1933.162.0044(常量)-1.199.344-3.491.002x2.808.0352.12423.165.000x1-1.567.138-1.384-11.394.000x4.165.037.2554.498.000x6-.058.019-.057-2.979.0075(常量)-1.138.325-3.503.002x21.171.1883.0776.237.000x1-1.487.136-1.313-10.966.000x4.155.035
26、.2404.445.000x6-.058.018-.057-3.151.005x3-2.4671.258-1.009-1.962.063a. 因变量: y故得到的回归方程为：y=0.202-1.181x1+0.760x2a进,a退 = 0.15, 0.20:模型汇总模型RR 方调整 R 方标准 估计的误差1.974a.949.947.162617462.994b.989.988.076818283.996c.992.991.065515374.997d.995.994.056547765.998e.995.994.05320788a. 预测变量: (常量), x2。b. 预测变量: (常量),
27、 x2, x1。c. 预测变量: (常量), x2, x1, x4。d. 预测变量: (常量), x2, x1, x4, x6。e. 预测变量: (常量), x2, x1, x4, x6, x3。Anovaf模型平方和df均方FSig.1回归12.223112.223462.225.000a残差.66125.026总计12.884262回归12.74326.3711079.703.000b残差.14224.006总计12.884263回归12.78634.262992.923.000c残差.09923.004总计12.884264回归12.81443.2041001.833.000d残差.07
28、022.003总计12.884265回归12.82552.565906.011.000e残差.05921.003总计12.88426a. 预测变量: (常量), x2。b. 预测变量: (常量), x2, x1。c. 预测变量: (常量), x2, x1, x4。d. 预测变量: (常量), x2, x1, x4, x6。e. 预测变量: (常量), x2, x1, x4, x6, x3。f. 因变量: y系数a模型非标准化系数标准系数tSig.B标准 误差试用版1(常量)-.015.045-.332.743x2.371.017.97421.499.0002(常量).202.0316.474.
29、000x2.760.0421.99717.970.000x1-1.181.126-1.043-9.383.0003(常量)-1.037.393-2.639.015x2.817.0402.14620.275.000x1-1.553.159-1.371-9.751.000x4.125.039.1933.162.0044(常量)-1.199.344-3.491.002x2.808.0352.12423.165.000x1-1.567.138-1.384-11.394.000x4.165.037.2554.498.000x6-.058.019-.057-2.979.0075(常量)-1.138.325-3.503.002x21.171.1883.0776.237.000x1-1.487.136-1.313-10.966.000x4.155.035.2404.445.000x6-.058.018-.057-3.151.005x3-2.4671.258-1.009-1.962.063a. 因变量: y故得到的回归方程为：y=0.202-1.181x1+0.760x2(6) 在你看来，上面写出的回归方程中，哪个最好？(写出理由)
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