用SPSS进行主成分回归实例分析

1、如何利用SPSS进行主成分回归实例分析主成分回归分析数据编辑、定义格式x1x2x3x4x5Y15.572463472.92184.45566.5244.0220481339.759.56.92696.8220.423940620.2512.84.281033.1518.746505568.3336.73.91603.6249.257231497.635.75.51611.3744.92115201365.83244.61613.2755.485779168743.35.621854.1759.2859691639.9246.75.152160.5594.3984612872.3378.76.1

2、82305.58128.02201063655.08180.56.153503.939613313291260.95.883571.89131.42107713921103.74.883741.4127.21155433865.67126.85.54026.52252.9361947684.1157.7710343.81409.23470312446.33169.410.7811732.17463.73920414098.4331.47.0515414.94510.228653315524371.66.3518854.45第一步，进行一般的线性回归分析：首先给出各个变量的平均值，标准差，膨胀系

3、数VIF，以便进行多重共线性诊断。变量平均值标准差膨胀系数VIFx1148.27588161.038589597.57076x218163.2352921278.110557.94059x34480.618244906.642068933.08650x4106.31765107.9541523.29386x55.893531.584074.27984y4978.480005560.53359然后给出各个变量之间的相关系数（右上角为显著水平）。x1x2x3x4x5yx11.000000.000000.000000.000000.003180.00000x20.907381.000000.0000

4、00.000000.072280.00000x30.999900.907151.000000.000000.003180.00000x40.935690.910470.933171.000000.061350.00000x50.671200.446650.671110.462861.000000.01497y0.985650.945170.985990.940360.578581.00000以及一般线性回归模型分析结果:方差分析表方差来源平方和df均方F值显著水平回归490177488.12165598035497.62433237.790080.00000剩余4535052.36735114

5、12277.48794总的494712540.489001630919533.78056相关系数R=0.995406，决定系数RR=0.990833，调整相关R'=0.993311变量x回归系数标准系数偏相关标准误t值显著水平b01962.948031071.361661.832200.09184b1-15.85167-0.45908-0.0488897.65299-0.162330.87375b20.055930.214030.621480.021262.630990.02194b31.589621.402690.153183.092080.514090.61652b4-4.2186

6、7-0.08190-0.174527.17656-0.587840.56754b5-394.31413-0.11233-0.49331209.63954-1.880910.08446剩余标准差 sse=642.08838, Durbin-Watson d=2.73322。第二步，对自变量进行主成分分析，给出主成分分析结果:No特征值百分率%累计百分率%14.1971283.9423483.9423420.6674813.3496897.2920230.094631.8926699.1846940.040710.8142399.9989250.000050.00108100.00000并显示如下

7、选择主成分个数的用户操作界面:NOr吾分出1419.711783.9483.9426E.748413.3597.2939.46331 8944.07120.&1100.0050J0540.00100.00主成分回归模型r愣宦主咸井牛類特征向量（转置）x1x2x3x4x5z10.485290.453240.484980.460970.33374z2-0.00203-0.33561-0.00085-0.310800.88925z3-0.166230.80424-0.15396-0.537200.11524z4-0.468190.18747-0.509260.633860.29073z5-0

8、.71948-0.001160.694080.023440.00678自变量主成分得分（取特征值累积达到 99%以上时的主成分个数）NoZ(i,1)Z(i,2)Z(i,3)yN(1)-1.81170-0.306090.00379566.52000N(2)-1.165041.111000.15353696.82000N(3)-1.80908-0.409930.063501033.15000N(4)-1.74265-0.732490.017231603.62000N(5)-1.242840.180370.048451611.37000N(6)-1.38486-0.382530.268861613.

9、27000N-1.146270.224860.009051854.17000N(8)-1.21993-0.05181-0.037322160.55000N(9)-0.585590.39431-0.102352305.58000N(10)0.26954-0.09984-0.230243503.93000N(11)-0.612670.200590.144883571.89000N(12)-0.48828-0.44453-0.305153741.40000N(13)-0.17553-0.23818-0.188554026.52000N(14)1.468500.186950.2977910343.81

10、000N(15)3.224792.295960.1474411732.17000N(16)3.55409-0.33631-0.8680315414.94000N(17)4.86750-1.592330.5771218854.45000第三步，进行主成分回归分析： 主成分回归分析分析结果如下：方差分析表方差来源平方和df均方F值显著水平回归484175253.055983161391751.01866199.111280.00000剩余10537287.4330313810560.57177总的494712540.489001630919533.78056相关系数 R=0.989293，决定系数

11、 RR=0.978700，调整相关 R'=0.986805变量z回归系数标准系数偏相关标准误t值显著水平b04978.47984218.3575822.799670.00000b12664.871530.981830.98913109.8644424.256000.00000b2-814.79027-0.11972-0.63421275.49407-2.957560.01039b3353.292640.019550.13274731.662810.482860.63666剩余标准差 sse=900.31137.Durbi n-Watson d=2.09706标准化回归方程:标准化变量系

12、数std(xi)的表达式：1236.148190std(x1)1765.393344std(x2)1238.704012std(x3)1291.872390std(x4)205.526701std(x5)std(x1)=(x1-148.2759)/161.0386 std(x2)=(x2-18163.2353)/21278.1105 std(x3)=(x3-4480.6182)/4906.6421 std(x4)=(x4-106.3176)/107.9542 std(x5)=(x5-5.8935)/1.5841主成分回归方程：y=-834.761535+7.676100x1+0.082968x

13、2+0.252455x3+11.966861x4+129.745739x5样本号观察值拟合值误差1566.52000401.26733165.252672696.820001022.80963-325.9896331033.15000513.94920519.2008041603.62000937.46236666.1576451611.370001536.6204574.7495561613.270001694.68043-81.4104371854.170001743.80506110.3649482160.550001756.55935403.9906592305.580003060.52759-754.94759103503.930005696.77520-2192.84520113571.890003233.525