用SPSS进行主成分回归实例分析

如何利用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X1x2x3x4x5Y15.572463472.92184.45566.5244.0220481339.759.56.92696.8220.423940620.2512.84.281033.1518.746505568.3336.73.91603.6249.257231497.635.75.51611.3744.92115201365.83244.61613.2755.485779168743.35.621854.1759.2859691639.9246.75.152160.5594.3984612872.3378.76.182305.58128.02201063655.08180.56.153503.939613313291260.95.883571.89131.42107713921103.74.883741.4127.21155433865.67126.85.54026.52252.9361947684.1157.7710343.81409.23470312446.33169.410.7811732.17463.73920414098.4331.47.0515414.94510.228653315524371.66.3518854.45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）。x1x2x3x4x5yx11.000000.000000.000000.000000.003180.00000x20.907381.000000.000000.000000.072280.00000x30.999900.907151.000000.000000.003180.00000x40.935690.910470.933171.000000.061350.00000x50.671200.446650.671110.462861.000000.01497y0.985650.945170.985990.940360.578581.00000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4535052.3673511412277.48794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b01962.948031071.361661.832200.09184b1-15.85167-0.45908-0.0488897.65299-0.162330.87375b20.055930.214030.621480.021262.630990.02194b31.589621.402690.153183.092080.514090.61652b4-4.21867-0.08190-0.174527.17656-0.587840.56754b5-394.31413-0.11233-0.49331209.63954-1.880910.08446剩余标准差sse=642.08838，Durbin-Watsond=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并显示如下选择主成分个数的用户操作界面：特征向量（转置）x1x2x3x4x5z10.485290.453240.484980.460970.33374z2-0.00203-0.33561-0.00085-0.310800.88925z3-0.166230.80424-0.15396-0.537200.11524z4-0.468190.18747-0.509260.633860.29073z5-0.71948-0.001160.694080.023440.00678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)-1.38486-0.382530.268861613.27000N(7)-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)1.468500.186950.2977910343.81000N(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，Durbin-Watsond=2.09706标准化回归方程：标准化变量系数std(xi)的表达式：1236.148190std(xl)1765.393344std(x2)1238.704012std(x3)1291.872390std(x4)205.526701std(x5)std(x1)=(x1-148.2759)/161.0386std(x2)=(x2-18163.2353)/21278.1105std(x3)=(x3-4480.6182)/4906.6421std(x4)=(x4-106.3176)/107.9542std(x5)=(x5-5.8935)/1.5841主成分回归方程：y=-834.761535+7.676100x1+0.082968x2+0.252455x3+11.966861x4+129.745739x5样本号观察值拟合值误差1566.52000401.26733165.252672696.820001022.80963-325.9896331033.15000513.94920519.2008041603.62000937.46236666.1576451611.370001536.6204574.7495561613.270001694.68043-81.4104371854.170001743.80506110.3649482160.550001756.55935403.9906592305.580003060.52759-754.94759103503.930005696.77520-2192.84520113571.890003233.52582338.36418123741.400003931.67223-190.27223134026.520004638.18570-611.665701410343.810008844.732731499.077271511732.1700011753.50015-21.330151615414.9400014417.03717997.902831718854.4500019451.04692-596.59692