多元统计--基于R

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1、习题6.3>data6.3<-read.table("clipboard",header=T)>R=round(cor(data6.3),3)>Rx1x2x3x4x5x6x11.0000.9560.8540.4140.1810.100x20.9561.0000.8060.4060.2460.235x30.8540.8061.0000.5330.2420.058x40.4140.4060.5331.000-0.0540.330x50.1810.2460.242-0.0541.0000.436x60.100

2、0.2350.0580.3300.4361.000>PCA6.3=princomp(data6.3,cor=T)>PCA6.3Call:princomp(x=data6.3,cor=T)Standarddeviations:Comp.1Comp.2Comp.3Comp.4Comp.5Comp.61.78112711.14764610.96759490.64812580.34995290.17810386variablesand28observations.>summary(PCA6.3,loadings

3、=T)Importanceofcomponents:Comp.1Comp.2Comp.3Comp.4Comp.5Standarddeviation1.78112711.14764610.96759490.648125790.34995293ProportionofVariance0.52873560.21951520.15604000.070011170.02041118CumulativeProportion0.52873560.74825090.90429080.974302000.99471317

4、Comp.6Standarddeviation0.178103814ProportionofVariance0.005286828CumulativeProportion1.000000000Loadings:Comp.1Comp.2Comp.3Comp.4Comp.5Comp.6x1-0.5220.195-0.191-0.2550.2160.736x2-0.525-0.166-0.3890.312-0.664x3-0.5110.181-0.1050.336-0.756x4-0.3460.7410.45

5、60.347x5-0.188-0.657-0.4710.4960.254x6-0.185-0.6990.392-0.465-0.315>screeplot(PCA6.3,type="lines")从输出结果看，主成分的标准差，及相关矩阵的六个特征值的开方分别为√λ1=1.7811271√λ2=1.1476461√λ3=0.9675949√λ4=0.64812579√λ5=0.34995293√λ6=0.178103814前三个主成分0.5287356+0.2195152+0.1560400=0.9042

6、908已经超过90%，所以取三个主成分就可以了。第一主成分z=-0.522x1-5.525x2-0.511x3-0.346x4-0.188x5-0.185x6第二主成分z=0.195x1+0.181x3-0.657x5-0.699x6第三主成分z=-0.191x1-0.166x2-0.105x3+0.741x4-0.471x5+0.392习题6.4>data6.4<-read.table("clipboard",header=T)>R=round(cor(data6.4),3)>RX1X2X3X4X5X

7、6X7X8X9X10X11.0000.893-0.3610.9950.9750.9400.919-0.4340.080-0.045X20.8931.000-0.3390.8700.7850.7960.761-0.397-0.064-0.058X3-0.361-0.3391.000-0.322-0.336-0.399-0.3840.625-0.0080.084X40.9950.870-0.3221.0000.9810.9250.908-0.4220.093-0.067X50.9750.785-0.3360

8、.9811.0000.9360.914-0.4000.108-0.038X60.9400.796-0.3990.9250.9361.0000.938-0.4600.107-0.027X70.9190.761-0.3840.9080.9140.9381.000-0.4670.176-0.063X8-0.434-0.3970.625-0.422-0.400-0.460-0.4671.000-0.5390.537X90.080-0.064-0.0