主成分分析之法国经济分析数据详解

#### 用数据框的形式输入数据
conomy<-data.frame(
  x1=c(149.3, 161.2, 171.5, 175.5, 180.8, 190.7, 
       202.1, 212.4, 226.1, 231.9, 239.0),
  x2=c(4.2, 4.1, 3.1, 3.1, 1.1, 2.2, 2.1, 5.6, 5.0, 5.1, 0.7),
  x3=c(108.1, 114.8, 123.2, 126.9, 132.1, 137.7, 
       146.0, 154.1, 162.3, 164.3, 167.6),
  y=c(15.9, 16.4, 19.0, 19.1, 18.8, 20.4, 22.7, 
      26.5, 28.1, 27.6, 26.3)
)
#### 作线性回归
lm.sol<-lm(y~x1+x2+x3, data=conomy)
summary(lm.sol)

 

#### 作主成分分析
conomy.pr<-princomp(~x1+x2+x3, data=conomy, cor=T)
summary(conomy.pr, loadings=TRUE)

Importance of components:
                         Comp.1    Comp.2       Comp.3
Standard deviation     1.413915 0.9990767 0.0518737839
Proportion of Variance 0.666385 0.3327181 0.0008969632
Cumulative Proportion  0.666385 0.9991030 1.0000000000

Loadings:
   Comp.1 Comp.2 Comp.3
x1  0.706         0.707
x2        -0.999       
x3  0.707        -0.707

#### 预测测样本主成分, 并作主成分分析
pre<-predict(conomy.pr)
conomy$z1<-pre[,1]
conomy$z2<-pre[,2]
lm.sol<-lm(y~z1+z2, data=conomy)
summary(lm.sol)

Call:
lm(formula = y ~ z1 + z2, data = conomy)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.89838 -0.26050  0.08435  0.35677  0.66863 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  21.8909     0.1658 132.006 1.21e-14 ***
z1            2.9892     0.1173  25.486 6.02e-09 ***
z2           -0.8288     0.1660  -4.993  0.00106 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.55 on 8 degrees of freedom
Multiple R-squared:  0.9883,	Adjusted R-squared:  0.9853 
F-statistic: 337.2 on 2 and 8 DF,  p-value: 1.888e-08

 

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