rm(list = ls())
library(car)
library(MASS)
library(openxlsx)
A = read.xlsx("data141.xlsx")
head(A)
fm = lm(y~x1+x2+x3+x4 , data=A ) #判断多重共线性 vif(fm)
> vif(fm)
x1 x2 x3 x4
38.49621 254.42317 46.86839 282.51286 #具有多重共线性
#进行主成分回归 A.pr = princomp(~x1+x2+x3+x4 , data = A,cor=T) summary(A.pr,loadings = T) #输出特征值和特征向量
> summary(A.pr,loadings = T) #输出特征值和特征向量
Importance of components:
Comp.1 Comp.2 Comp.3 Comp.4
Standard deviation 1.495227 1.2554147 0.43197934 0.0402957285
Proportion of Variance 0.558926 0.3940165 0.04665154 0.0004059364
Cumulative Proportion 0.558926 0.9529425 0.99959406 1.0000000000
Loadings:
Comp.1 Comp.2 Comp.3 Comp.4
x1 0.476 0.509 0.676 0.241
x2 0.564 -0.414 -0.314 0.642
x3 -0.394 -0.605 0.638 0.268
x4 -0.548 0.451 -0.195 0.677
pre = predict(A.pr) #主成分，组合向量，无实际意义 A$z1 = pre[,1] A$z2 = pre[,2] #根据累积贡献率，根据保留两个主成分变量
lm.sol = lm(y~z1 + z2,data = A) #与主成分预测变量线性回归 lm.sol
> lm.sol
Call:
lm(formula = y ~ z1 + z2, data = A)
Coefficients:
(Intercept) z1 z2
95.4231 9.4954 -0.1201
> summary(lm.sol) #模型详细
Call:
lm(formula = y ~ z1 + z2, data = A)
Residuals:
Min 1Q Median 3Q Max
-3.3305 -2.1882 -0.9491 1.0998 4.4251
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 95.4231 0.8548 111.635 < 2e-16 ***
z1 9.4954 0.5717 16.610 1.31e-08 ***
z2 -0.1201 0.6809 -0.176 0.864
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 3.082 on 10 degrees of freedom
Multiple R-squared: 0.965, Adjusted R-squared: 0.958
F-statistic: 138 on 2 and 10 DF, p-value: 5.233e-08
beta = coef(lm.sol) #主成分分析的预测变量的系数 beta
> beta (Intercept) z1 z2 95.4230769 9.4953702 -0.1200892
#预测变量还原 eigen_vec = loadings(A.pr) #特征向量 x.bar = A.pr$center #均值？ x.sd = A.pr$scale #标准误？ xishu_1 = (beta[2]*eigen_vec[,1])/x.sd xishu_2 = (beta[3]*eigen_vec[,2])/x.sd coef = xishu_1 + xishu_2 coef beta0 = beta[1] - sum(x.bar*coef) B = c(beta0,coef) B #还原后的回归系数
#岭估计 esti_ling = lm.ridge(y~x1+x2+x3+x4 , data = A, lambda = seq(0,15,0.01)) plot(esti_ling)
#取k=5 k = 5 X = cbind(1,as.matrix(A[,2:5])) y = A[,6] B_ = solve((t(X)%*%X) + k*diag(5))%*%t(X)%*%y B_
> B_
[,1]
0.06158362
x1 2.12614307
x2 1.16796919
x3 0.71043177
x4 0.49566883