PCR(Principal Component Regression)とPLSR(Partial Least Squares Regression

  • Y = XB + \epsilon
  • 重回帰 Multiple Linear Regression
    • B=(X^TX)^{-1}X^TY
# 重回帰 multiple linear regression
n<-6
m<-4
X<-matrix(runif(n*m),n,m)
m2<-2
Y<-matrix(runif(n*m2),n,m2)
B<-solve(t(X)%*%X)%*%t(X)%*%Y
Y-X%*%B
# n<m とすると解けない
m<-n+1
X<-matrix(runif(n*m),n,m)
m2<-2
Y<-matrix(runif(n*m2),n,m2)
B<-solve(t(X)%*%X)%*%t(X)%*%Y
Y-X%*%B