Principal Components Regression

This function computes the Principal Components Regression (PCR) fit.

Usage

pcr(
  X,
  y,
  scale = TRUE,
  m = min(ncol(X), nrow(X) - 1),
  eps = 1e-06,
  supervised = FALSE
)

Arguments

X: matrix of predictor observations.
y: vector of response observations. The length of y is the same as the number of rows of X.
scale: Should the predictor variables be scaled to unit variance? Default is TRUE.
m: maximal number of principal components. Default is m=min(ncol(X),nrow(X)-1).
eps: precision. Eigenvalues of the correlation matrix of X that are smaller than eps are set to 0. The default value is eps=10^{-6}.
supervised: Should the principal components be sorted by decreasing squared correlation to the response? Default is FALSE.

Value

coefficients: matrix of regression coefficients, including the coefficients of the null model, i.e. the constant model mean(y).
intercept: vector of intercepts, including the intercept of the null model, i.e. the constant model mean(y).

Details

The function first scales all predictor variables to unit variance, and then computes the PCR fit for all components. Is supervised=TRUE, we sort the principal correlation according to the squared correlation to the response.

Author

Nicole Kraemer

Examples


n<-50 # number of observations
p<-15 # number of variables
X<-matrix(rnorm(n*p),ncol=p)
y<-rnorm(n)

my.pcr<-pcr(X,y,m=10)