In statistics, principal component regression (PCR) is a regression analysis that uses principal component analysis when estimating regression coefficients. It is a procedure used to overcome problems which arise when the exploratory variables are close to being colinear.[1]
In PCR instead of regressing the dependent variable on the independent variables directly, the principal components of the independent variables are used. One typically only uses a subset of the principal components in the regression, making a kind of regularized estimation.
Often the principal components with the highest variance are selected. However, the low-variance principal components may also be important, — in some cases even more important.[2]
PCR (principal components regression) is a regression method that can be divided into three steps: