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 collinear.[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]

## The principle

PCR (principal components regression) is a regression method that can be divided into three steps:[citation needed]

1. The first step is to run a principal components analysis on the table of the explanatory variables,
2. The second step is to run an ordinary least squares regression (linear regression) on the selected components: the factors that are most correlated with the dependent variable will be selected
3. Finally the parameters of the model are computed for the selected explanatory variables.