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.
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.
PCR (principal components regression) is a regression method that can be divided into three steps:
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