# Principal component regression

Principal component regression

In statistics, principal component regression (PCR) is a regression analysis that uses principal component analysis when estimating regression coefficients.

In PCR instead of regressing the independent variables (the regressors) on the dependent variable 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, &mdash; in some cases even more important. [Cite journal
author = Ian T. Jolliffe
title = A note on the Use of Principal Components in Regression
journal = Journal of the Royal Statistical Society, Series C (Applied Statistics)
volume = 31
issue = 3
year = 1982
pages = 300&ndash;303
url = http://www.jstor.org/action/showArticle?doi=10.2307/2348005
]

* Canonical correlation
* Partial least squares regression
* Total sum of squares

References

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