Principal Components Regression (PCR)
Also known as: PCR, PCA regression, temel bileşenler regresyonu
Principal components regression first compresses a set of correlated predictors into a few principal components — the directions of greatest variance — and then regresses the response on those components. By discarding low-variance directions, PCR stabilizes estimation in the presence of multicollinearity and high dimensionality, at the cost of choosing components without reference to the response.
Read the full method
Sign in with a free account to read this section.
Method map
The neighbourhood of related methods — select a node to explore.
When to use it
Use PCR when predictors are highly collinear or numerous and you want a simple, stable model built on a few interpretable directions of variation. It is closely related to ridge regression (both shrink along low-variance directions, ridge smoothly and PCR by hard truncation) and is a natural baseline alongside PLS. Its defining limitation is that component selection is unsupervised: if the response is driven by a low-variance direction of the predictors, PCR may discard exactly the signal you need, in which case PLS — which forms components using the response — is preferable. Like all PCA-based methods it is scale-sensitive, so predictors should be standardized first.
Strengths & limitations
- Stabilizes regression under severe multicollinearity by using orthogonal components.
- Reduces dimensionality, helping when predictors are many relative to observations.
- Builds on well-understood PCA, with interpretable variance-explained diagnostics.
- Closely connected to ridge regression, providing a clear conceptual anchor.
- Component selection ignores the response, so predictive low-variance directions can be discarded.
- Often needs more components than PLS to achieve the same accuracy.
- Scale-sensitive; predictors must be standardized before PCA.
- Principal components can be hard to interpret substantively.
Frequently asked
How does PCR differ from PLS?
PCR selects components by predictor variance alone (unsupervised) and then regresses on them; PLS selects components to maximize covariance with the response (supervised). Consequently PCR can discard low-variance directions that predict the response well, whereas PLS keeps response-relevant directions and usually needs fewer components.
How is PCR related to ridge regression?
Both counter multicollinearity by down-weighting low-variance directions of the predictors. PCR does this abruptly — it keeps the top components and drops the rest — while ridge regression shrinks all directions smoothly, more for low-variance ones. Ridge often performs slightly better because it does not discard information entirely.
How many components should I keep?
Choose the number of principal components by cross-validation, picking the count that minimizes cross-validated prediction error. Keeping too few omits useful variation; keeping too many reintroduces the instability PCR was meant to avoid.
Sources
- Jolliffe, I. T. (1982). A note on the use of principal components in regression. Journal of the Royal Statistical Society: Series C (Applied Statistics), 31(3), 300–303. DOI: 10.2307/2348005 ↗
- Hastie, T., Tibshirani, R., & Friedman, J. (2009). The Elements of Statistical Learning (2nd ed.). Springer. ISBN: 978-0-387-84857-0
How to cite this page
ScholarGate. (2026, June 2). Principal Components Regression (PCR). ScholarGate. https://scholargate.app/en/machine-learning/principal-components-regression
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Multiple Linear RegressionStatistics↔ compare
- Partial Least SquaresMachine learning↔ compare
- Ridge RegressionMachine learning↔ compare