About: Principal component regression

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In statistics, principal component regression (PCR) is a regression analysis technique that is based on principal component analysis (PCA). More specifically, PCR is used for estimating the unknown regression coefficients in a standard linear regression model. In PCR, instead of regressing the dependent variable on the explanatory variables directly, the principal components of the explanatory variables are used as regressors. One typically uses only a subset of all the principal components for regression, making PCR a kind of regularized procedure and also a type of shrinkage estimator.

Attributes	Values
rdf:type	topical concept
rdfs:label	Hauptkomponentenregression (de) Régression sur composantes principales (fr) Principal component regression (en)
rdfs:comment	Die Hauptkomponentenregression (englisch principal component regression, kurz PCR) ist ein spezielles regressionsanalytisches Verfahren, das auf der Hauptkomponentenanalyse (PCA) basiert. Normalerweise wird bei einer Regression versucht, eine abhängige Variable durch eine Menge an unabhängigen Variablen zu erklären, z. B. basierend auf einem einfachen linearen Regressionsmodell. Die PCR verwendet die PCA, um in einem Zwischenschritt die Regressionskoeffizienten zu schätzen. Die PCR ist u. a. nützlich, wenn die Datenmatrix ein hohes Maß an Multikollinearität aufweist. (de) En statistiques, la Régression sur composantes principales est une analyse en régression sur les composantes d'une analyse en composantes principales. On utilise souvent cette technique lorsque les variables explicatives sont proches d'être colinéaires, lorsque par exemple le nombre de variables est très supérieur au nombre d'individus. La Régression sur composantes principales est souvent comparée à la Régression PLS (fr) In statistics, principal component regression (PCR) is a regression analysis technique that is based on principal component analysis (PCA). More specifically, PCR is used for estimating the unknown regression coefficients in a standard linear regression model. In PCR, instead of regressing the dependent variable on the explanatory variables directly, the principal components of the explanatory variables are used as regressors. One typically uses only a subset of all the principal components for regression, making PCR a kind of regularized procedure and also a type of shrinkage estimator. (en)
dcterms:subject	Regression analysis Factor analysis
Wikipage page ID	16960143 (xsd:integer)
Wikipage revision ID	1088086308 (xsd:integer)
Link from a Wikipage to another Wikipage	Sample mean and sample covariance Kernel methods Regression analysis Bias of an estimator Bergman kernel Ridge regression Variance Dependent and independent variables Column vector Correlation Estimation Estimator Gauss–Markov theorem Eigendecomposition of a matrix Eigenvalues and eigenvectors Eigenvectors Constrained optimization Coordinate system Cross-validation (statistics) Orthonormality Approximate Linear approximation Linear form Machine learning Singular value decomposition Statistics Deming regression Data matrix (multivariate statistics) Partial least squares regression Total sum of squares Collinear Column space Errors and residuals in statistics Feature space Linear combination Linear independence Linear regression Linearity Data transformation Centering matrix Dimension (vector space) Dimensionality reduction Principal component analysis Dimension reduction Prediction Rank (linear algebra) Regression analysis Regularization (mathematics) Covariance matrix Factor analysis Efficient estimator High-dimensional statistics Transformation matrix Positive-definite kernel Positive-definite matrix Inner product Ordinary least squares Orthogonal matrix Canonical correlation Mallows's Cp Map (mathematics) Mean squared error Multicollinearity Sample (statistics) Variance inflation factor Symmetric function Kernel trick Linear transformation Shrinkage estimator Eigenvalues Kernel PCA Kernel machine Partial least squares
Link from a Wikipage to an external page	https://archive.org/details/advancedeconomet00amem/page/57 https://archive.org/details/principlesofecon0000thei/page/46
sameAs	Principal component regression Principal component regression Principal component regression Principal component regression Principal component regression Principal component regression
dbp:wikiPageUsesTemplate	dbt:Regression_bar dbt:Cite_book dbt:Reflist
has abstract	Die Hauptkomponentenregression (englisch principal component regression, kurz PCR) ist ein spezielles regressionsanalytisches Verfahren, das auf der Hauptkomponentenanalyse (PCA) basiert. Normalerweise wird bei einer Regression versucht, eine abhängige Variable durch eine Menge an unabhängigen Variablen zu erklären, z. B. basierend auf einem einfachen linearen Regressionsmodell. Die PCR verwendet die PCA, um in einem Zwischenschritt die Regressionskoeffizienten zu schätzen. Die PCR ist u. a. nützlich, wenn die Datenmatrix ein hohes Maß an Multikollinearität aufweist. (de) En statistiques, la Régression sur composantes principales est une analyse en régression sur les composantes d'une analyse en composantes principales. On utilise souvent cette technique lorsque les variables explicatives sont proches d'être colinéaires, lorsque par exemple le nombre de variables est très supérieur au nombre d'individus. La Régression sur composantes principales est souvent comparée à la Régression PLS (fr) In statistics, principal component regression (PCR) is a regression analysis technique that is based on principal component analysis (PCA). More specifically, PCR is used for estimating the unknown regression coefficients in a standard linear regression model. In PCR, instead of regressing the dependent variable on the explanatory variables directly, the principal components of the explanatory variables are used as regressors. One typically uses only a subset of all the principal components for regression, making PCR a kind of regularized procedure and also a type of shrinkage estimator. Often the principal components with higher variances (the ones based on eigenvectors corresponding to the higher eigenvalues of the sample variance-covariance matrix of the explanatory variables) are selected as regressors. However, for the purpose of predicting the outcome, the principal components with low variances may also be important, in some cases even more important. One major use of PCR lies in overcoming the multicollinearity problem which arises when two or more of the explanatory variables are close to being collinear. PCR can aptly deal with such situations by excluding some of the low-variance principal components in the regression step. In addition, by usually regressing on only a subset of all the principal components, PCR can result in dimension reduction through substantially lowering the effective number of parameters characterizing the underlying model. This can be particularly useful in settings with high-dimensional covariates. Also, through appropriate selection of the principal components to be used for regression, PCR can lead to efficient prediction of the outcome based on the assumed model. (en)
gold:hypernym	Technique
prov:wasDerivedFrom	wikipedia-en:Principal_component_regression?oldid=1088086308&ns=0

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