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Die Hauptkomponentenregression (englisch p … 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. hohes Maß an Multikollinearität aufweist.
, En statistiques, la Régression sur composa … 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 PLSs est souvent comparée à la Régression PLS
, In statistics, principal component regress … 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.of the outcome based on the assumed model.
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Die Hauptkomponentenregression (englisch p … 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. hohes Maß an Multikollinearität aufweist.
, In statistics, principal component regress … 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.re and also a type of shrinkage estimator.
, En statistiques, la Régression sur composa … 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 PLSs est souvent comparée à la Régression PLS
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Régression sur composantes principales
, Hauptkomponentenregression
, Principal component regression
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