The REG Procedure
- Overview
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Getting Started
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Syntax
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DetailsMissing ValuesInput Data SetsOutput Data SetsInteractive AnalysisModel-Selection MethodsCriteria Used in Model-Selection MethodsLimitations in Model-Selection MethodsParameter Estimates and Associated StatisticsPredicted and Residual ValuesModels of Less Than Full RankCollinearity DiagnosticsModel Fit and Diagnostic StatisticsInfluence StatisticsReweighting Observations in an AnalysisTesting for HeteroscedasticityTesting for Lack of FitMultivariate TestsAutocorrelation in Time Series DataComputations for Ridge Regression and IPC AnalysisConstruction of Q-Q and P-P PlotsComputational MethodsComputer Resources in Regression AnalysisDisplayed OutputPlot Options Superseded by ODS GraphicsODS Table NamesODS Graphics
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Examples
- References
In ridge regression analysis, the crossproduct matrix for the independent variables is centered (the NOINT option is ignored if it is specified) and scaled to one on the diagonal elements. The ridge constant k (specified with the RIDGE= option) is then added to each diagonal element of the crossproduct matrix. The ridge regression estimates are the least squares estimates obtained by using the new crossproduct matrix.
Let X be an 
matrix of the independent variables after centering the data, and let Y be an 
vector corresponding to the dependent variable. Let D be a 
diagonal matrix with diagonal elements as in 
. The ridge regression estimate corresponding to the ridge constant k can be computed as
![\[ \mb{D}^{ - {\frac{1}{2}} } (\mb{Z}’\mb{Z} + k\mb{I}_{p})^{-1} \mb{Z}’\mb{Y} \]](images/statug_reg0170.png){kind=small}
where 
and 
is a 
identity matrix.
For IPC analysis, the smallest m eigenvalues of 
(where m is specified with the PCOMIT= option) are omitted to form the estimates.
For information about ridge regression and IPC standardized parameter estimates, parameter estimate standard errors, and variance inflation factors, see Rawlings, Pantula, and Dickey (1998); Neter, Wasserman, and Kutner (1990); Marquardt and Snee (1975). Unlike Rawlings, Pantula, and Dickey (1998), the REG procedure uses the mean squared errors of the submodels instead of the full model MSE to compute the standard errors of the parameter estimates.