The REG Procedure
- Overview
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Getting Started
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Syntax
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Details
Missing Values Input Data Sets Output Data Sets Interactive Analysis Model-Selection Methods Criteria Used in Model-Selection Methods Limitations in Model-Selection Methods Parameter Estimates and Associated Statistics Predicted and Residual Values Models of Less Than Full Rank Collinearity Diagnostics Model Fit and Diagnostic Statistics Influence Statistics Reweighting Observations in an Analysis Testing for Heteroscedasticity Testing for Lack of Fit Multivariate Tests Autocorrelation in Time Series Data Computations for Ridge Regression and IPC Analysis Construction of Q-Q and P-P Plots Computational Methods Computer Resources in Regression Analysis Displayed Output ODS Table Names ODS Graphics
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Examples
- References
| Computations for Ridge Regression and IPC Analysis |
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 
can be computed as
 |
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, refer to Rawlings (1988), Neter, Wasserman, and Kutner (1990), and Marquardt and Snee (1975). Unlike Rawlings (1988), 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.