Usage Note 22632: How is R-square redefined when the NOINT option is used in the MODEL statement?
R2 is still calculated as the regression sum of squares divided by the total sum
of squares. However, when there is no intercept in the model, the uncorrected,
rather than corrected, sum of squares (SS) is used. The best reference for exactly
how the calculations are being performed is the section on multiple correlation in Searle (1971, pp. 95-98). A good discussion of regression through the origin can also be found in SAS System for Regression. Note that PROC GLM calculates R2 for the NOINT model in the same way.
For a discussion of the properties of different estimators of R2, see Kvalseth (1985). It discusses eight different estimators of R2, all of which are equivalent for a linear model with an intercept, in terms of
both linear models without an intercept and nonlinear models.
The most important things to note are that the R2 for a nointercept model is
calculated differently from that for a linear model with an intercept and that the two should not be directly compared. For those wanting to make such
a comparison, Myers (1990) suggests calculating R2 for the NOINT model as follows:
1 - (Error SS from NOINT Model / Corrected Total SS) ,
If classification variables are present in the model, PROC GLM computes R2 as
(Corrected Model SS) / (Corrected Total SS) ,
while REG computes R2 as
Uncorrected Model SS) / Uncorrected Total SS) .
Operating System and Release Information
*
For software releases that are not yet generally available, the Fixed
Release is the software release in which the problem is planned to be
fixed.
Type: | Usage Note |
Priority: | low |
Topic: | Analytics ==> Multivariate Analysis Analytics ==> Regression SAS Reference ==> Procedures ==> REG SAS Reference ==> Procedures ==> GLM
|
Date Modified: | 2007-11-05 13:33:15 |
Date Created: | 2002-12-16 10:56:40 |