## Coding the Factor Variables

For the results of the canonical and ridge
analyses to be interpretable, the values of
different factor variables should be comparable.
This is because the canonical and ridge analyses of the
response surface are not invariant with respect to
differences in scale and location of the factor variables.
The analysis of variance is not affected by these changes.
Although the actual predicted surface does
not change, its parameterization does.
The usual solution to this problem is to code each factor
variable so that its minimum in the experiment is -1
and its maximum is 1 and to carry through the analysis
with the coded values instead of the original ones.
This practice has the added benefit of making 1 a reasonable
boundary radius for the ridge analysis since 1 represents
approximately the edge of the experimental region.
By default, PROC RSREG computes the linear transformation
to perform this coding as the data are initially
read in, and the canonical and ridge analyses
are performed on the model fit to the coded data.
The actual form of the coding operation
for each value of a variable is

where *M* is the average of the highest and lowest values for
the variable in the design and *S* is half their difference.

Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.