Linear and Non-linear transforms are just two types of transforms used. When a nonlinear response is present, with significant quadratic or interaction terms, a transform of the model may yield a linear model. In that case the concept of equally spaced factors used in setting design levels would have been best applied to the transformed parameter, rather than to the natural coordinates. In the absence of prior information, however, the appropriate transform may not be understood until at least the first experiment is analyzed.
Several Nonlinear transforms are available. They may be applied on the basis of prior experience, a theoretical model, or empirically from the data. Such transforms can be useful in improving the fit of the polynomial regression model to transcendental physical models. For example, a physical relationship of the form E = C * exp(k * F1) may have a LN (natural log) transform applied to E. The resulting regression model would be,
LN(E) = LN(C) + k * F1 = B0 + B1 * F1.
If multiple transforms are specified, the transforms are executed in the order Linear, then Nonlinear.
Learn more about the Regression tools in Six Sigma Demystified (2011, McGraw-Hill) by Paul Keller, in his online Regression short course (only $99), or his online Black Belt certification training course ($875).