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Extra resources for A Review of Digital Watermarking
We could rewrite Eq. 12 as where 1 is an implied (albeit constant) regressor. IfwenotethatX1+X2 = 1—that is, there is an exact linear dependency between the regressors — then we have an overparameterized model. To correct the problem we can carry out the following algebra: The parameters of Eq. 15 may be written in terms of the parameters of Eq. 12 as As a specific example, consider the fitted model Eq. 13. The necessary algebraic transformations would be the following: The reader may care to show that Eq.
Exceptions include Design-Expert Version 7 and MIXSOFT. 5. Piepel  also discusses checking constraints on linear combinations of components, such as Eq. 2. The procedures are much more complex and are beyond the intended scope of this text. The interested reader is referred to the discussion by Piepel.
One and two upper bounds in a 3-simplex. leads to a subspace that is now a parallelogram (shaded corner of the triangle in Fig. 4 (right)). 0. Clearly, we cannot state a simple property about the shape of the design region when there are upper bounds. The shape will depend on the nature of the particular bound(s). Before adding a third upper constraint and continuing with this example, it is useful to digress for a moment. Assume that there are the same two upper-bound constraints on X\ and X2, but now q — 4.