Least squares orthogonal design

A section has been added to Chapter 1 on the distinction between analytic vs. enumerative studies. A section on mixture designs has been added to Chapter 9. A new chapter on the application of linear models and matrix least squares to observational data has been added (Chapter 10). Chapter 13 attempts to give a geometric feel to concepts such as uncertainty, information, orthogonality, rotatability, extrapolation, and rigidity of the design. Finally, Chapter 14 expands on some aspects of factorial-based designs. 

The first term is known as the sum of squares, model (SSM). The second term is known as the sum of squares, residual (SSR), and the final term is known as the sum of squares, total (SST). Equation 3.16 is true for any least squares solution whatsoever. However, SSM can be apporhoned by component (i.e., Uq, a-, U2,. ..) only for so-called orthogonal models or data sets—that is, those that generate diagonal X X matrices (as is the case for factorial designs). Equation 3.16 also has a matrix formulation ... 

The coefficients are calculated by multi-linear regression, according to the least squares method. There are a very large number of different programs for doing these calculations. The use of properly structured experimental designs, which are usually quite close to orthogonality, has the result that the more sophisticated methods (partial least squares etc.) are not usually necessary. 

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