Orthogonal design, example

Kono s design matrix corresponds to second-order orthogonal design matrices so that in this case experimental outcomes from Example 2.51, Table 2.165, were used. The value of regression coefficient b0 is determined by adding coefficient yields of the associated column to the response column ... 

In order to illustrate the importance of orthogonal and orthonormal bases, a small real example is given. Consider a mixture of two chemical compounds ethanol and isopropanol. A good way to show plotting principles is by making an orthogonal design in the concentrations. The columns of C are the concentrations of ethanol (column 1) and isopropanol (column 2). 

Many other asymmetrical orthogonal designs exist, examples being the 4 2 design (24 experiments), and the 6 3"2 and 3"2 designs of 36 experiments. They consist of too many experiments to be generally useful for our purposes in pharmaceutical development. 

One class of designs directly applicable to computer experiments is orthogonal designs [17,27,35]. An example of such a design for three independent factorial variables (xi, X2, and X3) is shown in Table 1. Each row of this table represents a computer experiment—the hrst column designates its sequential number (1 through 15), the third to hfth columns, labeled Independent variables, list the factorial variable values held in this experiment, and the last column reports the computed response obtained in this computer run. Several different responses could be obtained in a single computer experiment. 

EXAMPLE 2.6 IDENTIFICATION OF IMPORTANT VARIABLES BY EXPERIMENTATION USING AN ORTHOGONAL FACTORIAL DESIGN... 

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