Screening by D-optimal designs

In Chapter 5 was discussed how the properties of the model matrix X is transmitted to different criteria of the quality of the estimated model parameters. 

One such criterion is that the joint confidence region should be as small as possible. This is obtained if the determinant of the dispersion matrix, (X X) , is as small as possible. 

The model matrix X is defined from the postulated model and the design matrix. Provided that a reasonable model can be suggested, it will thus be possible to select a series of experiments in such a way that X X has a maximum value. These experiments will then allow the parameters of the suggested model to be estimated with a maximum precision. Such a design is said to be D-optimal (D stands for determinant ). The D-optimality criterion can be used to select experiments for screening. 

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