It is used generally for the matrix which specifies a statistical model for a set of observations.
For instance, in a one-way design with the three observations in one group, two observations in the second group and a one observation in the third group, and where the model is the design matrix, X is By making use of this matrix the model for all the observations can be conveniently expressed in matrix form as It is also used specifically for the matrix X in the designed industrial experiments which specify the chosen values of the explanatory variables; these are frequently selected using one or the other criteria.