this matrix Z distinguishes one regression problem from another ,because the entries in Z determine the particular linear combinations of the unknown parameter
that are relevant in a given problem
the matrix Z for a particular problem is sometimes called the design matrix of the problem, because the entries in Z are often chosen by the experimenter to achieve a well-designed experiment
it should be kept in mind, however,that some or all of the entries in Z may be simply the observed values of certain variables,and may not actually be controlled by the experimenter.