1. Consider a CCD design for three independent variables and six center points. We want to explore possibilities for blocking this design. a) Suppose it has to be done in two blocks of equal size...

1. Consider a CCD design for three independent variables and six center points. We want to explore possibilities for blocking this design. a) Suppose it has to be done in two blocks of equal size (number of runs in each block). What should the axial parameter a be in order for the design to block orthogonally? b) Suppose now we want the design to be spherical (a = s.a). Is orthogonal blocking possible? Assume that all factorial runs go in one block and all axial runs go in the other. If perfectly orthogonal blocking is not possible, how should we block so that orthogonality is violated the least? c) Now suppose we want to block it in three blocks so that all axial runs go in the same block. Can we block orthogonally? What should a be? If the answer is positive describe the blocking and demonstrate orthogonality.