The rotatable central composite design. It can be shown that a second-order design is rotatable if n

The rotatable central composite design. It can be shown that a second-order design is rotatable if

Σn u=1 xa iuxb ju =

0, if a or b or both are odd, and if

Σn u=1 x4 iu = 3

Σn u=1 x2 iux2 ju.

Show that for the central composite design these conditions lead to ???? = (nF)1∕4 for rotatability, where nF is the number of points in the factorial portion.