Determination of formulas on the orthogonal central composite design (Box) - Batista, Lauro Boechat; Silva, Sueli Costa e (Pesquisa Agropecuaria Brasileira, 2014)
A theoretical study was devised to determine the formula of ʆ which makes orthogonal the central composite design (Box), with P + 1 central points and maximum of four factors. The following expressions of α was obtained: α = [-2k-1+ [22k-2 + 2k-2 (2k + 1 + P)]1/2]1/2 it was equally verified that in the case of the orthogonal central composite design, with P + 1 central points, the formulas which estimated the variances of the estimates of the polynomial equation coefficients, could be calculated through the following expressions: V (βi) = 1/r (2k+ 2α2) *α-2 V (βij) = 1/r2k *α-2 V (βii) = 1/r * [2k+ 2α4 - (2k+ 2α2)2/2k+ 2k + 1 + P]-1*α-2 Finally, it was verified that when the orthogonal central composite design has eight central points, the coefficients βii of the squared terms are estimated as precise as the coefficients βi and more precise than the coefficients βij.