Circles design

Abstract

A new design was developed specifically for fitting to data a second degree polynomial with two variables. The criterion in constructing the design was to make it orthogonal when two parameters are involved. What interests is the value of α, which makes the design orthogonal and which is given by a proper expression in this study. The formulas which estimate the variances of the polynomial regression coefficients, in the case of the Orthogonal Circles Design with P center points, were also calculated. It was verified that these estimates of variances are better (lower variance) when the value of P becomes larger; also the formulas which estimate the polynomial equation coefficients, as well as the sums of squares of the polynomial equation coefficients were calculated. In field experiments, it is recommended to use only one center point and then replicate it, as well as the other 16 treatment combinations, in randomized blocks. Finally, it is recommended that in the green-house or laboratory it may be necessary to replicate only the center point.