Statistical modeling of the impact of centre points replications on second-order spherical unit-radial points designs

Abstract

The study considered statistical modelling of the impact of centre point replications on second-order spherical unit-radial point designs. A second-order quadratic model was built with Gross Domestic Products of Nigerian as the response variable with replication of centre points from 1 to 5 inclusive. The second-order designs used in this study were Doehlert Design (DD), Equiradial Design (ED) and Inscribed Central Composite Design (INSD) all having radius of 1.0, hence the name (unit-radial point Designs). Ordinary Least Square method was applied on the model and the model parameters were estimated. The sum of square error was applied for each centre points to obtain better interpretation of the estimated parameters. It was observed that for radial point of n= 6, Inscribed CCD and Doehlert design gave grand means that slightly differs from that of equiradial design for 1 centre point. The sum of square error value of equiradial design is less than that of doehlert design by 0.000222. As the centre point replicates increases to 2, all the designs recorded maximum value of sum of square errors with the error value of doehlert, equiradial and inscribed designs as 1.547889, 1.546521 and 1.938783 respectively. The study recommends among other things that in order to maximize the economy of Nigeria using spherical second-order unit-radial point design(s) one should consider the addition of 4 centre points.