Formulae for Slopes and Curvatures of Two Curves in Quadratic Polynomial Regression Equations with Response Surface Analysis

Abstract

Response Surface Methodology (RSM) constitutes a suite of statistical and mathematical techniques employed for the development, enhancement, and optimization of processes with the aim of achieving the maximum (or minimum) value of a response variable. In the realm of organizational research, scholars have embraced RSM, utilizing quadratic regression equations illustrated on a three-dimensional surface to investigate congruence phenomena such as fit, match, similarity, or agreement. To date, RSM has found extensive application in exploring nuanced relationships among combinations of two predictor variables and an outcome variable within organizational studies. This paper takes a novel approach by incorporating directional derivatives and the rotation of axes from multivariable calculus. It formulates a set of equations to calculate the slopes and curvatures of two curves in quadratic polynomial regression equations through response surface analysis.