Optimization and Simulation of Interactive Effects of a Generalized Quadratic Regression Model: A Comprehensive Analytical Framework and Application

Understanding and quantifying interaction effects among multiple variables is critical in complex systems analysis. This paper presents a comprehensive analytical framework for the optimization and simulation of interactive effects as a second-order regression model using the Generalized Quadratic Regression (GQR) model. The GQR model extends traditional quadratic regression by incorporating interaction terms and non-linear components, making it particularly suitable for modeling multifactorial systems with synergistic or antagonistic interactions. In this work, we develop a systematic methodology that integrates model fitting, parameter estimation, interaction visualization, and response surface analysis. Optimization is performed using heuristic technique to identify factor combinations that maximize the squared distance from target of a given response. Simulation techniques are applied to assess model robustness and explore sensitivity under varying input scenarios. The proposed framework is validated using synthetic datasets and a real-world case study, demonstrating its effectiveness in capturing complex interaction patterns and providing actionable insights. This approach offers a versatile tool for researchers and practitioners across diverse fields such as engineering, agriculture, healthcare, and environmental science. Keywords: Generalized Quadratic Regression Model, Response Surface Methodology, Interaction Effects, Experimental Design, Model Fitting, Heuristic Techniques Eguasa, O & Okungbowa, A.I. (2025): Optimization and Simulation of Interactive Effects of a Generalized Quadratic Regression Model: A Comprehensive Analytical Framework and Application. Journal of Advances in Mathematical & Computational Science. Vol. 13, No. 2. Pp 53-68. Available online at www.isteams.net/mathematics-computationaljournal. dx.doi.org/10.22624/AIMS/MATHS/V13N1P4