Journal of Advances in Mathematics and Computer Science

Three growth models (Richards, Gompertz, and Weibull) were estimated using a computer program employing a modified version of the Levenberg-Marquardt approach for solving non-linear regression models. With both small and high sample sizes, three data sets were collected. The most suitable model for growth studies was added by decomposing the growth models into their component parts: additive and multiplicative error factors. The analysis based on the mathematical properties was conducted using Gretl statistics software. Prior to using an iterative strategy, a third-order polynomial (cubic function) solves the issue of the initial parameters. The final estimate of the parameters, standard errors, p-values, and model adequacy standards used to choose the best growth model are included in the result. Out of the five growth models considered suitable for the agricultural data, this study was able to pinpoint the Weibull Growth Model with Multiplicative Error Term. The Hill Growth Model with Additive Error Term is the best growth model for the engineering data out of the five growth models. Among the Five Growth Models for Population Growth, the Weibull Growth Model with Additive Error Term is a viable growth model. Several growth models are suggested or recommended by this study for use in forecasting this growth behavior.