Open source development in Octave for function adjustments through linearization and OLS

Abstract

All engineering studies rely on mathematical foundations for their realization, whether they involve probability, statistics, differential and integral calculus, vector algebra, etc. The mathematical approach is indeed a crucial part of the development process. In studies dealing with discrete data, the need for parameterizations that demonstrate the behavior of such data sets is evident, making curve fitting indispensable. In this regard, the broad context of the work stands out, aiming to write code in Octave for the parameterization of discrete data. The implemented methodology is the Ordinary of Least Squares (OLS), as well as its quantitative evaluation of quality through the coefficient of correlation ( ). Additionally, mathematical resources for linearizing models are used for subsequent adaptation in OLS. As a result, an Octave code is obtained that performs parameterization for the following models: linear, power, exponential, reciprocal, and Michaelis-Menten. The code is validated with various results from the literature. In conclusion, the ease of the Octave script is observed, not only enabling parameterization and curve fitting for data sets but also providing a basis for the insertion of additional models within the script. Furthermore, the developed code leads to new propositions, such as programs that perform similar tasks in 3D, or even programs that automate calculations.