Nonlinear regression methodology: exponential behavior of microwave sensors

There are microwave sensors where the predictive variable (X) and the response variable (Y) present nonlinear and exponential type relationships, performing regressions where they do not establish compliance with the corresponding assumptions and do not make a fair comparison between regressions. This paper presents a methodology for evaluating nonlinear regression assumptions, which include outliers, normality, homoscedasticity, and independence. Additionally, the dynamic range, the maximum sensitivity, the resolution, and the accuracy are considered parameters for evaluating the quality of the regression. To implement the methodology, the snl_regression_quality package was developed, which runs in Python. Regressions for ring resonator and complementary split-ring sensors were considered. Both met the assumptions and, considering the dynamic range, resolution, and accuracy, the Split ring complementary resonator sensor regression was the one that showed the best performance. This methodology aims to make a fairer comparison between exponential nonlinear regressions of microwave sensors.