Methodology for the Evaluation of Linear Response Microwave Sensors

Abstract

Most microwave sensors establish a relationship between electrical parameters or dielectric properties with the property of interest of a sample using simple linear regression to make predictions. These do not implement the assumptions of linear regression and evaluate their quality in different ways, making fair comparisons between regressions impossible. In this article, a methodology is proposed to evaluate the assumptions. The assumption of anomalies is implemented with standardized and studentized residuals; the assumption of normality, with the Shapiro-Wilk test; the assumption of homoscedasticity, with the Breusch-Pagan test; the assumption of independence, with the Durbin-Watson test; and linearity, with the F-test. This methodology includes the evaluation of the quality of the linear regression. The dynamic range is considered, such as the difference between the highest and the lowest value of the property of interest, the sensitivity using ordinary least squares (OLSs), the resolution with analysis of variance, and the accuracy with root-mean-squared error of cross-validation. The sl-regression-quality package is provided to perform the methodology using Python software. As an example, a resonator sensor is considered to determine the moisture content of meat. This methodology can be used for the fairest comparison between simple linear regressions of microwave sensors.