Symmetry in Regression Analysis: Perpendicular Offsets—The Case of a Photovoltaic Cell

Abstract

It is known that, for paired measurements subjected to experimental error, better suited linear regression is obtained by using perpendicular offsets. Even so, the great majority of statistical software still uses classical vertical offsets for reasons of convenience. The same convenience leads to the preference of the least squares method in the favor of maximum-likelihood estimation. The treatise for perpendicular offsets for simple linear regression is slightly trickier than the corresponding one for vertical offsets. However, there is no general treatise for perpendicular offsets for nonlinear cases to date. In this work, a typical case of nonlinear dependence—potential versus intensity of current produced by a photovoltaic cell—is subjected to study. A series of paired potential/current data was collected from a commercial photovoltaic device and served for introducing the perpendicular offsets approach in the case of a nonlinear regression. Photovoltaic cell parameters—internal resistance, short-circuit current intensity, potential of open-circuit, and the maximum power point—have been determined by using the perpendicular offsets approach. Several issues were addressed in this work, such as exploring the intrinsic symmetry in the treatment of current versus potential diagrams, the suitability of perpendicular offsets in obtaining of the regression coefficients, and the implementation of nonlinear regression models with perpendicular offsets. Even if both the treatises of perpendicular offsets and nonlinear regression are known for some time now, there is no report in the literature of using both. Furthermore, since both potential and current measurements are affected by errors, it is more natural to use the proposed approach of perpendicular offsets.