The benefits of the orthogonal LSM models

Abstract

In the last few decades both the volume of high-quality observing data on variable stars and common access to them have boomed; however the standard used methods of data processing and interpretation have lagged behind this progress. The most popular method of data treatment remains for many decades Linear Regression (LR) based on the principles of Least Squares Method (LSM) or linearized LSM. Unfortunately, we have to state that the method of linear regression is not as a rule used accordingly namely in the evaluation of uncertainties of the LR parameters and estimates of the uncertainty of the LR predictions. We present the matrix version of basic relations of LR and the true estimate of the uncertainty of the LR predictions. We define properties of the orthogonal LR models and show how to transform general LR models into orthogonal ones. We give relations for orthogonal models for common polynomial series.