The benefits of the orthogonal LSM models

TL;DR

This paper discusses the advantages of orthogonal least squares models, providing methods to transform general linear regression models into orthogonal forms and accurately estimate uncertainties in predictions.

Contribution

It introduces the matrix relations for orthogonal LR models and demonstrates how to convert standard models into orthogonal ones for improved analysis.

Findings

Orthogonal LR models have specific properties that enhance data interpretation.

Transformations to orthogonal models improve uncertainty estimation.

Relations for polynomial series in orthogonal models are provided.

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.