IJDSBDA International Journal of Data Science and Big Data Analytics 2710-2599 SvedbergOpen ijdsbda-1-3-001 10.51483/IJDSBDA.1.3.2021.1-5 Research Note Generalized Least-Squares Ftting with Procedures for Uncorrelated Data of Constant Variance WalewskiJoachim W. 1 * MetzThomas 2 1Division of Combustion Physics, Lund University, P.O. Box 118 221 00, Lund, Sweden. E-mail: joachim.walewski@gmail.com 2Trimble Jena GmbH, Carl-Zeiss-Promenade 10, 07745 Jena, Germany *Corresponding author: Joachim W. Walewski, Division of Combustion Physics, Lund University, P.O. Box 118221 00, Lund, Sweden.. E-mail: joachim.walewski@gmail.com 11 2021 1 3 1 5 Abstract

We show how generalized least-squares fitting, namely, the fitting of correlated data, can be carried out with algorithms for uncorrelated data of constant variance. Doing so requires only a simple linear transformation of the measurement data.

 Keywords Constant variance Correlated data Curve fitting Generalized least-squares fitting Least squares Least-squaresfitting Maximum-likelihood estimation Ordinary leastsquares fitting References MetzT.WalewskiJ.KaminskiC.F. (2003). Maximum-likelihood Curve Fitting Scheme for Experiments with Pulsed Lasers Subject to Intensity Fluctuations. Applied Optics, 42, 1551–1563. TaupinD. (1988). Probabilities, Data Reduction and Error Analysis in the Physical Sciences. Les editions de physique, Les Ulis. Wikipedia Contributors. (2020). Eigendecomposition of a Matrix—Wikipedia, the Free Encyclopedia [Online at https://en.wikipedia.org/w/index.php?title=Eigendecomposition_of_a_matrix&oldid=1012755753; accessed 2021-03-20]. Wikipedia Contributors. (2021a). Hermitian Matrix—Wikipedia, the Free Encyclopedia [Online at https://en.wikipedia.org/w/index.php?title=Hermitian_matrix&oldid=999254083; accessed 11-January-2021]. Wikipedia Contributors. (2021b). Isomorphism—Wikipedia, the Free Encyclopedia [Online at https://en.wikipedia.org/w/index.php?title=Isomorphism&oldid=1007734513; accessed 20-March-2021].