TY - JOUR
T1 - Linear regression in astronomy. I
AU - Isobe, Takashi
AU - Feigelson, Eric D.
AU - Akritas, Michael G.
AU - Babu, Gutti Jogesh
N1 - Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
PY - 1990/11/20
Y1 - 1990/11/20
N2 - Five methods for obtaining linear regression fits to bivariate data with unknown or insignificant measurement errors are discussed: ordinary least-squares (OLS) regression of Y on X, OLS regression of X on Y, the bisector of the two OLS lines, orthogonal regression, and "reduced major-axis" regression. These methods have been used by various researchers in observational astronomy, most importantly in cosmic distance scale applications. Formulae for calculating the slope and intercept coefficients and their uncertainties are given for all the methods, including a new general form of the OLS variance estimates. The accuracy of the formulae was confirmed using numerical simulations. The applicability of the procedures is discussed with respect to their mathematical properties, the nature of the astronomical data under consideration, and the scientific purpose of the regression. We find that, for problems needing symmetrical treatment of the variables, the OLS bisector performs significantly better than orthogonal or reduced major-axis regression.
AB - Five methods for obtaining linear regression fits to bivariate data with unknown or insignificant measurement errors are discussed: ordinary least-squares (OLS) regression of Y on X, OLS regression of X on Y, the bisector of the two OLS lines, orthogonal regression, and "reduced major-axis" regression. These methods have been used by various researchers in observational astronomy, most importantly in cosmic distance scale applications. Formulae for calculating the slope and intercept coefficients and their uncertainties are given for all the methods, including a new general form of the OLS variance estimates. The accuracy of the formulae was confirmed using numerical simulations. The applicability of the procedures is discussed with respect to their mathematical properties, the nature of the astronomical data under consideration, and the scientific purpose of the regression. We find that, for problems needing symmetrical treatment of the variables, the OLS bisector performs significantly better than orthogonal or reduced major-axis regression.
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U2 - 10.1086/169390
DO - 10.1086/169390
M3 - Article
AN - SCOPUS:11944270352
SN - 0004-637X
VL - 364
SP - 104
EP - 113
JO - Astrophysical Journal
JF - Astrophysical Journal
IS - 1
ER -