Linear regression in astronomy. I

Takashi Isobe, Eric D. Feigelson, Michael G. Akritas, Gutti Jogesh Babu

Research output: Contribution to journalArticlepeer-review

738 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)104-113
Number of pages10
JournalAstrophysical Journal
Volume364
Issue number1
DOIs
StatePublished - Nov 20 1990

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science

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