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Linear regression in astronomy.
Isobe, Takashi; Feigelson, Eric D.; Akritas, Michael G.; Babu, Gutti Jogesh
AA(Pennsylvania State University, University Park), AB(Pennsylvania State University, University Park), AC(Pennsylvania State University, University Park), AD(Pennsylvania State University, University Park)
Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 364, Nov. 20, 1990, p. 104-113. Research supported by NASA. (ApJ Homepage)
Publication Date:
NASA/STI Keywords:
Astronomy, Least Squares Method, Regression Analysis, Computational Astrophysics, Galaxies, Slopes
Bibliographic Code:


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. Formulas 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 formulas 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. It is found 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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