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Title:
Linear regression in astronomy. II [ Erratum: 2011ApJ...728...72F ]
Authors:
Feigelson, Eric D.; Babu, Gutti J.
Affiliation:
AA(Pennsylvania State University, University Park), AB(Pennsylvania State University, University Park)
Publication:
Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 397, no. 1, p. 55-67. (ApJ Homepage)
Publication Date:
09/1992
Category:
Astronomy
Origin:
STI
NASA/STI Keywords:
Astronomical Models, Elliptical Galaxies, Least Squares Method, Regression Analysis, Distance, Error Analysis, Fortran, Mathematical Models, Regression Coefficients
DOI:
10.1086/171766
Bibliographic Code:
1992ApJ...397...55F

Abstract

A wide variety of least-squares linear regression procedures used in observational astronomy, particularly investigations of the cosmic distance scale, are presented and discussed. The classes of linear models considered are (1) unweighted regression lines, with bootstrap and jackknife resampling; (2) regression solutions when measurement error, in one or both variables, dominates the scatter; (3) methods to apply a calibration line to new data; (4) truncated regression models, which apply to flux-limited data sets; and (5) censored regression models, which apply when nondetections are present. For the calibration problem we develop two new procedures: a formula for the intercept offset between two parallel data sets, which propagates slope errors from one regression to the other; and a generalization of the Working-Hotelling confidence bands to nonstandard least-squares lines. They can provide improved error analysis for Faber-Jackson, Tully-Fisher, and similar cosmic distance scale relations.

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