Linear Regression in Astronomy. II.
Abstract
A wide variety of leastsquares 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 fluxlimited 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 WorkingHotelling confidence bands to nonstandard leastsquares lines. They can provide improved error analysis for FaberJackson, TullyFisher, and similar cosmic distance scale relations.
 Publication:

The Astrophysical Journal
 Pub Date:
 September 1992
 DOI:
 10.1086/171766
 Bibcode:
 1992ApJ...397...55F
 Keywords:

 Astronomical Models;
 Elliptical Galaxies;
 Least Squares Method;
 Regression Analysis;
 Distance;
 Error Analysis;
 Fortran;
 Mathematical Models;
 Regression Coefficients;
 Astronomy;
 COSMOLOGY: DISTANCE SCALE;
 METHODS: NUMERICAL