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SLOPES: least-squares linear regression lines for bivariate datasets
Eric Feigelson
Penn State University
Abstract:
SLOPES computes six least-squares linear regression lines for bivariate
datasets of the form (x_i,y_i) with unknown population distributions.
Measurement errors, censoring (nondetections) or other complications
are not treated. The lines are: the ordinary least-squares regression
of y on x, OLS(Y|X); the inverse regression of x on y, OLS(X_Y); the
angular bisector of the OLS lines; the orthogonal regression line; the
reduced major axis, and the mean-OLS line. The latter four regressions
treat the variables symmetrically, while the first two regressions are
asymmetrical. Uncertainties for the regression coefficients of each
method are estimated via asymptotic formulae, bootstrap resampling, and
bivariate normal simulation. These methods, derivation of the regression
coefficient uncertainties, and discussions of their use are provided in three
papers listed below. The user is encouraged to read and reference these studies.
Subject headings: distance scale -- methods: data analysis --
methods: statistical
Latest Version: June 1990
Submitted: 1999 June 8
Papers:
Isobe, T. et al., 1990ApJ...364..104I;
Babu G. J. & Feigelson E. D., 1992,
Analytical and Monte Carlo comparisons of six different
linear least squares fits, Communcations in Stat
Simulation & Computation, 21, 533;
Feigelson, E. D. & Babu G. J., 1992ApJ...397...55F
Preprint: None
Language: Fortran 77
Platform: Any
Canned Routines Called: None
External Explanatory Pages:
StatCodes,
slopes.html
Source Code(s):
slopes.f