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      Compute linear regression coefficients by six different methods.


      Adapted from the FORTRAN program (Rev. 1.1) supplied by Isobe,
      Feigelson, Akritas, and Babu Ap. J. Vol. 364, p. 104 (1990).
      Suggested when there is no understanding about the nature of the
      scatter about a linear relation, and NOT when the errors in the
      variable are calculable.

Calling Sequence

      SIXLIN, xx, yy, a, siga, b, sigb, [WEIGHT = ]


      XX - vector of X values
      YY - vector of Y values, same number of elements as XX


      A - Vector of 6 Y intercept coefficients
      SIGA - Vector of standard deviations of 6 Y intercepts
      B - Vector of 6 slope coefficients
      SIGB - Vector of standard deviations of slope coefficients
      The output variables are computed using linear regression for each of
      the following 6 cases:
              (0) Ordinary Least Squares (OLS) Y vs. X (c.f. linfit.pro)
              (1) Ordinary Least Squares X vs. Y
              (2) Ordinary Least Squares Bisector
              (3) Orthogonal Reduced Major Axis
              (4) Reduced Major-Axis
              (5) Mean ordinary Least Squares

Optional Input Keyword

      WEIGHT - vector of weights, same number of elements as XX and YY
                For 1 sigma Gausssian errors, the weights are 1/sigma^2 but
                the weight vector can be more general. Default is no


      Isobe et al. make the following recommendations
      (1) If the different linear regression methods yield similar results
              then quoting OLS(Y|X) is probably the most familiar.
      (2) If the linear relation is to be used to predict Y vs. X then
              OLS(Y|X) should be used.
      (3) If the goal is to determine the functional relationship between
              X and Y then the OLS bisector is recommended.

Revision History

      Written Wayne Landsman February, 1991
      Corrected sigma calculations February, 1992
      Added WEIGHT keyword J. Moustakas February 2007

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