Implements the unified regression algorithm of York et al. (2004) which, although based on least squares, yields results that are consistent with maximum likelihood estimates of Titterington and Halliday (1979).
york(dat, alpha = 0.05, plot = TRUE, fill = NA, ...)A two-element list of vectors containing:
the intercept and slope of the straight line fit
the covariance matrix of the coefficients
a 4 or 5-column matrix with the X-values, the analytical uncertainties of the X-values, the Y-values, the analytical uncertainties of the Y-values, and (optionally) the correlation coefficients of the X- and Y-values.
cutoff value for confidence intervals.
logical. If true, creates a scatter plot of the data with the best fit line shown on it.
the fill colour of the error ellipses. For additional
plot options, use the IsoplotR package.
optional arguments for the scatter plot.
Given n pairs of (approximately) collinear measurements \(X_i\)
and \(Y_i\) (for \(1 \leq i \leq n\)), their uncertainties
\(s[X_i]\) and \(s[Y_i]\), and their covariances
cov[\(X_i,Y_i\)], the york function finds the best fitting
straight line using the least-squares algorithm of York et
al. (2004). This algorithm is modified from an earlier method
developed by York (1968) to be consistent with the maximum
likelihood approach of Titterington and Halliday (1979).
Titterington, D.M. and Halliday, A.N., 1979. On the fitting of parallel isochrons and the method of maximum likelihood. Chemical Geology, 26(3), pp.183-195.
York, Derek, et al., 2004. Unified equations for the slope, intercept, and standard errors of the best straight line. American Journal of Physics 72.3, pp.367-375.
data(rbsr,package='geostats')
fit <- york(rbsr)
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