york {geostats} | R Documentation |
Linear regression of X,Y-variables with correlated errors
Description
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).
Usage
york(dat, alpha = 0.05, plot = TRUE, fill = NA, ...)
Arguments
dat |
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. |
alpha |
cutoff value for confidence intervals. |
plot |
logical. If true, creates a scatter plot of the data with the best fit line shown on it. |
fill |
the fill colour of the error ellipses. For additional
plot options, use the |
... |
optional arguments for the scatter plot. |
Details
Given n pairs of (approximately) collinear measurements
and
(for
), their uncertainties
and
, and their covariances
cov[
], 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).
Value
A two-element list of vectors containing:
- coef
the intercept and slope of the straight line fit
- cov
the covariance matrix of the coefficients
References
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.
Examples
data(rbsr,package='geostats')
fit <- york(rbsr)