The δ18O-δD relationship for ice and water is frequently summarized with a line fitted by least-squares linear regression. Properly, however, each sample has an individual analytical error in both variables, defined by the variance in estimates of isotope concentration provided by the mass spectrometer. Where individual errors are known, the least-squares cubic method, which assigns a weight to each sample and generates the summary line by an iterative method, may be used. An algorithm sufficient to determine both the functional fit and the least-squares cubic regression line is presented. Illustrations are provided, one of which demonstrates that if the plot of δ18O versus δD is scattered both the functional fit and the least squares cubic regression line may be significantly different from the least-squares linear regression lines. -from Authors
Canadian Journal of Earth Sciences
Department of Geography and Environmental Studies

Burn, C, & Maxwell, M.G. (M. G.). (1993). Proper determination of the δ18O-δD relationship for ice and water by least-squares cubic regression. Canadian Journal of Earth Sciences, 30(1), 109–112. doi:10.1139/e93-010