The least-squares line and plane and the analysis of palaeomagnetic data

The classic, multivariate technique of principal component analysis can be used to find and estimate the directions of lines and planes of best least-squares fit along the demagnetization path of a palaeomagnetic specimen, thereby replacing vector subtraction, remagnetization circles and difference vector paths with one procedure. Eigenvalues from the analysis are the variance of the data along each principal axis, and provide a relative measure of collinearity or coplanarity which may be used to define a general palaeomagnetic precision index. Demagnetization planes found with principal component analysis may be used in place of difference vector paths for locating Hoffman—Day directions, avoiding unnecessary vector subtraction and intensity truncation steps. Two methods are discussed for jointly estimating an average remanence direction from demagnetization lines and planes.