On the misuse of regression in earth science

Simple least-squares regression analysis is applied to almost all empirical curve-fitting problems in earth science (and related fields). Its use, however, should be restricted to predictive situations. For comparisons with theory or among fitted lines, the related technique termed functional analysisshould be employed. To apply this method, the ratio of the random components of the variances of the variables must be estimated. Principles are illustrated with examples from geomorphometry, especially the stream frequency-drainage density relation.