Coefficient of determination in some atypical situations: use in chemical correlation analysis

The popular statistics used in correlation analysis, the correlation coeffi cient R and coefficient of determination R-2, belong to the model of common linear regression with an exact explanatory variable and freely fitted int ercept. When they are used in other models, the common equation must be mod ified and the interpretation revised. The resulting equations are discussed for the model with a fixed intercept. For the models with errors in either variable and with both modifications, new equations are suggested. Under t hese conditions, R may be defined differently, always in at least two ways; the different interpretations are discussed. Some properties of these defi nitions are shown, particularly the sensitivity to coordinate transformatio ns. These properties and interpretations differ from those of R in the comm on linear regression, hence the values in different models must not be dire ctly compared. Applications in chemistry and some cases of misuse in the li terature are mentioned. Copyright (C) 1999 John Wiley & Sons, Ltd.