It has been the author's experience that researchers will routinely use linear models to describe the relationships between correlated variables when that approach to modeling may not be the most rational. This article illustrates some of thecircumstances when linear modeling is and is not the most viable alternative in characterizing the relationship between correlated variables.In this study, several data sets are examined to illustrate how amenable they are to linear modeling. One data set selected shows a nearly ideal example of when linear least-squares regression is a realistic descriptor of the relationship betweencorrelated variables. A second data set shows how material idiosyncrasies, such as species, size, or grade effects, can result in misleading models for parameter prediction. A third data set illustrates a more subtle inhomogeneity that is frequently found in experimental data involving tests of clear wood. When the relationship between correlated variables changes due to a shifting failure mechanism, a presumed linear relationship may misrepresent the relationship between variables in a large portion ofthe domain. It is the intent of this paper to remind or make researchers aware of the subtle characteristics of data sets that can influence modeling results.One possible mechanism for modeling nonlinearly related variables (the univariate S{sub}B and the bivariate S{sub}(BB) distribution) is offered for consideration. This model has the unique feature of quantifying, in an analytic, closed-form fashion, theprobability of a predicted variable for any value of the domain. In addition, when certain input values used to calculate S{sub}(BB) bivariate distribution parameters are defined correctly, convergence to the clear wood strength of a material or productis achieved.
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