METHODOLOGY: MISUSE OF R2 VALUES FROM LINEAR REGRESSION IN FRACTAL ANALYSIS

Least squares linear regression (LSLR) analysis is often used for estimating fractal dimension from the slope of scatterplots produced by fractal analysis. Coefficients of determination close to unity are commonly accepted as sufficient evidence of linearity, and hence statistical self-similarity (or affinity). In this study, high R ² values derived from linear regression analyses are shown to increase the likelihood of detecting significant curvature in a relation. While this curvature is unlikely to hinder the use of LSLR in predicting y from x, it is demonstrated that large variations in the slope coefficient, and hence in estimates of fractal dimension, can exist in the presence of R ² values close to unity. Therefore, coefficients of determination close to unity should not be used as evidence of linearity. In light of this finding, it is strongly suggested that even in the presence of high coefficients of determination, residual analysis and/or other tests for linearity always be conducted when linear regression is employed in fractal analysis. Key words: coefficient of determination, statistical self-similarity, fractal dimension.]