Some Plots Are not that Equivalent

摘要

In many scientific and chemistry-related fields it is very common to represent in a bidimcnsional plot calculated and observed data in many scientific and chemistry-related fields. If calculated values are obtained via a linear or multilinear regression procedure it will be shown how the two representation choices, fitted vs. observed and observed vs. fitted values, are not equivalent. The slopes of the bidimensional regression lines in both plots bear distinct properties: the former representation exhibits a regression line with a slope always equal to r~2 and the later line coincides exactly with the bisector of the first and third quadrants representation. The general proof of this problem is here exemplified by the aid ofa simple numerical example. An alternative method for obtaining a graphical 'symmetric' representation is exposed, which relies on the minimization of the sum or quadratic orthogonal distances.