Regression analysis: A new methodology to compare equations

When working on modeling with regression analysis, several models are generally tested in order to select a more accurate equation after fitting in relation to some statistical tests. The decision becomes more difficult when the results of the statistical tests are similar because they are usually tests by equation, meaning that they provide statistics for each equation separately. A methodology which classifies them according to the averages of estimates in relation to the average of actual data does not exist because the averages of estimates and actual data are the same. This work proposes a methodology where the average sum of squares of the fitted equations and the average sum of squares of the real data are used. Thus, it becomes possible to apply a mean comparison test to group similar equations and separate different equations. For this work, 105 trees of Eucalyptus spp. clones were used, rigorously cubed by the Smalian method at seven and a half years of age in their second rotation, in a forest experiment located in a semi-arid zone of Pernambuco, Brazil. In turn, five linear volumetric models and one non-linear model were fitted and comparisons among equations were performed using several statistical tests usually employed in forest modeling. The Tukey, Duncan, Dunnett and Scott-Knott tests were used to test the proposed methodology, which, in addition to presenting similar results to the traditional tests, enabled grouping similar equations, and having the real volumes of the trees as the control.