The aim of the present paper is two-fold. First, it attempts to support previous findings on the role of some psychometric variables, such as, M-capacity, the degree of field dependence-independence, logical thinking and the mobility-fixity dimension, on students' achievement in chemistry problem solving. Second, the paper aims to raise some methodological and epistemological issues concerning the implementation of the general linear model (GLM) in this type of research. Multiple regression analysis was used to analyze the data, which were taken from students (N = 86) in tenth grade of high school taking a compulsory course in chemistry. Three different techniques were implemented in order to support a linear model: The Added Variable Plots, the Stepwise Regression and the Best Subsets Regression. Residual analysis and collinearity diagnosis were also performed in order to test the robustness of inferential statistics. The GLM explained 39% of the variance and suggested that only M-capacity and logical thinking were the significant predictors, even though all the correlation coefficients with achievement were statistically significant. The extensive analysis of the linear regression procedures revealed their advantages and also their limitations in terms of statistical robustness. Moreover, a discussion is initiated concerning the explanatory power of linear models and suggests rethinking variance explained under a different philosophical perspective. It is argued that the weakness of the GLM in studying complex dynamical processes, such as problem solving, is rooted not merely in the statistical assumptions that do not hold, or in the variables that are ignored, but substantially it is deeply epistemological. (Contains 7 notes, 6 tables, and 6 figures.)