## Introduction

Multiple linear regression (MR) is widely used to identify models that capture the essence of ecological systems (Whittingham *et al*. 2006). MR extends simple linear regression to model the relationship between a dependent variable (*Y*) and more than one independent (also known as ‘predictor’ and so-called henceforth) variables (Sokal & Rohlf 1995). Owing to the complexity of ecological systems, multicollinearity among predictor variables frequently poses serious problems for researchers using MR (Graham 2003).

Quite often, ecologists pose the question, to what extent is variation in each predictor variable associated (linearly) with variation in the dependent variable? To answer this, in MR, there are three main effects that need to be assessed: (i) *total effects* – total contribution of each predictor variable to the regression when the variance of other predictors are accounted for; (ii) *direct effects* –contribution of a predictor, independent of all other predictors; and (iii) *partial effects* –contribution of a predictor when accounting for variance of a specific subset or subsets of remaining predictors (LeBreton, Ployhart & Ladd 2004). However, conventionally, one reports the coefficient of determination (*R*^{2}) and regression coefficients, where the *P*-values of the regression coefficients are the information one mostly relies upon to answer the fairy-tale question, ‘Mirror, mirror on the wall, what is the best predictor of them all?’ (Nathans, Oswald & Nimon 2012; p. 1).

The *R*^{2} quantifies the extent to which the variance of the dependent variable is explained by variance in the predictor set, and regression coefficients help rank the predictor variables according to their contributions in the regression equation (Nimon *et al*. 2008). However, relying only on the unstandardized slope of regression (also known as partial regression coefficients, Sokal & Rohlf 1995) or standardized (partial) regression coefficients (also known as beta coefficients and so-called henceforth, Sokal & Rohlf 1995) may generate erroneous interpretations, particularly when multicollinearity is involved (Courville & Thompson 2001; Kraha *et al*. 2012). It is not uncommon for researchers to erroneously refer to beta coefficients as measures of relationship between predictors and the dependent variable (Courville & Thompson 2001). Hence, it is often advisable to use multiple methods while interpreting MR results, especially when the intentions are not strictly predictive (Nimon & Reio 2011). In this paper, we use simulated and empirical data to demonstrate how a relatively similar approach, regression commonality analysis (CA), can be used along with beta coefficients and structure coefficients to better interpret MR results in the face of multicollinearity.