Understanding the Results of Multiple Linear Regression
- 25 July 2013
- journal article
- research article
- Published by SAGE Publications in Organizational Research Methods
- Vol. 16 (4), 650-674
- https://doi.org/10.1177/1094428113493929
Abstract
Multiple linear regression (MLR) remains a mainstay analysis in organizational research, yet intercorrelations between predictors (multicollinearity) undermine the interpretation of MLR weights in terms of predictor contributions to the criterion. Alternative indices include validity coefficients, structure coefficients, product measures, relative weights, all-possible-subsets regression, dominance weights, and commonality coefficients. This article reviews these indices, and uniquely, it offers freely available software that (a) computes and compares all of these indices with one another, (b) computes associated bootstrapped confidence intervals, and (c) does so for any number of predictors so long as the correlation matrix is positive definite. Other available software is limited in all of these respects. We invite researchers to use this software to increase their insights when applying MLR to a data set. Avenues for future research and application are discussed.Keywords
This publication has 40 references indexed in Scilit:
- Isolating and Examining Sources of Suppression and Multicollinearity in Multiple Linear RegressionMultivariate Behavioral Research, 2012
- Exploratory regression analysis: A tool for selecting models and determining predictor importanceBehavior Research Methods, 2011
- Confidence Intervals for Squared Semipartial Correlation Coefficients: The Effect of NonnormalityEducational and Psychological Measurement, 2010
- R is for RevolutionOrganizational Research Methods, 2010
- Comparing Predictors in Multivariate Regression Models: An Extension of Dominance AnalysisJournal of Educational and Behavioral Statistics, 2006
- Beyond Global Measures of Relative Importance: Some Insights from Dominance AnalysisOrganizational Research Methods, 2004
- The dominance analysis approach for comparing predictors in multiple regression.Psychological Methods, 2003
- Use of Structure Coefficients in Published Multiple Regression Articles: β is not EnoughEducational and Psychological Measurement, 2001
- Dominance analysis: A new approach to the problem of relative importance of predictors in multiple regression.Psychological Bulletin, 1993
- Hierarchical PartitioningThe American Statistician, 1991