An Ezekiel’s Adjusted R-Squared-Based Decision Rulefor Regression Hypothesis Testing

Abstract

Prior studies have reported that a minimal bias-variance tradeoff for Ezekiel’s adjusted R-squared provides a more accurate representation of a model’s explanatory power. Motivated by the advantages of Ezekiel’s adjusted R-squared, this study proposes its integration into the framework of null hypothesis significance testing for regression models. The primary objective is to develop a new decision rule for the F-test in regression analysis based on Ezekiel’s adjusted R-squared and to evaluate the influence of various parameters (the number of explanatory variables, sample size and alpha value) on the critical value in the new decision rule. This new adjusted R-squared based decision rule is useful because it provides researchers a way to gauge the practical significance of a model at the same time testing statistical significance. In this study, an analysis using linear regression models based on forty-eight cases revealed that low values of adjusted R-squared were observed in statistically significant regression models. The results of this study are consistent with prior research, in which conclusions derived from hypothesis testing are regarded as uncertain and have been subject to criticism. In conclusion, the hypothesis testing procedure, including its application in linear regression analysis, need not be dismissed outright. Rather, it should be regarded as one of several screening tools to be interpreted in conjunction with other relevant factors and domain-specific considerations.