Despite the availability and potential usefulness of demographic and contextual data in many quantitative studies within engineering education, the preference for ANOVA over regression models remains prevalent, often without clear justification. A mapping review of literature from the EJEE and JEE spanning 2012-2022 identified 98 studies using ANOVA or t-tests. Further investigation suggested that 62% and 78% of these studies, in the two flagship journals, respectively, potentially could have benefitted from employing regression analyses. This article argues for the broader adoption of regression analysis when appropriate, and its potential superiority over ANOVA in numerous contexts based on statistical and practical considerations. This argument is supported through both conceptual discussions and statistical evidence, alongside simulation studies utilising three widely used databases. The findings of simulation studies showed that regression analyses not only use demographic and contextual data more effectively but also offer enhanced analytical power, accuracy, and robustness against Type I errors, particularly in identifying disparities in educational outcomes and exploring intersectionality. Thus, we advocate for a more proactive consideration of adopting regression methods, especially integrating meaningful covariates, for research design and method choice.