in relation to how this addressed the question, you should develop an experimental design, with the application of ANOVA. could also seek variation in RATIO between emotional intelligence and academic achievement in the latter the presence of regression models should be the answer. As not know the shape of the association (linear or nonlinear), it is difficult to tell which apply regression model.
the design is key, since many variables should control for the thorough understanding of the effect that would have IE, on achievement.
Please see two articles at http://www.aabri.com/manuscripts/10535.pdf, http://www.ncsu.edu/aern/TAS10.2/TAS10.2Ogundokun.pdf, which explore the relationship between the two and have used ANOVA & Hierarchical Regression Analysis in their design.