Processes and evaluation methods are gaining prominence in the social and educational contexts. In this context, it is proposed to contribute to the improvement of the higher education quality, through the analysis of information obtained in six engineering courses offered by the Federal University of Ceará. The study seeks to strengthen the interface among data analysis methods typically used of engineering contexts in order to allow the analysis of the relationship between academic management processes of engineering courses and outcomes from external evaluations. This discussion aims to propose a mathematical model to support the academic management, based on multivariate analysis (MVA) and data processing, such as Principal Component Analysis (PCA). The instrument created aims to identify professors' point of view about the management practices developed in their academic courses where they work. The application of the reliability tests revealed the suitability of the sample for the application of PCA. In the PCA application, we observed the formation of three responses' clusters, that has been well characterized by the similarity of their factor loadings that are related to students' academic education, academic formation processes and institutional environment. It should stand out even that the application of MVA showed strong evidence for a relationship among the methods of management in higher education, through the manifestation of latent variables in order to define a mathematical model based on MVA academic management support.