An Analysis of Final Grades in a Mathematics Course for the Enhancement of Upcoming Engineering Students' Academic Performance by Using Multivariate Statistical Techniques

The objective of this work is to show the importance of the use of Multivariate Statistics in the field of Research, particularly in Teaching Innovation. With the required mathematical support, it was proven that it is possible to improve the grading system semiannually providing feedback on the evaluation instruments and the weightings used in the formulas to obtain the final average of a previous subject, in which unsatisfactory results were obtained, using different methods of multivariate statistical analysis such as multiple linear regression, multivariate normal distribution, the principal components method and factorial analysis. The results obtained suggest that it is preferable to condense classic evaluations such as exams and assignments, in learning outcomes by units, and that it is necessary to incorporate a different evaluation, which allows assessing punctual attendance to classes, since, although usually this variable is not part of the evaluation, it was found to be a key piece in the approval of a subject. Finally, a Chernoff face analysis was carried out for the comparison of the final results obtained in the “MATLAB” 2018-II and “Numerical Methods” 2019-I subjects, taught at the School of Environmental Civil Engineering of the participant university, concluding that the implementation of this proposal, with which the approval of the entire second group of students was achieved, allows the optimization of academic performance through a methodology that is aimed at any teacher who wishes to replicate the same.