The debate on the primary cross-curricular skills or fundamental competencies that must be improved in higher education has increased in the last few years. This is especially important in the new distant learning environments, which bring new challenges to the educational process. Econometric models have been designed to explain the students’ academic performance, which has been measured using their qualifications average, the number of failed subjects, passed subjects, and withdrawn subjects, and the level of progress, among other indicators, to try to understand the influence of variables such as students’ self-esteem, reading comprehension, English proficiency level, and performance in a mathematics-related subject on the students of accountant auditor program from Pontificia Universidad Católica de Valparaiso. Students were asked to fill in a questionnaire to collect data on the psychological and pedagogical variables, while the socio-economic and socio-demographic data were collected from the university. The results have shown that the most significant variables in the development level of this skill type are socio-demographic and socio-economic characteristics. Some of the psychological and pedagogical variables that have, to a lesser degree, some influences are self-regulation in the learning process and the self-perception of anxiety levels. Lastly, some recommendations to intervene in the students’ learning process are presented with the objective of achieving a higher level of development in this type of competences.