Student dropout, defined as the abandonment of a high education program before obtaining the degree without reincorporation, is a problem that affects every higher education institution in the world. This study uses machine learning models over two Chilean universities to predict first-year engineering student dropout over enrolled students, and to analyze the variables that affect the probability of dropout. The results show that instead of combining the datasets into a single dataset, it is better to apply a model per university. Moreover, among the eight machine learning models tested over the datasets, gradient-boosting decision trees reports the best model. Further analyses of the interpretative models show that a higher score in almost any entrance university test decreases the probability of dropout, the most important variable being the mathematical test. One exception is the language test, where a higher score increases the probability of dropout.