Currently, the higher education sector can be considered a marketplace, within which university education is considered a marketable service in the literature on higher education management. The analysis of the variables that generate university image has been the subject of numerous studies on higher education institutions (HEIs). The purpose of this study was to analyse the comparative weightage of these variables to increase the robustness of the model developed in a previous study by Alcaide-Pulido et al. (2017) for the purpose of identifying the variables with greater explanatory power of the image that undergraduate students have of their universities. This work uses a sample of 438 undergraduate students (Spain and Portugal), using a support vector machine to classify them and conduct sensitivity analysis to detect key variables with greater weights. The findings reveal four determining variables: 'value for money', 'ethical values and social responsibility', 'social networks', and 'university rankings'.