Resumo: Beta prime regression provides a flexible framework for modeling positive continuous response variables; however, reliable tools for model assessment and selection remain scarce for this class of models. In this paper, we propose three versions of the prediction coefficient P2 as model selection criteria for beta prime regression. These measures are based on the Predictive Residual Sum of Squares (PRESS) statistic computed from quantile, weighted, and standardized weighted residuals, along with their corrected forms. We compare the proposed measures with existing R2-type goodness-of-fit criteria and information criteria through Monte Carlo simulations under both correct and incorrect model specifications. The P2 measures consistently outperform competing criteria in detecting misspecification and selecting the correct model. Two empirical applications illustrate the practical utility of the proposed measures.