Keiser University - Institutional RepositoryPolynomial Model Selection with Small Samples: Fitting, Generalization, and Cross-Validation in the Analysis of International Tourism in Nicaragua (2020–2024)Sara SamiraSilwany GarciaauthorThis study addresses model selection in data-scarce regimes using five annual observations of international tourism arrivals in Nicaragua (2020–2024). Four candidate specifications (linear, quadratic, cubic, and exponential) are fitted and evaluated via leave-one-out cross-validation (LOOCV), the PRESS statistic, and the corrected AICc. The results demonstrate that R2 is a severely biased proxy for predictive performance when p/n≥0.4. The cubic model (R2 = 0.971) exhibits an out-of-sample prediction error six times larger than that of the linear model (PRESS = 2.61 ×106 vs. 4.31 ×105) and yields physically impossible forecasts. All criteria converge on the linear model as the optimal specification. Projections for 2025–2030 with 95% parametric bootstrap intervals are provided, together with a fully reproducible Python pipeline. --------------------- Este estudio aborda la selección de modelos en regímenes con escasez de datos utilizando cinco observaciones anuales de llegadas de turistas internacionales a Nicaragua (2020-2024). Se ajustan cuatro especificaciones candidatas (lineal, cuadrática, cúbica y exponencial) y se evalúan mediante validación cruzada de exclusión de un elemento (LOOCV), el estadístico PRESS y el AICc corregido. Los resultados demuestran que el R² es un indicador sesgado del rendimiento predictivo cuando p/n ≥ 0,4. El modelo cúbico (R² = 0,971) presenta un error de predicción fuera de muestra seis veces mayor que el del modelo lineal (PRESS = 2,61 × 10⁶ frente a 4,31 × 10⁵) y genera pronósticos físicamente imposibles. Todos los criterios convergen en el modelo lineal como la especificación óptima. Se proporcionan proyecciones para el periodo 2025-2030 con intervalos de bootstrap paramétricos del 95 %, junto con un flujo de trabajo en Python totalmente reproducible.Probabilities. Mathematical statistics [QA273-280]Keiser University Latin American Campus, San Marcos, NicaraguaMonograph

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