Background: The relationship between partial pressure of oxygen (PaO₂)/fraction of inspired oxygen (FiO₂) (PF) and oxygen saturation (SpO₂)/FiO₂ (SF) ratios, as well as between oxygenation index (OI) and oxygen saturation index (OSI), provide valuable insights for clinical decision-making in the critically ill patient. This study aims to evaluate these relationships using linear regression and machine learning (ML) models across different time intervals and in patients with and without shock. Subjects and Methods: Data from 68 pediatric patients admitted to a tertiary pediatric intensive care unit (PICU) were collected at predefined time intervals. Linear regression was used to assess relationships between PF and SF ratios and OI and OSI. In addition, eight ML models were evaluated for predictive accuracy. The analysis was stratified based on time intervals and shock status. Model performance was assessed using root mean squared error (RMSE) and the coefficient of determination (R2). Results: Both linear regression and ML models demonstrated a strong relationship between PF and SF ratios and OI and OSI. ML models outperformed linear regression in predictive accuracy. Correlations between SF and PF ratios were time-dependent, strengthening over longer durations. Although no correlation was observed initially among patients with shock, the non-shock patients showed a consistent correlation, which became stronger at higher SpO₂ levels. An online predictor was developed using ML models to estimate PF from SF and OI from OSI at different time intervals. Conclusions: A clinically significant relationship was found between PF and SF ratios and OI and OSI, reinforcing their potential for noninvasive respiratory monitoring in pediatric patients.