Fitness club attendance dynamics modelling as a data-driven approach for managing population engagement in physical activity

Purpose. The study aimed to analyse the dynamics of fitness club attendance and verify a stable regression model for its forecasting as a scientific and methodological tool for optimizing population engagement in health-enhancing and recreational physical activity. Materials & Methods. A retrospective analysis of a daily attendance time series from the APPOLO Next fitness club in Kyiv, Ukraine, was conducted. The dataset comprised 1690 daily observations collected from September 1, 2021 to July 1, 2026. Statistical analysis included descriptive statistics, the Shapiro–Wilk test, spectral analysis with a five-point Hamming window, Auto-ARIMA modelling, and General Regression Modelling (GRM). Calendar variables (day of the week and month), a linear time trend, and a seven-day autoregressive lag were included in the final regression model. Model performance was assessed using an 80/20 training–testing split and mean absolute error (MAE) and root mean square error (RMSE). Results. The attendance time series demonstrated significant non-normality and substantial variability, with coefficients of variation ranging from 25.8% to 37.7%. A pronounced weekly periodicity and its harmonic components, as well as seasonal fluctuations and a long-term increasing trend, were identified. The initial ARIMA model demonstrated limitations in describing the observed variability, with a forecast error of approximately 102 visitors and non-normally distributed residuals. The final GRM showed substantially improved explanatory and predictive performance (F=21.05, p<0.001, R²=0.553). The inclusion of the linear time trend and seven-day lag significantly improved model accuracy: MAE decreased from approximately 294 to 129 visitors in the training sample, while cross-validation MAE decreased from 198.0 to 131.7 and RMSE from 242.4 to 173.9. The seven-day lag demonstrated a significant autoregressive effect (β=0.402, p<0.001), indicating inertia in patterns of attendance. Conclusions. Fitness club attendance can be considered not only an operational indicator of facility utilization but also a measurable temporal characteristic of population engagement in organized health-enhancing and recreational physical activity. The combination of spectral analysis and GRM enabled the identification and modelling of weekly, seasonal, and autoregressive patterns in attendance. The resulting model (R²=0.553) provides a quantitative basis for evidence-based management of fitness services, including attendance forecasting and optimization of organizational decisions. Further research should validate the approach using data from multiple fitness clubs and incorporate individual, behavioural, and contextual factors.