Abstract
This study analyses population data of Afyonkarahisar covering the 1982–2024 period to generate and validate a forecast for the year 2025 using three statistical modelling approaches: linear regression, second-order polynomial regression, and the ARIMA(1,1,0) time series model. These models were selected to capture both long-term trend behaviour and temporal dynamics within the population series. Model performances were evaluated using error metrics including Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and the coefficient of determination (R²). The polynomial regression model achieved the highest historical fit (RMSE = 4,607; MAE = 3,121; R² ≈ 0.993), while the linear regression model provided stable trend representation (RMSE = 11,569; MAE = 10,656; R² ≈ 0.961). The ARIMA model demonstrated balanced short-term forecasting capability (RMSE = 6,482; MAE = 5,476; R² ≈ 0.942). To assess real-world predictive accuracy, model outputs were compared with the actual 2025 population value. The ARIMA model exhibited the lowest deviation (0.28%), followed by linear regression (2.03%), whereas the polynomial model showed higher projection error (7.74%). The results confirm that no single model fully captures all characteristics of population behaviour; instead, a multi-model framework provides a more reliable and interpretable forecasting structure. The projected population range of approximately 255,000–260,000 individuals is consistent with observed trends and supports evidence-based regional planning.