Traffic collisions continue to pose a significant threat to road safety, underscoring the need for accurate, interpretable predictive models to support preventive strategies. This research employs fourth-degree polynomial regression to predict traffic accident trends based on historical data from 2017 to 2022 for Vidisha city. A statistical method effective for modelling non-linear trends was used to analyse and forecast traffic accident patterns in Vidisha, Madhya Pradesh, using data from 2017 to 2022. The model includes all types of collisions, including hit-and-run accidents, head-on collisions, side collisions, vehicle overturns, and others. Data were divided into training (80%) and testing (20%) sets to evaluate model performance. The calibrated models were assessed using key performance metrics—R2, MAE, and RMSE—with R2 values ranging from 0.90 to 0.96, indicating excellent predictive performance. Projections for 2023–2025 suggest a significant rise in hit-and-run and other uncategorised crashes, underscoring the need for proactive safety measures. The research provides practical recommendations for policymakers and transport authorities. The findings demonstrate that traditional statistical methods, such as polynomial regression, can support data-driven decision-making in road safety planning and urban traffic management, especially in medium-sized cities like Vidisha.