There are few road accident studies that use heart rate as an indicator of driving fatigue. This study offers a mathematical regression analysis to discover which independent variables (driving speed, driving duration, body mass index (BMI), gender and types of roads) are significant in influencing the heart rate and the way these parameters interact to indicate driver fatigue. The regression analysis was conducted using a Box-Behnken design by Design Expert software. The results revealed that the values of Prob>F for all variables were less than 0.01%, indicating that all variables influenced heart rate significantly. The heart rate increased when driving speed, driving duration and BMI increased. The similar pattern was observed as the driving path shifted from urban to a moderately difficult uphill/downhill road. However, the pulse rate reduced when a female driver was replaced by a male driver. The model’s accuracy was evaluated by comparing the output data obtained from actual road driving with software prediction. First, the prediction interval of both techniques’ output data was within 95%, meeting the minimum quantitative criteria of 90% predictive interval. Subsequently, the residual errors were less than 10%. The application of regression analysis to investigate the driver’s physiological system as a factor in driving fatigue is becoming less common. The majority of current research focuses on perceptual, psychological and electrophysiological methods to detect driving fatigue. As a result, a future study will assess the effect of cognitive skills impairment, such as decision-making, on driving fatigue using the same methodology. The regression model will be useful to shed light on traffic safety measures for preventing fatigue-related road accidents.