In order to achieve reliable information about deterioration, it is important to differentiate between changes in structural behaviour due to service loading (temperature, wind and traffic) and changes resulting from damage when interpreting measurement data. Although many studies have investigated this topic, the simultaneous effects of temperature, wind and traffic loading on the behaviour of suspension bridges are poorly understood. This paper investigates the effects of service loading on the natural frequency of a suspension bridge. Using more than two years of measurement data from continuous monitoring of the Tamar suspension bridge (UK), regression of the service loading and natural frequencies of the bridge and stay cables is developed using: (i) the multiple linear-regression method and (ii) the random-forest method. The effects are quantitatively evaluated by determining the relative importance of variables using the regression methods. The regression methods are also employed to predict changes in the structural behaviour of the bridge. This study finds that while the primary environmental factor influencing the behaviour of the cables is temperature, the behaviour of the whole bridge is affected by temperature and traffic loading. The effect of traffic loading on the first three natural frequencies of the bridge is even higher than that of temperature. The random-forest method is better for predicting changes in natural frequencies of the whole bridge than the multiple linear-regression method.