The wheel-rail contact mechanics and dynamics that are of great importance to the railroad industry are evaluated by applying statistical methods to the large volume of data that is collected on the VT-FRA state-of-the-art roller rig. The intent is to use the statistical principles to highlight the relative importance of various factors that exist in practice to longitudinal and lateral tractions and to develop parametric models that can be used for predicting traction in conditions beyond those tested on the rig. The experiment-based models are intended to be an alternative to the classical traction-creepage models that have been available for decades. Various experiments are conducted in different settings on the VT-FRA Roller Rig at the Center for Vehicle Systems and Safety at Virginia Tech to study the relationship between the traction forces and the wheel-rail contact variables. The experimental data is used to entertain parametric and non-parametric statistical models that efficiently capture this relationship. The study starts with single regression models and investigates the main effects of wheel load, creepage, and the angle of attack on the longitudinal and lateral traction forces. The assumptions of the classical linear regression model are carefully assessed and, in the case of non-linearities, different transformations are applied to the explanatory variables to find the closest functional form that captures the relationship between the response and the explanatory variables. The analysis is then extended to multiple models in which interaction among the explanatory variables is evaluated using model selection approaches. The developed models are then compared with their non-parametric counterparts, such as support vector regression, in terms of "goodness of fit," out-of-sample performance, and the distribution of predictions. / Master of Science / The interaction between the wheel and rail plays an important role in the dynamic behavior of railway vehicles. The wheel-rail contact has been extensively studied through analytical models, and measuring the contact forces is among the most important outcomes of such models. However, these models typically fall short when it comes to addressing the practical problems at hand. With the development of a high-precision test rig—called the VT-FRA Roller Rig, at the Center for Vehicle Systems and Safety (CVeSS)—there is an increased opportunity to tackle the same problems from an entirely different perspective, i.e. through statistical modeling of experimental data. Various experiments are conducted in different settings that represent railroad operating conditions on the VT-FRA Roller Rig, in order to study the relationship between wheel-rail traction and the variables affecting such forces. The experimental data is used to develop parametric and non-parametric statistical models that efficiently capture this relationship. The study starts with single regression models and investigates the main effects of wheel load, creepage, and the angle of attack on the longitudinal and lateral traction forces. The analysis is then extended to multiple models, and the existence of interactions among the explanatory variables is examined using model selection approaches. The developed models are then compared with their non-parametric counterparts, such as support vector regression, in terms of "goodness of fit," out-of-sample performance, and the distribution of the predictions. The study develops regression models that are able to accurately explain the relationship between traction forces, wheel load, creepage, and the angle of attack.