Utilizing a computational approach, this study quantifies the onset of lubrication starvation for line contacts of rough surfaces operating under typical ranges of automotive gearing applications. The response parameter is selected as the critical film thickness supply, at which starvation initiates. The potential influential parameters (predictors) considered include normal force density, rolling velocity, sliding, lubricant viscosity, and surface roughness amplitude. A non-Newtonian thermal mixed lubrication model is employed to determine the critical lubricant supply under various operating and surface roughness conditions. General linear regression is implemented to reach an easy-to-use equation (R-squared value higher than 97%), facilitating the quantification of starvation dependence on the predictors that are statistically significant.