Measurements of the source levels of 9880 passes of 3188 different large commercial ships from the Enhancing Cetacean Habitat and Observation (ECHO) program database were used to investigate the dependencies of vessel underwater noise emissions on several vessel design parameters and operating conditions. Trends in the dataset were analyzed using functional regression analysis, which is an extension of standard regression analysis and represents a response variable (decidecade band source level) as a continuous function of a predictor variable (frequency). The statistical model was applied to source level data for six vessel categories: cruise ships, container ships, bulk carriers, tankers, tugs, and vehicle carriers. Depending on the frequency band and category, the functional regression model explained approximately 25%-50% of the variance in the ECHO dataset. The two main operational parameters, speed through water and actual draft, were the predictors most strongly correlated with source levels in all of the vessel categories. Vessel size (represented via length overall) was the design parameter with the strongest correlation to underwater radiated noise for three categories of vessels (bulkers, containers, and tankers). Other design parameters that were investigated (engine revolutions per minute, engine power, design speed, and vessel age) had weaker but nonetheless significant correlations with source levels.