In this paper, noise annoyance from a mixture of multiple single sources is studied with emphasis on subjective evaluation and objective prediction. From 10 subjects, annoyance values for all single and artificially combined noise samples are collected using the semantic differential method with a suitable verbal scale. We propose a novel method to determine the utility weights of a multivariate linear regression model by comparing the total annoyance T of the combined noise sample to every single annoyance i from its componential single sound sample. This method predicts T on the premise of given i. Our results demonstrate that the multivariate linear regression model and the calculated utility weights provide a good and conceptually simple framework to predict the total noise annoyance.