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Our analysis focuses on identifying relations between properties of the voice and depression symptom severity. On a novel corpus of 3,374 longitudinal speech recordings from 71 patients clinically diagnosed with major depressive disorder (MDD), we use a statistical modelling approach to identify associations between depression symptom severity and 38 acoustic and cognitive features. Significant negative associations with daily within-individual fluctuations of depression include speaking rate and articulation rate. Furthermore, when analysing how the changes in speech-derived features covary over time with the change in depression severity, we find that the standard deviation of the pitch has a significant negative association, as well as the speaking and articulation rate. We also discover that several performance metrics derived from the cognitive tasks (digit-span and Stroop) have significant associations with fluctuations or changes in depression symptom severity.