Depression affects approximately 300 million people worldwide, resulting in significant suffering and economic costs. Millions of sufferers remain undiagnosed and untreated due to a shortage of trained personnel, social stigma, and expensive treatments. Two novel machine learning architectures, used to predict depression severity from audio recordings, are presented and compared in this study. The data was taken from the Distress Analysis Interview Corpus, which contains recordings of 189 participant interviews and their Public Health Questionnaire 8 depression scores. Feature extraction and feature selection were performed on the participants' speech, and two machine learning architectures were designed to provide prediction models for depression severity. In the first architecture, participants' data were initially classified into depressed or not-depressed classes, and a regression model was trained on each class. The second architecture sorted the data into depression severity classes, which were then used in addition to the original features to predict the depression scores. The second architecture outperformed the first in both the classification and regression stages, achieving an RMSE value of 4.1, a significant improvement over previous studies that reported RMSE values of 6.32 to 6.94 for the same data. The results demonstrate a potential for a speech-based depression screening tool, able to assist healthcare professionals in the diagnosis and monitoring of patients, and to provide a scalable depression screening method enabling individuals to recognise their illnesses and seek professional help.