Subjective tests are the gold standard for evaluating speech quality and intelligibility, but they are time-consuming and expensive. Thus, objective measures that align with human perceptions are crucial. This study evaluates the correlation between commonly used objective measures and subjective speech quality and intelligibility using a Chinese speech dataset. Moreover, new objective measures are proposed combining current objective measures using deep learning techniques to predict subjective quality and intelligibility. The proposed deep learning model reduces the amount of training data without significantly impacting prediction performance. We interpret the deep learning model to understand how objective measures reflect subjective quality and intelligibility. We also explore the impact of including subjective speech quality ratings on speech intelligibility prediction. Our findings offer valuable insights into the relationship between objective measures and human perceptions.