This paper presents a new trial approach to early detection of cognitive impairment in the elderly with the use of speech sound analysis and multivariate statistical technique. In this paper, we focus on the prosodic features from speech sound. Japanese 115 subjects (32 males and 83 females between ages of 38 and 99) participated in this study. We collected speech sound in a few segments of dialogue of HDS-R examination. The segments corresponds to speech sound that is answering for questions on time orientation and number backward count. Firstly, 130 prosodic features have been extracted from each of the speech sounds. These prosodic features consist of spectral and pitch features (53), formant features (56), intensity features (19), and speech rate and response time (2). Secondly, these features are refined by principal component analysis and/or feature selection. Lastly, we have calculated speech prosody-based cognitive impairment rating (SPCIR) by multiple linear regression analysis. The results indicated that there is moderately significant correlation between HDS-R score and synthesis of several selected prosodic features. Consequently, adjusted coefficient of determination R²=0.50 suggests that prosody-based speech sound analysis has possibility to screen the elderly with cognitive impairment.