Dementia is a general term for a group of syndromes that affect cognitive functions such as memory, thinking, reasoning, and the ability to perform daily tasks. The number of dementia patients is increasing as the population ages, and it is estimated that over 10 million people develop dementia each year. Dementia progresses gradually, and the sooner a patient receives help and support, the better their chances of maintaining their functional abilities. For this reason, early diagnosis of dementia is important. In recent years, machine learning models based on naturally spoken language have been developed for the early diagnosis of dementia. These methods have proven to be user-friendly, cost-effective, scalable, and capable of providing extremely fast diagnoses. This study utilizes the well-known ADReSS challenge dataset for classifying healthy controls and Alzheimer's patients. The dataset contains speech recordings from a picture description task featuring a kitchen scene, collected from both healthy controls and dementia patients. Unlike most studies, this research does not segment the audio recordings into active speech segments; instead, acoustic features are extracted from entire recordings. The study employs Ridge linear regression, Extreme Minimal Learning Machine, and Linear Support Vector Machine machine learning models to compute feature importance scores based on model outputs. The Ridge model performed best in Leave-One-Subject-Out cross-validation, achieving a classification accuracy of 87.8%. The EMLM model, proved to be effective in both cross-validation and the classification of a separate test dataset, with accuracies of 85.3% and 79.2%, respectively. The study's results rank among the top compared to other studies using the same dataset and acoustic feature extraction for dementia diagnosis.