Human pose and gesture estimation are crucial in correcting physiotherapy fitness exercises. In recent years, advancements in computer vision and machine learning approaches have led to the development of sophisticated pose estimation models that accurately track and analyze human movements in real time. This technology enables physiotherapists and fitness trainers to gain valuable insights into their client's exercise forms and techniques, facilitating more effective exercise corrections and personalized training regimens. This research aims to propose an efficient artificial intelligence method for human pose estimation during physiotherapy fitness exercises. We utilized a multi-class exercise dataset based on human skeleton movement points to conduct our experimental research. The dataset comprises 133 features derived from human skeleton movements during various exercises, resulting in high feature dimensionality that affects the performance of human pose estimation with machine learning and deep learning methods. We have introduced a novel Logistic regression Recursive Feature elimination (LogRF) method for feature selection.Extensive experiments demonstrate that using the top twenty selected features, the random forest method outperformed state-of-the-art studies with a high-performance score of 0.998. The performance of each applied method is validated through a k-fold approach and further enhanced using hyperparameter tuning. Our proposed study assists specialists in identifying and addressing potential biomechanical issues, improper postures, and incorrect movement patterns, which are essential for injury prevention and optimizing exercise outcomes. Furthermore, this study enhances the capabilities of remote monitoring and guidance capabilities, allowing physiotherapists to support their patient's progress with prescribed exercises continually.