This study presents an innovative method for classifying the health of dairy cattle by leveraging their behavior patterns. The proposed approach integrates correlation analysis and machine learning techniques, utilizing motion data collected from sensors affixed to the cattle's collar and legs. By extracting behavioral features and employing a pre-trained behavior classification model with the Random Forest (RF) algorithm, this research identifies some combined behaviors such as resting-lying, feeding-standing, and ruminating-standing as features significantly correlated with the cattle's health status. The correlation coefficients are also of diverse levels across different farming periods during the day. A health classification model is developed using a filtered dataset of behaviors with high correlation coefficients, achieving a classification accuracy rate surpassing 90% and a high AUC value of up to 0.96. This study illustrates that the correlation analysis method not only facilitates the examination of the link between cattle health status and behavior but also enhances the health classification model's performance by eliminating redundant features and reducing misdiagnosis. In summary, this work offers a comprehensive data analysis approach to develop a highperformance, machine learning-based health status classifier using combined behavioral features, making strides towards the realization of smart agriculture.