Sleep is crucial for physical, mental, and emotional well-being. Physical activity and sleep are known to be interrelated; however, limited research has been performed to investigate their interactions in long-term. Conventional studies have presented sleep quality prediction, focusing on a single sleep quality aspect, such as sleep efficiency. In addition, the relationship between daily physical activity and sleep quality has yet to be explored, despite physical activities being utilized in previous studies for sleep quality prediction. In this paper, we develop an Extreme Gradient boosting method to predict sleep duration, sleep efficiency, and deep sleep based on users' daily activity information collected from wearable devices. Our model is trained and tested using data collected with an OURA ring from 34 pregnant mothers for six months under free-living conditions. Our finding shows an accuracy of 90.58%, 95.38%, and 91.45% for sleep duration, efficiency, and deep sleep, respectively. Moreover, we assess the contribution of each physical activity parameter to the prediction results using the Shapley Additive Explanations method. Our results indicate that sedentary time is the most influential parameter for sleep duration prediction, while the inactive time feature (e.g., resting or lying down) has a strong negative relationship with sleep efficiency, and the pregnancy week is the most critical parameter for deep sleep prediction.