Yield trend, random crop yield, and random noise factors are the major components that affect plant yield. The mechanism of random crop yield is complex and can be simulated by multiple factors, such as weather factors like evaporation, precipitation, temperature, humidity, and solar radiation. In addition to weather, an index representing the health condition of plants and plant cover, defined by remote sensing, is also an important feature affecting yield prediction. In this paper, we present an optimization algorithm, machine learning, and agricultural knowledge to predict rice yield in several regions of the Mekong River Delta using information about yield trends, environment, and plant health. The first contribution of this research was the successful implementation of an interaction regression model that demonstrated superior predictive accuracy compared to traditional machine learning approaches. This model effectively identified and utilized significant weather variables and their interactions, leading to lower Root Mean Squared Error (RMSE) and higher R-squared values across multiple test years (2018–2020). The research identified several critical weather-related factors influencing rice yield, including evaporation in January and April, rain days in October and December, minimum temperatures in February, average maximum temperatures in September, and solar radiation in January, September, and October. Additionally, the Normalized Difference Vegetation Index (NDVI) emerged as a vital indicator of plant health throughout the year, consistently correlating with yield predictions. The successful output of the mathematical model is promising for predicting rice yield in different cultivation areas.