This paper constructs a multiple regression analysis model of the agricultural industry chain with rural environment and economic management and estimates the model parameters using the least squares method. The linear correlation between the variables is analyzed based on the variance expansion coefficient, standardization coefficient, complex correlation coefficient and other indicators, and the regression problem is analyzed for significance. Then the antidifferential Kalman filter optimization method of least squares and the threshold denoising optimization method based on wavelet decomposition and reconstruction transformation are introduced to optimize the model parameters to improve the model performance. Finally, the impact of agricultural industry chain construction on the rural environment and economic management is analyzed based on the model. The correlation coefficients between the three dimensions of agricultural product industry chain management and the performance of rural economic management are 0.318, 0.468, 0.416, and the correlation coefficients between them and the performance of rural environmental management are 0.297, 0.528, and 0.529, respectively, which indicates that rural agricultural product industry chain construction can promote rural management.