This paper presents a robust methodology for multidimensional regression analysis aimed at predicting the state of dynamic systems. Building on the foundation of univariate linear regression, the study extends the approach to accommodate multiple interrelated predictors—encompassing both control and state parameters—to effectively model complex technological processes. By formulating the regression problem in matrix form, the authors derive parameter estimates using the least squares method, demonstrating that, under Gaussian error assumptions, these estimates coincide with those obtained via maximum likelihood. A key innovation is the incorporation of a sliding observation window, which dynamically refines the regression model by automatically selecting the most correlated predictors as system conditions evolve. The resulting RA forecaster software not only simplifies the forecasting process through an intuitive user interface but also ensures accuracy through quantitative metrics such as root mean square error and mean relative error. Overall, the methodology provides a versatile and effective framework for state prediction in multifactorial systems, with promising potential for future integration with advanced machine learning techniques.