This paper introduces a unified regression framework based on the Lagrange formalism, demonstrating how polynomial and logistic regression can all be formulated within a common variational (Lagrangian formalism) structure. Within this framework, the DCT-based (Discrete Cosine Transform) model naturally emerges as a novel and effective approach to traditional or unsupervised regression. The DCT is used as the constraints in the Lagrangian formalism. By leveraging the nearly orthogonal and bounded nature of the cosine basis, the DCT model offers computational advantages and improved convergence properties compared with traditional polynomial methods. The results further support the potential of the DCT-based neuron as a powerful tool for regression analysis and related learning tasks.