Our paper [Fukuchi and Sakuma(2023)], titled Demographic Parity Constrained Minimax Optimal Regression under Linear Model, has been accepted at the Thirty-Seventh Annual Conference on Neural Information Processing Systems (NeurIPS 2023). This paper explores the regression problem under a fairness constraint known as demographic parity. We demonstrate the best (minimax optimal) algorithm for addressing this fair regression problem within a specific linear model.