Directional regression is an effective sufficient dimension reduction method which implicitly synthesizes the first two conditional moments. In this paper, we extend directional regression to a general family of estimators via the notion of general empirical directions. Data-driven method is used to identify the optimal estimator within this family. Based on the proposed general directional regression estimators, we develop new methodology for marginal dimension test as well as nonlinear dimension reduction. Improvement of general directional regression over classical
directional regression is demonstrated via simulation studies and an empirical study with the wine recognition data.