Understanding in the field of face perception is borne from advances in computer graphics techniques. Here, a new and fully data-driven algorithm is introduced for studying the social perception of the face, termed face regression. Given a set of photographs representing facial texture, coordinates delineating facial shape, and measured social traits, the algorithm learns relationships between each dimension of the faces (pixel values and coordinate points) and their associated social traits. Using the learned weights, the algorithm is capable of predicting faces of any score for any or all of the modelled traits, allowing for a fine-grained examination of facial features associated with social traits when compared to common facial averaging and transforming methods. In two applications, the algorithm addresses theoretical concerns with common methodologies in face perception, and demonstrates its utility through its ability to recreate face averages, and isolate the actual appearances associated with social traits. Perceptual validation experiments indicate participant reactions differ between composite images and those generated through face regression, giving novel insight to the function of social perception. A dedicated software package for utilising the algorithm is introduced, and future applications are discussed.