Supervised transfer learning has received considerable attention due to its potential to boost the predictive power of machine learning in scenarios where data are scarce. Generally, a given set of source models and a dataset from a target domain are used to adapt the pre-trained models to a target domain by statistically learning domain shift and domain-specific factors. While such procedurally and intuitively plausible methods have achieved great success in a wide range of real-world applications, the lack of a theoretical basis hinders further methodological development. This paper presents a general class of transfer learning regression called affine model transfer, following the principle of expected-square loss minimization. It is shown that the affine model transfer broadly encompasses various existing methods, including the most common procedure based on neural feature extractors.