  Transfer learning, also referred as knowledge transfer, aims at reusing
knowledge from a source dataset to a similar target one. While many empirical
studies illustrate the benefits of transfer learning, few theoretical results
are established especially for regression problems. In this paper a theoretical
framework for the problem of parameter transfer for the linear model is
proposed. It is shown that the quality of transfer for a new input vector $x$
depends on its representation in an eigenbasis involving the parameters of the
problem. Furthermore a statistical test is constructed to predict whether a
fine-tuned model has a lower prediction quadratic risk than the base target
model for an unobserved sample. Efficiency of the test is illustrated on
synthetic data as well as real electricity consumption data.
