  Recently a distribution free approach for testing parametric hypotheses based
on unitary transformations has been suggested in \cite{Khm13, Khm16, Khm17} and
further studied in \cite{Ngu17} and \cite{Rob19}. In this note we show that the
transformation takes extremely simple form in distribution free testing of
linear regression. Then we extend it to general parametric regression with
vector-valued covariates.
