  Functional linear models are one of the most fundamental tools to assess the
relation between two random variables of a functional or scalar nature. This
contribution proposes a goodness-of-fit test for the functional linear model
with functional response that neatly adapts to functional/scalar
responses/predictors. In particular, the new goodness-of-fit test extends a
previous proposal for scalar response. The test statistic is based on a
convenient regularized estimator, is easy to compute, and is calibrated through
an efficient bootstrap resampling. A graphical diagnostic tool, useful to
visualize the deviations from the model, is introduced and illustrated with a
novel data application. The R package goffda implements the proposed methods
and allows for the reproducibility of the data application.
