  A scalar-response functional model describes the association between a scalar
response and a set of functional covariates. An important problem in the
functional data literature is to test the nullity or linearity of the effect of
the functional covariate in the context of scalar-on-function regression. This
article provides an overview of the existing methods for testing both the null
hypotheses that there is no relationship and that there is a linear
relationship between the functional covariate and scalar response, and a
comprehensive numerical comparison of their performance. The methods are
compared for a variety of realistic scenarios: when the functional covariate is
observed at dense or sparse grids and measurements include noise or not.
Finally, the methods are illustrated on the Tecator data set.
