  This paper presents tests to formally choose between regression models using
different derivatives of a functional covariate in scalar-on-function
regression. We demonstrate that for linear regression, models using different
derivatives can be nested within a model that includes point-impact effects at
the end-points of the observed functions. Contrasts can then be employed to
test the specification of different derivatives. When nonlinear regression
models are defined, we apply a $J$ test to determine the statistical
significance of the nonlinear structure between a functional covariate and a
scalar response. The finite-sample performance of these methods is verified in
simulation, and their practical application is demonstrated using a chemometric
data set.
