  Regression models with a response variable taking values in a Hilbert space
and hybrid covariates are considered. This means two sets of regressors are
allowed, one of finite dimension and a second one functional with values in a
Hilbert space. The problem we address is the test of the effect of the
functional covariates. This problem occurs for instance when checking the
goodness-of-fit of some regression models for functional data. The significance
test for functional regressors in nonparametric regression with hybrid
covariates and scalar or functional responses is another example where the core
problem is the test on the effect of functional covariates. We propose a new
test based on kernel smoothing. The test statistic is asymptotically standard
normal under the null hypothesis provided the smoothing parameter tends to zero
at a suitable rate. The one-sided test is consistent against any fixed
alternative and detects local alternatives \`a la Pitman approaching the null
hypothesis. In particular we show that neither the dimension of the outcome nor
the dimension of the functional covariates influences the theoretical power of
the test against such local alternatives. Simulation experiments and a real
data application illustrate the performance of the new test with finite
samples.
