  In this work, a goodness-of-fit test for the null hypothesis of a functional
linear model with scalar response is proposed. The test is based on a
generalization to the functional framework of a previous one, designed for the
goodness-of-fit of regression models with multivariate covariates using random
projections. The test statistic is easy to compute using geometrical and matrix
arguments, and simple to calibrate in its distribution by a wild bootstrap on
the residuals. The finite sample properties of the test are illustrated by a
simulation study for several types of basis and under different alternatives.
Finally, the test is applied to two datasets for checking the assumption of the
functional linear model and a graphical tool is introduced. Supplementary
materials are available online.
