  This paper presents a goodness-of-fit test for parametric regression models
with scalar response and directional predictor, that is, a vector on a sphere
of arbitrary dimension. The testing procedure is based on the weighted squared
distance between a smooth and a parametric regression estimator, where the
smooth regression estimator is obtained by a projected local approach.
Asymptotic behavior of the test statistic under the null hypothesis and local
alternatives is provided, jointly with a consistent bootstrap algorithm for
application in practice. A simulation study illustrates the performance of the
test in finite samples. The procedure is applied to test a linear model in text
mining.
