The so-called Functional Linear Regression model consists in
explaining a scalar response by a regressor which is a random
function observed on a compact subset of R: in this context,
the 'parameter' of linear model is a function of the weights.
In order to estimate this functional coefficient some estimators
such as Functional Principal Component Regression Estimator,
Smooth Principal Component Regression Estimator, Penalized
B-Splines Estimator, have been introduced in literature. We focus
our attention on the Functional Principal Component Regression
Estimator and in particular on the connected dimensionality
Our aim is to apply and compare some different selection methods,
which have been proposed in the classical regression field. These
methods are illustrated and compared by the means of simulations.