With this notation, the terms {〈Xi,β〉}i=1n can be approximated by C Ψφ′ b = Z b which, in essence, is a reformulation of a classical multivariate linear model that approximates the functional model. Here, the matrix Z takes into account all the approximation steps done with the available information: the chosen basis for X and β with the selected components: Kx and Kβ.