Distance correlation R is a measure of dependence between random vectors introduced by Székely et al. . The distance correlation satisfies 0≤R(X,Y)≤1 and its interpretation is similar to the squared Pearson’s correlation. However, the advantages of distance correlation over the Pearson correlation is that it defines R(X,Y) in arbitrary finite dimensions of X and Y and R characterises independence, i.e. R(X,Y)=0⇔X,Y are independent. Recently, Lyons  provided conditions for the application of the distance correlation to functional spaces. So, this measure seems to be a good indicator of the correlations between functional and multivariate variables that may be useful for designing a functional linear model (for instance, avoiding variates with high collinearity). The empirical distance correlation Rn,s(X,Y) can be easily computed as Rn,s(X,Y)=Vn,s2(X,Y)Vn,s2(X)Vn,s2(Y). where Vn,s(X,Y) is the empirical distance covariance defined by Vn,s2(X,Y)=1n2∑k,l=1nAklBkl where Akl=akl-a¯k.-a¯.l+a¯.. and Bkl=bkl-b¯k.-b¯.l+b¯... with akl = ‖Xk − Xl‖, bkl = ‖Yk − Yl‖, k, l = 1, …, n, and the subscript. denotes that the mean is computed for the index that it replaces. Similarly, Vn,s(X) is the non-negative number defined by Vn,s2(X)=Vn,s2(X,X)=1n2∑k,l=1nAkl2.