Identification of smoothing parameter values for regression coefficients
With the functional data objects for each model component now ready, a cell array containing each model component along with a constant predictor term is generated for use in the functional liner regression. Before the final regression analysis can be run, a smoothing parameter for the regression coefficient beta basis system has to be selected. This is achieved by calculating leave-one-out cross-validation scores (i.e. error sum of squares values) for functional responses using a range of different smoothing parameter values, as per section 9.4.3 and 10.6.2 of \cite{Ramsay_2009}. The results of this cross-validation exercise are shown in Fig. \ref{650456} and Fig. \ref{342847} for the number of non-corporates by priority year beta basis system smoothing parameter during the emergence phase of the Technology Life Cycle: