A new method was developed to estimate regression functions in a model that combines parametric and nonparametric components. By using a smoothing spline, the researchers found a way to balance the goodness of fit and smoothness of the model curve. They used weighted least squares to estimate parametric parameters and a reproducing kernel Hilbert space method to determine goodness of fit and penalty functions. The result was a linear estimation of the multi-response model, combining both parametric and nonparametric components. This method could be useful in medical fields for predictive purposes.