ABSTRACT
This chapter introduces the function-on-scalar model and shows how it can be easily estimated using the least squares principle. It focuses on penalized estimation of this model. Penalized estimation of function-on-function regression is explained. The implementation of these penalized estimation approaches in the refund package is illustrated. The chapter focuses on inference for the function-on-function regression which is based on functional principal components. It then concerns estimation and a hypothesis test. The chapter explains how the validity of the assumption that the data follow a functional linear regression can be evaluated. It then shows how to construct suitable diagnostic plots similar to the plots used in scalar linear regression models. The chapter considers inference for the fully functional model based on FPC's. Morris (2015) provides an extensive review of literature on functional regression. The chapter focuses on Ivanescu et al. (2015) who discusses connections to mixed models.
