ABSTRACT
Linear regression is one of the most fundamental tools in statistics. Functional regression models are subdivided into three broad categories, depending on whether the responses or the regressors, or both, are curves. The regressors are curves, but the responses are scalars. This chapter presents several examples of data that can be modeled using scalar-on-function regression. It then reviews the standard regression theory. The chapter explains chief differences between the cases of functional and vector regressors. It provides several approaches to the estimation the regression function. Implementation of these approaches in the R package refund is illustrated. The chapter discusses nonlinear approaches to scalar-on-function regression. Scalar-on-function regression has been applied to Diffusion Tensor Imaging data. The responses are various scores of patients, for example The PASAT (Paced Auditory Serial Addition Test) scores. These scores measure cognitive function and assess auditory information processing speed and flexibility, as well as calculation ability.
