  Modeling and analysis of spectroscopy data is an active area of research with
applications to chemistry and biology. This paper focuses on analyzing Raman
spectra obtained from a bone fracture healing experiment, although the
functional regression model for predicting a scalar response from
high-dimensional tensors can be applied to any spectroscopy data. The
regression model is built on a sparse functional representation of the spectra,
and accommodates multiple spatial dimensions. We apply our models to the task
of predicting bone-mineral-density (BMD), an important indicator of fracture
healing, from Raman spectra, in both the in vivo and ex vivo settings of the
bone fracture healing experiment. To illustrate the general applicability of
the method, we also use it to predict lipoprotein concentrations from spectra
obtained by nuclear magnetic resonance (NMR) spectroscopy.
