  Experimental studies often fail to appropriately account for the number of
collected samples within a fixed time interval for functional responses. Data
of this nature appropriately falls under an Infill Asymptotic domain that is
constrained by time and not considered infinite. Therefore, the sample size
should account for this infill asymptotic domain. This paper provides general
guidance on selecting an appropriate size for an experimental study for various
simple linear regression models and tuning parameter values of the covariance
structure used under an asymptotic domain, an Ornstein-Uhlenbeck process.
Selecting an appropriate sample size is determined based on the percent of
total variation that is captured at any given sample size for each parameter.
Additionally, guidance on the selection of the tuning parameter is given by
linking this value to the signal-to-noise ratio utilized for power calculations
under design of experiments.
