  Physical activity plays a significant role in the well-being of individuals
with Chronic obstructive Pulmonary Disease (COPD). Specifically, it has been
directly associated with changes in hospitalization rates for these patients.
However, previous investigations have primarily been conducted in a
cross-sectional or longitudinal manner and have not considered a continuous
perspective. Using the telEPOC program we use telemonitoring data to analyze
the impact of physical activity adopting a functional data approach. However,
Traditional functional data methods, including functional regression models,
typically assume a consistent data domain. However, the data in the telEPOC
program exhibits variable domains, presenting a challenge since the majority of
functional data methods, are based on the fact that data are observed in the
same domain. To address this challenge, we introduce a novel fully functional
methodology tailored to variable domain functional data, eliminating the need
for data alignment, which can be computationally taxing. Although models
designed for variable domain data are relatively scarce and may have inherent
limitations in their estimation methods, our approach circumvents these issues.
We substantiate the effectiveness of our methodology through a simulation
study, comparing our results with those obtained using established
methodologies. Finally, we apply our methodology to analyze the impact of
physical activity in COPD patients using the telEPOC program's data. Software
for our method is available in the form of R code on request at
\url{https://github.com/Pavel-Hernadez-Amaro/V.D.F.R.M-new-estimation-approach.git}.
