Functional Linear Regression with Points of Impact: A Real Data Application with Scalar Response

Functional linear regression (FLR) is a fundamental model in functional data analysis for relating scalar responses to functional predictors. In many applied problems, however, the response is influenced not by the entire functional trajectory but by localized regions of the domain, known as points of impact (Pol). This paper presents a real-data application of functional linear regression with points of impact using near-infrared (NIR) spectroscopy data. Through numerical evaluation, graphical analysis, and cross-validation, we demonstrate that incorporating points of impact leads to improved predictive accuracy and substantially enhanced interpretability compared to classical FLR.

کلیدواژه ها:

Functional Data Analysis ، Functional Linear Regression ، Points of Impact ، Spectroscopy