Analysis of the functional regression problem of temperature on Ozone concentration

Abstract With the continuous improvement of computer storage capabilities and online observation technology, functional data emerged as the times required. Among the various research methods, regression analysis of functional data stands out as one of the most commonly employed techniques. This study employed Fourier spline basis functions to smooth the gathered data and preprocess it to establish a functional linear regression model with scalar response. Specifically, we investigated temperature regression on Ozone concentration across 17 cities in Henan Province in 2022. In our functional regression prediction, we compared the results obtained with and without the addition of a roughness penalty. Through this comparison, we observed that the absence of a roughness penalty led to overfitting, while including the penalty yielded more detailed results. Moreover, the coefficient of determination R 2 approached one more closely when using the roughness penalty, indicating a better-fitting regression effect. Lastly, for those interested in monitoring the regression residuals of the estimated Ozone concentration, we provide a detailed flowchart outlining the process for monitoring these residuals.