Spline-Based Generalised Additive Models for Interpretable Nonlinear Regression: An Application to Air Quality Data

Maurice Wanyonyi — 2026-06-12

Nonlinear relationships frequently arise in environmental data, challenging conventional linear regression models. This study investigates spline-based Generalised Additive Models (GAMs) as an interpretable semiparametric framework for capturing such nonlinearities. Using the UCI Air Quality dataset (9,358 hourly observations), we compare GAMs with linear regression and Random Forest models using blocked crossvalidation and multiple performance metrics. GAMs consistently outperformed linear regression, reducing root mean squared error (RMSE) by 11% for CO and by over 95% for benzene (from 0.796 to 0.034). GAMs achieved predictive accuracy comparable to Random Forest while retaining explicit, interpretable representations of predictor effects. Estimated smooth functions revealed meaningful nonlinear structures, including sensor saturation, nonlinear temperature dependencies, and a significant temperature–humidity interaction. Residual diagnostics confirmed improved model adequacy relative to linear specifications, and robustness analyses supported the stability of the proposed framework. These findings demonstrate that spline-based GAMs offer a statistically coherent and interpretable alternative to both classical linear models and black-box machine learning methods in environmental applications.

Statistical Analysis of Undergraduate Sleep Pattern and Lifte Style at Federal University of Lafia, Nasarawa State, Nigeria

D.M.O. Omebo — 2026-06-13

All is well that ends well is a common adage to emphasize the need to focus on the end of every activities in life. It is therefore imperative to focus on any factor that can lead to the success of student’s end. It is on this note that this research attempt to x-ray those factors that can lead to a successful end. Therefore, this study presents a comprehensive statistical analysis of sleep patterns and lifestyle factors among students at the Federal University of Lafia, with the goal of understanding how these variables influence academic performance. As sleep quality and lifestyle choices increasingly emerge as critical elements of student well-being and academic success, this research aim to uncover meaningful patterns and relationships among key behavioral indicators, including sleep duration, caffeine intake, screen time, and study habits. The sample size of 500 students was considered.

Inferential statistical tests were conducted to explore deeper relationships within the data. Independent samples t-test results showed no statistically significant difference in sleep quality between male and female students (p = 0.201). Similarly, ANOVA results indicated no significant variation in sleep quality across departments (p = 0.774), suggesting that academic field and gender do not play major roles in determining sleep quality. However, a strong negative Pearson correlation (r = -0.742, p < 0.01) was found between caffeine intake and sleep hours, indicating that increased caffeine consumption significantly reduces sleep duration. Based on the findings, the study concludes that while gender and academic department do not significantly affect sleep quality, lifestyle habits—particularly caffeine consumption—have a substantial impact on students’ sleep duration. The study recommends the implementation of sleep awareness programs, lifestyle management campaigns, and policy changes within the university to promote better sleep hygiene and healthier living among students. These efforts are crucial for fostering academic success, physical health, and mental well-being in the student population.

Asian Journal of Probability and Statistics

Spline-Based Generalised Additive Models for Interpretable Nonlinear Regression: An Application to Air Quality Data

Statistical Analysis of Undergraduate Sleep Pattern and Lifte Style at Federal University of Lafia, Nasarawa State, Nigeria