Statistical algorithms for processing air pollution monitoring data using regression, variance and matrix analysis

The paper presents a comprehensive study of statistical algorithms for processing and analysing air pollution monitoring data, specifically focusing on regression and variance analysis techniques. Various methods are discussed, including the least squares method, Bartlett-Kenyon method, Kerrich method, and Fisher's criterion for assessing model adequacy. The significance of handling excessive measurement errors and identifying observations with such errors is also highlighted. The study elaborates on dispersion analysis, utilising variance array formation, calculation, and hypothesis testing with Bartlett's, Cochrane, and Neumann-Pearson criteria. A significant portion of the research is devoted to a matrix algorithm for air pollution data analysis, involving linear transformations and similarity measures. Additionally, the paper evaluates the air pollution monitoring system in Kyiv, Ukraine, comparing different observation posts and proposing visualisation techniques using numerical and colour matrices. The use of cluster analysis for system operation insights is suggested. While the regression and variance methods are presented primarily as a theoretical toolkit, the matrix-based comparison is demonstrated on real monitoring data from four Kyiv observation posts: the correct functioning of the selected posts, expressed as the share of days with a complete daily sampling programme, ranged from 56.6 to 76.3%, and the paired posts 3–5 and 7–20 showed 96.6% and 91% agreement, respectively, in their day-by-day data-completeness category. The paper concludes by underscoring the importance of these methods for accurate air quality assessments and offers examples of practical implementation.