Abstract <p>Mathematical modeling permits synchronous forecasting of the output of coking byproducts on the basis of four predictors (tar, benzene, ammonium sulfate, and coke oven gas), with simultaneous analysis of the proportion of ten coal ranks (G, GZhO, GZh, Zh, KZh, K, KO, KSN, KS, and OS) and nine chemical components of coal (moisture content, ash content, sulfur content, basicity of ash and coal, yield of volatiles in terms of dry mass and hot mass, plastic layer thickness, and mean vitrinite reflection coefficient). The goal of the present work is mathematical modeling of the output predictors (tar, benzene, ammonium sulfate, and coke oven gas) as a function of the lag period with zero inertia. The relation between the predictors and the Pearson correlation coefficient is determined, with sorting of the basic data set in terms of the covariation function. The relations between the covariation function and the Pearson correlation coefficient is plotted for the predictors. Correlations between the ratio of ten coal ranks and tar with a lag of 1–60 days and zero inertia are established, and the relation between a lag period of 1–60 days and the Pearson correlation coefficient with zero inertia is plotted for the given coal ranks. The results indicate that the physicochemical processes at the coke plant are complex. That imposes constraints on the development of the mathematical apparatus and the details of modeling for each rank of coal.</p>