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This study is focused on dry longitudinal turning of AISI steel using CVD coated cutting inserts. The machining was conducted at different levels of cutting speed, feed, depth of cut, corner radius, rake, inclination and approach angles. Surface roughness was measured after each experiment, and statistical analysis was used to derive an empirical, regression model for arithmetical mean surface roughness. The regression model was used to theoretically minimize surface roughness, followed by additional verification experiments. The 95 % confidence interval constructed using ten additional batteries of experiments, contained the theoretically predicted minimum roughness of Ra = 0.238 μm. The mean absolute prediction error of the optimal roughness equals 0.006 μm. The results reveal practical applicability of the developed model. (Received in March 2022, accepted in July 2022. This paper was with the authors 1 week for 1 revision.). © 2022, DAAAM International Vienna. All rights reserved.