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Surface finish is one of the prime requirements of customers for mechanical parts. This research paper is focused on the analysis of optimum cutting conditions to get lowest surface roughness in turning by regression analysis. An experimental study was carried out to investigate the effect of cutting parameters like spindle speed, feed and depth of cut on surface finish in turning on Aluminum 7075 alloy. A multiple regression analysis (Ra) using analysis of variance is conducted to determine the performance of experimental measurements and to it show the effect of cutting parameters on the surface roughness. Multiple regression modeling was performed to predict the surface roughness by using machining parameters. Machining was done by using tungsten carbide tool. The objective was to establish correlation between cutting speed, feed rate and depth of cut and optimum the turning conditions based on surface roughness. These correlations are obtained by multiple regression analysis (RA).