The study aims to evaluate the growth kinetics of two different Baker’s yeast (S. cerevisiae) strains and to establish regression models for predicting and optimizing of the growth conditions of the strains. Two yeast strains of S. cerevisiae; one was commercial strain (CS) and another was isolated from traditional dry wine residue of Madhupur region, Bangladesh (MS), were used in the study. The effects of four different factors viz., time, temperature, agitation and the potato powder concentrations were assessed. The performance of the growth of the strains was monitored using three responses like OD at 600 nm, ethanol production and biomass yield (g.L-1). Fractional factorial design (24-1) was used to generate the experimental trials as well as to analyze the data to design a geometrical representation. The highest value of optical density, ethanol and biomass production for S. cerevisiae (CS) were obtained 1.439, 6.56 (g.L-1) and 0.39 (g.L-1) respectively, and for S. cerevisiae (MS) were 0.645, 0.621 (g.L-1) and 0.23 (g.L-1), respectively. The best conditions for biomass production were at 1% of potato powder concentration, temperature at 30ºC and agitation at 150 rpm. By using regression model it can be said that for two factor interaction: potato powder concentration with time and time with agitation had the significant effects but three factor interactions had no significant effect on the experiment. By establishing regression models from the obtained data, prediction and optimization of the strains’ growth conditions can be easily done.