Graph invariants or topological indices play an essential role in defining a chemical compound numerically. They are widely used in QSPR/QSAR analysis. Using this analysis, physicochemical properties of the compounds and the topological indices are studied. Various statistical parameters are determined and they are interpreted according to their numerical values obtained. This article concentrates on studying curvilinear regression models of Quinolone antibiotics. Quinolones are synthetic antibiotics employed for treating the diseases caused by bacteria. Across the years, Quinolones have shifted its position from minor drug to a very significant drug to treat the infections caused by bacteria and in urinary tract. They are largely used in the treatment of various gram-positive and gram-negative bacteria. A study is carried out on Quinolone antibiotics by computing eleven topological indices through QSPR analysis. Linear, quadratic and cubic regression models are determined for all topological indices. These regression models are depicted graphically by extending for fourth degree and fifth degree models for significant topological indices with its corresponding physical property showing the variation between each model.