Reduced-order models (ROMs) have attracted considerable attention due to the recent advances in computational capacity. ROMs are known for their ability to reduce large amounts of data by projecting a high-dimensional system into a lower-dimensional subspace. The Dynamic Mode Decomposition (DMD) method, as one of the powerful ROM variants, is recognized for enhancing the computational efficiency of numerical and experimental studies of complex phenomena. Using these methods, a high-dimensional system is reduced to a low-dimensional subsystem while preserving the pivot features of the original system, with a new, similar system with the same dynamics. It demonstrates broad adaptability and applicability across fluid dynamics and other data-centric applications. On the other hand, regression methods are statistical methods that analyze and model relationships between two or more variables. In this study, a fast and accurate technique is used to obtain a good approximation of the velocity field of a given fluid by using the calculated velocity fields of fluids with Reynolds numbers in the defined neighborhood. Specifically, using the DMD modes, the essential features of the fluid flow velocity domain are extracted, and then, using the regression method, these features are extended to other fluid velocity fields. To reach this goal, the initial conditions of each DMD mode with the highest energy are used to add the regression method. Finally, as a case study, this algorithm is applied to a lid-driven cavity fluid flow. In this case, the fluid flow velocity field is studied for Re numbers between 400 and 600. The features of the velocity field are extracted from the fields with Re numbers of 400, 500, and 600. The features are defined by the first 9 modes, which account for 99% of the energy. The results show a good agreement between the velocity field estimated using this cost-effective variant of the parametric DMD method.