In recent years, Additive Manufacturing (AM), more especially Fused Deposition Modeling (FDM), has emerged as a very promising technique for the production of complicated forms while using a variety of materials. Polyethylene Terephthalate Glycol, sometimes known as PETG, is a thermoplastic material that is widely used and is renowned for its remarkable strength, resilience to chemicals, and ease of processing. Through the use of Taguchi Grey Relational Analysis (GRA), the purpose of this investigation is to improve the process parameters of the FDM technology for PETG material. In order to investigate the influence that several FDM process parameters, such as layer thickness, infill density, printing speed, and nozzle temperature, have on significant outcome variables, such as dimensional accuracy, surface quality, and mechanical qualities, an empirical research was conducted. For the purpose of constructing the regression prediction model, the obtained dataset is used to make predictions about printing characteristics by means of the study of input process components. Statistical methods are used by the regression model in order to investigate the dynamics of the connection between the process variables. It is shown that the model is capable of properly predicting printing characteristics, which enables the identification of optimum process parameter settings for the purpose of improving FDM performance when PETG material is used. In additive manufacturing operations that make use of PETG material, this model serves as an essential tool for businesses to help them improve the efficiency of their operations and the quality of the items they produce. This research contributes to a better knowledge of Fused Deposition Modelling (FDM) processes and provides ideas that may be used to enhance Additive Manufacturing (AM) procedures in a variety of industries.