Three-dimensional printing, or additive manufacturing, represents one of the fastest growing branches of the industry, and fused deposition modeling (FDM) is one of most frequently used technologies. Three-dimensional printing does not provide high-quality surfaces, so finishing is required, and milling is one of the best methods for improving surface quality. The combination of 3D printing and traditional manufacturing technologies is known as hybrid manufacturing. In order to improve quality and determine optimal machining parameters, researchers increasingly use artificial intelligence methods. In the context of manufacturing technologies, both multiple regression analysis (MRA) and artificial neural networks (ANNs) have proven to be highly reliable in predicting and optimizing machining processes. This study focuses on the use of MRA and an ANN to analyze the influence of machining parameters such as feed rate, depth of cut, and spindle speed on the surface roughness of a 3D-printed part in a milling process. The study compares the measured results with the outcomes obtained through MRA and the ANN to assess their effectiveness in predicting and optimizing surface roughness. The results show that higher accuracy was obtained from the ANN method.