Implementing impedance control in Cartesian task space or directly at the joint level is a popular option for achieving desired compliance behavior for robotic manipulators performing tasks. The damping ratio is an important control criterion for modulating the dynamic response; however, tuning or selecting this parameter is not easy, and can be even more complicated in cases where the system cannot be directly solved at the joint space level. Our study proposes a novel methodology for calculating the local optimal damping ratio value and supports it with results obtained from five different scenarios. We carried out 162 different experiments and obtained the values of the inertia, stiffness, and damping matrices for each experiment. Then, data preprocessing was carried out to select the most significant variables using different criteria, reducing the seventeen initial variables to only three. Finally, the damping ratio values were calculated (predicted) using automatic regression tools. In particular, five-fold cross-validation was used to obtain a more generalized model and to assess the forecasting performance. The results show a promising methodology capable of calculating and predicting control parameters for robotic manipulation tasks.