Modeling the interrelationships between the input parameters and outputs (responses) in any machining processes is essential to understand the process behavior and material removal mechanism. The developed models can also act as effective prediction tools in envisaging the tentative values of the responses for given sets of input parameters. In this paper, the application potentialities of nine different regression models, such as linear regression (LR), polynomial regression (PR), support vector regression (SVR), principal component regression (PCR), quantile regression, median regression, ridge regression, lasso regression and elastic net regression are explored in accurately predicting response values during turning and drilling operations of composite materials. Their prediction performance is also contrasted using four statistical metrics, i.e., mean absolute percentage error, root mean squared percentage error, root mean squared logarithmic error and root relative squared error. Based on the lower values of those metrics and Friedman rank and aligned rank tests, SVR emerges out as the best performing model, whereas the prediction performance of median regression is worst. The results of the Wilcoxon test based on the drilling dataset identify the existence of statistically significant differences between the performances of LR and PCR, and PR and median regression models.