Regression models are widely used as data-driven methods for predicting a continuous target variable. From a set of input variables, regression models predict a deterministic point value for the target variable. But the deterministic point value prediction is not always sufficient because a target variable value often varies due to diverse sources of uncertainty. For instance, in the fused deposition modeling process, the inconsistent results of replications are associated with natural randomness, environmental condition, and noisy process parameters. The point value estimation is not sufficient to represent the variability in this kind of scenario. Instead of point estimation, the interval prediction of a target variable is more useful in this application. In this paper, linear optimization-based techniques are proposed to predict conservative confidence intervals for linear and polynomial regression models. Two linear optimization models, one for ordinary least squares (OLS) regression and the other for weighted least squares (WLS) regression, are proposed. The proposed methods are implemented on several datasets, including an experimental fused deposition modeling dataset to demonstrate the effectiveness of the proposed methods. The results show that the proposed method is useful for the fused deposition modeling process where the level of uncertainty or the lack of knowledge of uncertainty sources is high. The proposed method can also be leveraged to the Bayesian neural network (BNN), where the optimization techniques for interval prediction will be nonlinear optimization instead of linear optimization.