Regression analysis is undoubtedly an important tool to understand the relationship between one or more explanatory and independent variables of interest. The problem of estimating a generic regression function in a model with normal errors is considered. For this purpose, a novel objective prior for the regression function is proposed, defined as the distribution maximizing entropy (subject to a suitable constraint) based on the Fisher information on the regression function. This prior is called the I-prior. The regression function is then estimated by its posterior mean under the I-prior, and accompanying hyperparameters are estimated via maximum marginal likelihood. Estimation of I-prior models is simple and inference straightforward, while predictive performances are comparative, and often better, to similar leading state-of-the-art models–as will be illustrated by several data examples. Further plans for research in this area are also presented, including variable selection for interaction effects and extending the I-prior methodology to non-Gaussian errors.