In this paper, a new process to deal with measurement error is proposed using smoothing, regression, and model selection. The main objectives of this research are to construct a theoretically reliable process to deal with the measurement errors and to validate the process with a case study for refractive index estimation of water. The proposed process for measurement error treatment consists of (1) smoothing of spiky fluctuation, (2) integration of multiple measurements into a single prediction model with statistical regression, and (3) physics-based model selection. The first and third processes enhance the nominal accuracy, and the second process improves the precision of the estimation. In particular, a methodology for intensive local smoothing with a new criterion is proposed for physically unreasonable spikes that cannot be smoothed enough with existing criteria. Before applying all the proposed processes to refractive index estimation of water, three candidate models of the refractive index are generated according to their physics-based possibility. The generated models are tested through the proposed processes, and a final model is selected according to the principle of Occam's razor. The proposed process results in much improved estimation of the refractive index of water by reducing the estimation error from 3.90% to 1.95% of absolute error. Through this study, a useful methodology to deal with measurement errors is successfully established and it can be also applied to problems with similar type of measurement data.