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The authors develop an approach for assessing confidence in a parameter estimate when the order of the model is clearly less than that of the system being modeled. The approach does not require a parameter to have a single value located within a region of confidence. Instead, the parameter value is allowed to vary over the data set in such a way as to provide a good fit to the entire data set. The approach is applied to the estimation of the resistance of a respiratory system in which a simple model is fitted to measurements of tracheal pressure and flow by recursive multiple linear regression. The values of resistance required to achieve a good fit are represented as a modified histogram in which the contribution of a particular resistance value to the histogram is weighted by the amount of information used in its determination. The approach provides parameter frequency distribution functions that convey the degree of confidence one may have in the parameter, while not being based on erroneous statistical assumptions.