Errors-in-Variables Regression for CER Development

Regression techniques used to statistically derive cost estimating relationships (CERs) have traditionally been limited to curve fitting of vectors of discrete dependent variables (cost) with vectors of discrete independent variables (cost drivers). The independent variables on which CERs are based are typically assumed to be discrete and non-random in nature. That is one of the primary assumptions underlying the classical least-squares linear regression process (“ordinary least squares” or OLS). However, uncertainty in the dependent and independent variables can arise as a result of the data collection and normalization process, and in such cases, considering the independent as well as the dependent variables to be random variables may be a more realistic assumption. Errors-in-variables (EIV) regression techniques can be used to find appropriate CERs under the assumption that there may be errors in either the dependent or independent variables or even when both are random variables. This technique is applicable to any regression problem where there is uncertainty in some or all of the data. This article provides an introduction to the application of EIV regression to CER development. First, it provides a history and description of EIV. Next, it provides insight into the sources of uncertainty in data used to develop CERs. It also offers a description of some suitable EIV regression techniques and demonstrates one of these techniques using an EIV regression example. Finally, the article discusses other potential applications of EIV regression in the costestimating context.