Experimentation, Validation, and Uncertainty Analysis for Engineers, 4th Edition

8THE UNCERTAINTY ASSOCIATED WITH THE USE OF REGRESSIONS

As experimentalists we usually wish to obtain and report mathematical expressions to represent experimental results once they have been obtained. An equation is a much more compact representation of the data than tabular listings or even graphic representations, and it allows us to interpolate between the discrete data points. Also, as users of experimental information—values of properties are a prime example—we often use mathematical expressions that are regressions based on experimental data. Information that should be included with the regression expressions is the uncertainty in the regression output variable due to the uncertainties in the original data upon which the regression is based. This uncertainty effect propagated from the data uncertainties has rarely been reported in the past—the classical regression “uncertainty” does not use the uncertainties in the data as inputs, so does not include these effects. It is instead more of a statement of how well the chosen regression expression models the data.

In this chapter we present methodology that allows determination of the uncertainty associated with the use of the regression due to the uncertainties in the data upon which the regression is based. The error introduced by choice of an inappropriate regression model is not included in the methods discussed in this chapter. It is assumed in the techniques presented that the correct model is being used.

The approach ...