Logarithmic Transformations in Regression: Do You Transform Back Correctly?

Abstract The logarithmic transformation is often used in regression analysis for a variety of purposes such as the linearization of a nonlinear relationship between two or more variables. We have noticed that when this transformation is applied to the response variable, the computation of the point estimate of the conditional mean of the original response variable is often incorrect. Although the correct procedure has long been known in the scientific community and is well documented, an incorrect or misleading procedure is used in many business statistics textbooks. This incorrect procedure results in errors that can be quite significant. Our article uses a real-data business example which, in the context of making a decision about an advertising charge for a magazine, illustrates the correct procedure. This example also provides a sense of the magnitude of the error that would result if the incorrect procedure were used. The six percent error in our example could be substantially higher for other applications.