A Practical Suggestion for Log-Linear Workers Compensation Cost Models

It is standard practice to use log-linear and log-log regression models in the analysis of workers compensation claim costs. While useful for the investigation of proportional cost relationships, those transformed models are not well suited for predicting individual or even average claim costs. There is, however, enormous potential for using regression equations as a computational device for generating tabular reserves and for benchmarking select sets for claim costs. This paper suggests that changing the assigned weights of observations in the determination of the logged cost model can improve its predicted values for conversion back to a dollar scale. The derivation of a specific reweighing formula is motivated from the basic data fitting geometry of OLS regression. The technique is tested in a simulation and on a large database of actual workers compensation lost time claims. Both show a marked improvement in the claim cost estimates determined from the modified regression equations.