Coefficients of three regressions for the effect of the magnitude of the median forecast on expected scores.

The first regression was log[WIS(F, y)] = α + β × log[median(F)], where F is the predictive distribution and y the observed value. The second one was WIS(Flog, log y) = αlog + βlog ⋅ log (median(F)), where Flog is the predictive distribution for log y. The third one was where is the predictive distribution for .