Regression Estimation Following the Square-Root Transformation of the Response - Timothy G. Gregoire; Qi Feng Lin; Johnathan Boudreau; Ross Nelson (Forest Science, 2008)
In a variety of regression situations, there is interest in predicting the value of Y2, yet it is useful to model it using a square root transformation, such that Y rather than Y2 is regressed on one or more covariates. The back-transformation bias of the square root transformation of the response variable of interest is presented in detail. An unbiased estimator is presented: . Its performance is compared against that of two biased estimators: and . The first two moments of these estimators are derived analytically and verified by means of a simulation study. Both biased estimators have lower mean square errors than the unbiased estimator. An example wherein aboveground biomass is the response variable is presented for illustration.