Publication

In a variety of regression Situations, there is interest in predicting the Value of Y(2), yet it is useful to model it using a square root trans formation, 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 42 in detail. All unbiased estimator is presented: (E) over cap [Y(2)/x(*)] = (mu) over cap (2)(y/x*) + (sigma) over cap - (V) over cap((mu) over cap (2)(y/x*)). Its performance is compared against that of two biased estimators: (E) over cap (b)[Y(2)/x(*)] = (mu) over cap (2)(y/x*) + (sigma) over cap and (E) over cap [Y(2)/x(*)] = (mu) over cap (2)(y/x*). 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, FOR. Sci. 54(6):597-606.