@article {Gregoire:2008-10-01T00:00:00:0015-749X:597,
author = "Gregoire, Timothy G. and Lin, Qi Feng and Boudreau, Johnathan and Nelson, Ross",
title = "Regression Estimation Following the Square-Root Transformation of the Response",
journal = "Forest Science",
volume = "54",
number = "6",
year = "2008-10-01T00:00:00",
abstract = "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 transformation, such that *Y* rather than *Y* ^{2} 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: *Ê*[*Y* ^{2}|*x* _{∗}] = _{ y|x∗} ^{2} + − *V*(_{ y|x∗} ^{2}). Its performance is compared against that of two biased estimators: *Ê*_{b} [*Y* ^{2}|*x* _{∗}] = _{ y|x∗} ^{2} + and *Ê*_{p} [*Y* ^{2}|*x* _{∗}] = _{ y|x∗} ^{2}. 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.",
pages = "597-606",
url = "http://www.ingentaconnect.com/content/saf/fs/2008/00000054/00000006/art00004",
keyword = "nonlinearity, back-transformation bias"
}