Corrections for Bias in Regression Estimates After Logarithmic Transformation

Experience with biological data, such as dimensions of organisms, often confirms that logarithmic transformations should precede the testing of hypotheses about regression relations. However, estimates also may be needed in terms of untransformed variables. Just taking antilogarithms of values from a log-log regression line or function leads to biased estimates. This note compares corrections for this bias, and includes an example relating mass of tree parts (bole, branches, and leaves) to tree diameter of tulip poplar (Liriodendron tulipifera L.) in Oak Ridge, Tennessee, forests. An Appendix summarizes derivation of exact and approximate unbiased estimators of expected values from log-antilog regression, and of variance around the unbiased regression line.