Corrections for Bias in Regression Estimates After Logarithmic Transformation

Abstract

Experience with biological data, such as dimensions of organisms often confirms that .logarithmic transf~rmations should precede the testing of hypotheses ;bout regression relat10ns. 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 (b~le, branches, and leaves) to tree diameter of tulip poplar (Liriodendron tulipifera L.) m Oa~ R1dge, ~ennessee, 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.

Aboveground biomass relationships for mixed ash (Fraxinus excelsior L. and Ulmus glabra Hudson) stands in Eastern Prealps of Friuli Venezia Giulia (Italy)

“…In fact, using equation (9) produces a systematic overestimation of the dependent variable B when converting ln (B) back to the original scale B. Many procedures to correct this difference have been advocated [1,2,16]. In the present study, at first equation (1) was transformed into linear regression equation (Eq.…”

Aboveground biomass in a beech forest and a Scots pine plantation in the Sierra de la Demanda area of northern Spain

“…It is also important to study carbon and nitrogen, both as regards the distribution of these elements within (ie, structural) and among (ie, com-positional) community types since they affect the development processes and pathways of the ecosystem (Ohmann and Grigal, 1985). (Baskerville, 1972;Beauchamp, 1973;Sprugel, 1983) (Canadell et al, 1988;Rapp et al, 1992). (table II), the productivity of the beech trees seem to be greater than that of the pines.…”

The impact of genetics on retail meat value in Australian lamb

“…The log e transformation introduces a systematic bias into the calculations and it is well recognised that a correction factor is required to correct for this bias when back-transforming predictions (Baskerville, 1972;Beauchamp & Olson, 1973;Sprugel, 1983). Hence the correction described by Sprugel (1983) was used when data were back-transformed from log e lean weight to kg lean weight.…”