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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.

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This study was conducted to better understand total residual chlorine (TRC) dynamics and ambient toxicity in two chlorine‐contaminated streams in eastern Tennessee. The study used stepwise logistic analysis of Ceriodaphnia survival and water quality factors measured in 169 7‐d chronic toxicity tests of water from four sites in one stream to determine the factors significantly affecting the survival. The 7‐d mean concentrations of TRC and a measure of day‐to‐day variation in TRC concentration in each test were included as dominant factors in explaining Ceriodaphnia mortality. The logistic regression model correctly predicted the mortality or survival in individual Ceriodaphnia in 89.9% of the cases and had a low rate of false positives and false negatives. A simpler pass‐or‐fail model, which used a Ceriodaphnia survival criterion of 60%, yielded slightly better results (correctly predicted outcomes, 91.7%). We also measured TRC concentrations in situ by monitoring at two sites in one of the streams and at one site in the other stream. This monitoring showed that TRC concentrations in both streams varied approximately three‐fold in daily cycles, with TRC concentrations at night greater than those during the day. Laboratory and field experiments indicated that the diel cycles in TRC were probably driven by sunlight and stream periphyton. Two key points emerged from this study. First, the analysis show that logistic regression can be used effectively to relate temporally varying chemical conditions to the outcomes of static‐renewal ambient toxicity tests. In some situations, this method of analysis is more appropriate than other methods, such as ANOVA, that there are used to evaluate dose‐response patterns. Second, diel changes in TRC in streams, apparently caused by sunlight and periphyton, can be large and have important implications for predicting the fate and ecological effects of this widespread contaminant.