[R-sig-eco] Estimating Q10

[Dixon, Philip M [STAT]]

Scott and Alan,

The two forms of your regression:
1) Y = a exp(b x),  and
2) log Y = log a + b x

are mathematically the same model if you ignore random variation.  If you include random variation, these are different models for the variance of the observations around the mean.  Carroll and Rupert explore this in the statistical literature (their book on transformations and weighting, and particularly their paper on the difference between three approaches to fit the Michaelis-Menton model).  They call this approach 'transform both sides', which might be a useful search term.

In 1), observations are assumed to have equal variances.
In 2), observations are assumed to have the same coefficient of variation, i.e. variance increases with the predicted value.
Because of this, the estimated regression coefficients will not be the same.  But, you can use plots of predicted values vs residuals to decide which variance assumption is most reasonable for your data.

Philip Dixon