= Gaussian log-response model
{c}
{title2=$\log Y=\eta+\varepsilon$}
For a positive response, the model $\log Y=\eta+\varepsilon$ with $\varepsilon\sim N(0,\sigma^2)$ gives conditional <median> $e^\eta$ and conditional mean $e^{\eta+\sigma^2/2}$. The latter follows from the <moment-generating function> of a <normal distribution>. Additive <factor> effects in $\eta$ become multiplicative effects on these response summaries. Its constant log-scale <variance> corresponds to original-scale <variance> proportional to the square of the mean; direct exponentiation of fitted log means incurs <retransformation bias>.
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