Linear regression of dependent variable squared & retransformation I have performed linear regression of a dependent variable squared, & my statistics package produced least squares means for each level of categorical variables that I would like in original units. 
There is much research on the retransformation bias when the transformation power is a positive fractional one (i.e. <0 AND <1), though what about when the power is >1 - is there bias & if so how may it be corrected?
 A: In statistics, if $\hat \theta$ is unbiased estimate of $\theta$, $f(\hat\theta)$ is biased estimate of $f(\theta)$, given function $f(\theta)$ is not linear on $\theta$.
In your situation, suppose least squares means ($\hat\theta$) are your unbiased estimate of $\theta$, and you want the estimate of $\sqrt{\theta}$. Because it is not linear function, so $\sqrt{\hat\theta}$ is biased estimate of  $\sqrt{\theta}$.
Let look at the Taylor series:
$$\sqrt\theta = \sqrt{\hat\theta} + \frac 12\hat\theta^{-1/2}(\theta-\hat\theta)-\frac18\hat\theta^{-3/2}(\theta-\hat\theta)^2 +...$$
Take the expectation on right hand side, you will know the unbiased estimate of $\sqrt\theta$. But we have no knowledge on the high order moments of the estimate $\hat\theta$, the approximation is stooped at the second order.
So you can use following ti adjust the biased:
$$\sqrt{\hat\theta} -\frac18\hat\theta^{-3/2}var(\hat\theta)$$
From this estimate, you can say, if your sample size is large such that $var(\hat\theta)$ is very small, and/or $\hat\theta$ is large (far from zero), the effect of second order adjustion is so small such that it is ignorable. 
