Smearing retransformation

The Smearing retransformation is used in regression analysis, after estimating the logarithm of a variable. Estimating the logarithm of a variable instead of the variable itself is a common technique to more closely approximate normality. In order to retransform the variable back to level from log, the Smearing retransformation is used. If the log-transformed variable y is normally distributed with mean

$f(X)$ and variance ${\sigma }^2$

then, the expected value of y is given by:

$y=\exp (f(X))\exp (\frac{1}{2}{\sigma }^2).$