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

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

then, the expected value of y is given by:

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