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 estimated as:

$\log(y) = f(X) + \mathrm{er}$

then, the level variable is given by:

$y = \exp(f(X))\exp(\mathrm{er}).$