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:

$log(y)\; =\; f(X)\; +\; er$

then, the level variable is given by:

$y\; =\; exp(f(X))exp(er).$