  Aims:We introduce analytical response functions and their main properties as
an important diagnostic tool that help understand Stokes profile formation
physics and the meaning of well-known behaviors of standard inversion codes of
the radiative transfer equation often used to measure solar magnetic fields.
Methods: A Milne-Eddington model atmosphere is used as an example where
response functions are analytical. A sample spectral line has been chosen to
show the main qualitative properties. Results: We show that analytic response
functions readily provide explanations for various well-known behaviors of
spectral lines, such as the sensitivity of visible lines to weak magnetic
fields or the trade-offs often detected in inversion codes between the
Milne-Eddington thermodynamic parameters. We also show that response functions
are helpful in selecting sample wavelengths optimized for specific parameter
diagnostics.
