  Markarian 421 (Mrk 421) is a high-synchrotron-peaked blazar showing
relentless variability across the electromagnetic spectrum from radio to
gamma-rays. We use over 7-years of radio and GeV observations to study the
correlation and connected variability in radio and GeV bands. Radio data was
obtained in a 15GHz band by the OVRO 40-m radio telescope, and GeV data is from
Fermi Large Area Telescope. To determine the location of the gamma-ray emission
regions in Mrk 421 we correlate GeV and radio light curves. We found that GeV
light curve varies independently and accurately leads the variations observed
in radio. Using a fast-rise-slow-decay profile derived for shock propagation
within a conical jet, we manage to reproduce the radio light curve from GeV
variations. The profile rise time is comparable with the Fermi-LAT binning the
decay time is about 7.6 days. The best-fit value for the response profile also
features a 44 days delay between the GeV and radio, which is compatible with
the wide lag range obtained from the correlation. Such a delay corresponds to
$10^{17}$ cm/c, which is comparable with the apparent light crossing time of
the Mrk 421 radio core. Generally, the observed variability matches the
predictions of the leptonic models and suggests that the physical conditions
vary in the jet. The emitting region moving downstream the jet, while the
environment becomes first transparent to gamma rays and later to the radio.
