The exact location of the \gamma -ray emitting region in blazars is still controversial . In order to attack this problem we present first results of a cross-correlation analysis between radio ( 11 cm to 0.8 mm wavelength , F-GAMMA program ) and \gamma -ray ( 0.1–300 GeV ) \sim 3.5 year light curves of 54 Fermi -bright blazars . We perform a source stacking analysis and estimate significances and chance correlations using mixed source correlations . Our results reveal : ( i ) the first highly significant multi-band radio and \gamma -ray correlations ( radio lagging \gamma rays ) when averaging over the whole sample , ( ii ) average time delays ( source frame : 76 \pm 23 to 7 \pm 9 days ) , systematically decreasing from cm to mm/sub-mm bands with a frequency dependence \tau _ { \mathrm { r, \gamma } } ( \nu ) \propto \nu ^ { -1 } , in good agreement with jet opacity dominated by synchrotron self-absorption , ( iii ) a bulk \gamma -ray production region typically located within/upstream of the 3 mm core region ( \tau _ { \mathrm { 3 mm, \gamma } } = 12 \pm 8 days ) , ( iv ) mean distances between the region of \gamma -ray peak emission and the radio “ \tau = 1 photosphere ” decreasing from 9.8 \pm 3.0 pc ( 11 cm ) to 0.9 \pm 1.1 pc ( 2 mm ) and 1.4 \pm 0.8 pc ( 0.8 mm ) , ( v ) 3 mm/ \gamma -ray correlations in 9 individual sources at a significance level where one is expected by chance ( probability : 4 \times 10 ^ { -6 } ) , ( vi ) opacity and “ time lag core shift ” estimates for quasar 3C 454.3 providing a lower limit for the distance of the bulk \gamma -ray production region from the supermassive black hole ( SMBH ) of \sim 0.8–1.6 pc , i.e . at the outer edge of the Broad Line Region ( BLR ) or beyond . A 3 mm \tau = 1 surface at \sim 2–3 pc from the jet-base ( i.e . well outside the “ canonical BLR ” ) finally suggests that BLR material extends to several pc distances from the SMBH .