  The radio emission in radio loud quasars originates in a jet carrying
relativistic electrons. In radio quiet quasars (RQQs) the relative radio
emission is ~10^3 times weaker, and its origin is not established yet. We show
here that there is a strong correlation between the radio luminosity (L_R) and
X-ray luminosity (L_X) with L_R~10^-5L_X, for the radio quiet Palomar-Green
(PG) quasar sample. The sample is optically selected, with nearly complete
radio and X-ray detections, and thus this correlation cannot be due to direct
selection biases. The PG quasars lie on an extension of a similar correlation
noted by Panessa et al., for a small sample of nearby low luminosity type 1
AGN. A remarkably similar correlation, known as the Guedel-Benz relation, where
L_R/L_X~10^-5, holds for coronally active stars. The Guedel-Benz relation,
together with correlated stellar X-ray and radio variability, implies that the
coronae are magnetically heated. We therefore raise the possibility that AGN
coronae are also magnetically heated, and that the radio emission in RQQ also
originates in coronal activity. If correct, then RQQ should generally display
compact flat cores at a few GHz due to synchrotron self-absorption, while at a
few hundred GHz we should be able to see directly the X-ray emitting corona,
and relatively rapid and large amplitude variability, correlated with the X-ray
variability, is likely to be seen. We also discuss possible evidence that the
radio and X-ray emission in ultra luminous X-ray sources and Galactic black
holes may be of coronal origin as well.
