The radio emission in radio-loud quasars originates in a jet carrying relativistic electrons. In radio-quiet quasars (RQQs) the relative radio emission is ∼103 times weaker, and its origin is not established yet. We show here that there is a strong correlation between the radio luminosity (LR) and X-ray luminosity (LX) with LR∼ 10−5LX, 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 active galactic nuclei (AGN). A remarkably similar correlation, known as the Güdel–Benz relation, where LR/LX∼ 10−5, holds for coronally active stars. The Güdel–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 ultraluminous X-ray sources and Galactic black holes may be of coronal origin as well.