  Radio emission in the brightest radio quasars can be attributed to processes
inherent to SMBHs, while the origins of the radio fluxes in quasars without
radio detections is still uncertain. We investigate the radio-infrared
continuum of LOFAR radio-detected quasars (RDQs) and LOFAR radio-undetected
quasars (RUQs) in the $9.3\:\textrm{deg}^{2}$ NDWFS-Bo\"otes field; RUQs are
quasars that are individually undetected at $\geq5\sigma$ by LOFAR. We used a
median image stacking procedure. This was done in the frequencies of 150 MHz,
325 MHz, 1.4 GHz and 3.0 GHz, and in nine infrared (ir) bands between $8$ and
$500\;\mu\textrm{m}$. The radio and ir photometry allow us to derive the median
spectral energy distributions of RDQs and RUQs in four z-bins between
$0<z<6.15$. The ir star-formation rate (SFR) is compared with two independent
radio-based star-formation (SF) tracers using the far-ir radio correlation
(FIRC) of SF galaxies. We find a good agreement between our radio and ir SFR
measurements and the FIRC predictions. Moreover, we use the FIRC predictions to
establish the contribution due to SMBH accretion to the total radio-luminosity
(RL). We show that SMBH accretion can account for $\sim5-41\%$ of the total RL
in median RUQs, while for median RDQs the contribution is $\sim50-84\%$. This
implies that vigorous SF activity is coeval with SMBH growth in our median
stacked quasars. Furthermore, we investigated the radio-loudness parameter,
$R$. For quasars with $R\geq-4.5$, the RL is consistent with being dominated by
SMBH accretion, while for low RL quasars with $R<-4.5$ the relative
contribution of SF to the radio fluxes increases as the SMBH component becomes
weaker. We also find signatures of negative AGN feedback in the brightest
median RDQs at 150 MHz. Finally, we found that spectral indices of quasars do
not evolve significantly with z, but they become flatter towards lower freqs.
