  (Abridged) We attempt to infer the accretion mechanism and radiative
processes giving rise to the SEDs of a well-defined optically-selected sample
of LINERs showing a definite detection of broad Halpha emission (LINER 1s). We
construct SEDs for six LINER~1s with simultaneous UV and X-ray fluxes, and we
looked for multiwavelength, radio to X-ray and UV to X-ray, correlations. At a
given X-ray luminosity, the average SED of the six LINER 1s in our sample: (1)
resembles the SED of radio-loud quasars in the radio band, <log R_X>~-2.7, (2)
exhibits a weak UV bump, <alpha_ox>~-1.17+-0.02 with a dispersion sigma=0.01,
and (3) displays a X-ray spectrum similar to radio-quiet quasars. The
bolometric luminosities inferred from the SEDs are extremely faint, at least
two orders of magnitude lower than AGN. The X-ray bolometric correction,
kappa_(2-10 keV), of our sample is lower than in the case of AGN, with a mean
value of 16. We find a strong anticorrelation between the radio loudness
parameter, R_X, and the Eddington ratio for our sample, confirming previous
results. Moreover, we find a positive correlation between the radio luminosity
and the X-ray luminosity which places AGN-powered LINERs, on a radio-power
scale, right between low luminosity Seyferts and low luminosity radio galaxies.
We complement our alpha_ox list with values derived on a well defined sample of
UV-variable LINERs, and establish a strong positive correlation between
alpha_ox (considering negative values) and the Eddington ratio, in contrast to
the correlation found for luminous AGN. Lastly, we tested two different
fundamental planes existing in the literature on our sample, in an attempt to
put constraints on the debated origin of the X-ray emission, "RIAF versus jet".
The results came contradictory with one pointing toward a RIAF-dominated X-ray
emission process and the other pointing toward a jet domination.
