(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.
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