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tokens: where A and B are the regression coefficients (intercept and slope), and ε is the intrinsic random scatter about the regression. and are the 1σ uncertainty of L 6 and L X , respectively. We conducted a Markov chain Monte Carlo (MCMC) simulation, where the Markov chain is created using the Metropolis–Hastings algorithm. We assumed uniform prior distributions for the regression parameters, and estimated the linear correlation coefficient between and . The best-fitting regression parameters and correlation coefficient with uncertainties are provided by calculating the mean and standard deviation from the posterior probability distributions of the model parameters with 10 000 iterations from the MCMC sampler (see also Mateos et al. 2015 ; Chen et al. 2017 ). The resultant linear relation is as follows: and the correlation coefficient is r = 0.84 ± 0.01, confirming again a tight correlation between L 6 and L X for our type 1 AGN sample. This linear L 6 – L X correlation is roughly consistent with that reported by Mateos et al. ( 2015 ) and Chen et al. ( 2017 ) in the low-luminosity region for log L X 44.5−45. We also performed a partial correlation analysis between log L 6 and log L X , with the correlation component due to redshift removed. The resultant partial correlation coefficient is 0.61, which is still indicating a tight correlation. We conclude that our type 1 AGN sample with RASS allows us to see a tight correlation for a wide luminosity range. However, it cannot explain the L 6 – L X relations of hyper-luminous quasars selected from the SDSS/WISE (e.g. Hot DOGs, ERQs, and WISSH quasars); these objects show a negative offset with respect to the linear relation. To describe this non-linear behaviour seen over a wide luminosity range, a luminosity-dependent relation would be required, as Stern ( 2015 ) and Chen et al. ( 2017 ) suggested. 3.2 Dependence of <italic>L</italic><sub>X</sub>/<italic>L</italic><sub>6</sub> on Eddington ratio In Section 3.1 , we confirmed that hyper-luminous quasars tend to be ‘X-ray weak’ with respect to their MIR luminosities. Some possibilities were suggested in previous works, as the origin of this X-ray deficit in hyper-luminous quasars. For example, Chen et al. ( 2017 ) reported that the different L 6 – L X relations provided in the literature were due to the different X-ray flux limits. Other possibilities to explain the deficit may be a luminosity-dependent covering factor ( C f ) and may be a dependence of the MIR to X-ray luminosity ratio on hydrogen column density ( N H ). However, Martocchia et al. ( 2017 ) concluded that the observed X-ray deficit in hyper-luminous quasars cannot be explained by a luminosity-dependent C f (see also Ichikawa et al. 2017 ), and Mateos et al. ( 2015 ) found no clear dependence of the MIR to X-ray luminosity ratio on N H , in AGNs with log N H 24 cm −2 (see also Lutz et al. 2004 ; Gandhi et al. 2009 ; Ichikawa et al. 2012 ). As described in Section 1 , the X-ray emission