An analysis of the radio and X-ray luminosities , along with black hole masses has led to a relationship , the fundamental plane of black hole activity , where logL _ { R } = 0.60logL _ { X } + 0.78logM _ { BH } .
We show that this same relationship can be obtained by using upper limit data or by randomizing the radio fluxes .
In those cases , the relationship arises because one is effectively plotting distance vs distance in a flux-limited sample of objects .
To correctly establish a relationship between L _ { R } , L _ { X } , and M _ { BH } , one would need to analyze a volume-limited sample of objects .

The distance effect can be removed from the sample , where a relationship between L _ { R } /L _ { X } and M _ { BH } is found , showing that the L _ { R } rises more quickly than L _ { X } with increasing M _ { BH } .
However , until a well-define sample is used , it is unclear the degree to which this relationship is influenced by the sample-selection .