Cosmological Distance Scale. Part 12. Confluent Analysis, Rank Inversion, and Lack-of-Fit Tests

The measuring problem of calibrating the cosmological distance scale is considered from the perspective of applicability conditions for regression analysis. The rank inversion and statistical inhomogeneity of information on SN Ia supernovae, used in the works of 1998–1999 and 2004–2007 to detect the “accelerating expansion of the Universe” and as an “extraordinary evidence” of its existence, respectively, are demonstrated to be the reason for the discrepancy and inconsistency of the obtained parametric estimates of the Friedman–Robertson–Walker model. Although the use of lack-of-fit tests for cosmological distance scale models reduces the above negative effects, the fact remains that the cosmological distance scale based on the redshift has neither metric nor ordinal status.