A note on the interpretation of the statistical analysis of the $M_{\bullet }-M_G{\sigma }^2$ scaling relation

Abstract

In the context of scaling relations between Supermassive Black Holes and host-galaxy properties, we aim to enhance the comparison between $M_{\bullet }-M_G{\sigma }^2$ and $M_{\bullet }-\sigma$ relations from a statistical point of view. First, it is suggested to take into account the predictive accuracy of the scaling relation, in addition to the classical measures of goodness of fit. Here, prediction accuracy is fairly evaluated according to a leave-one-out cross-validation strategy. Then, we spread more light on the analysis of residuals from the fitted scaling relation, in order to provide more useful information on the role played by the different variables in their correlation with the black hole mass. The findings from six samples are discussed.

Accepted for publication in Astrophysics and Space Science

References in corpus (12)

• First M87 Event Horizon Telescope Results. VI. The Shadow and Mass of the Central Black Hole
• Some Aspects of Measurement Error in Linear Regression of Astronomical Data
• Unification of the Fundamental Plane and Super-Massive Black Holes Masses
• The luminosities, sizes and velocity dispersions of Brightest Cluster Galaxies: Implications for formation history
• An Observed Fundamental Plane Relation for Supermassive Black Holes
• A Theoretical Interpretation of the Black Hole Fundamental Plane
• Host Galaxy Bulge Predictors of Supermassive Black Hole Mass
• Black hole scaling relations of active and quiescent galaxies: Addressing selection effects and constraining virial factors
• Selection bias in dynamically-measured super-massive black hole samples: dynamical masses and dependence on Sérsic index
• Relation Between Globular Clusters and Supermassive Black Holes in Ellipticals as a Manifestation of the Black Hole Fundamental Plane
• Improved tests on the relationship between the kinetic energy of galaxies and the mass of their central black holes
• A study of the scaling relation $M_{\bullet }\propto R_e{\sigma }^3$ for supermassive black holes and an update of the corresponding theoretical model