关于$M_{\bullet}-M_{G}σ^2$标度关系统计分析的一个注记
A note on the interpretation of the statistical analysis of the $M_{\bullet}-M_{G}σ^2$ scaling relation
摘要：
在超大质量黑洞和宿主星系性质之间的标度关系的背景下，我们的目标是从统计的角度加强$M_{\bullet} - M_{G}σ^2$和$M_{\bullet} - σ$关系之间的比较。首先，建议除了考虑经典的拟合优度测量外，还考虑标度关系的预测精度。在这里，预测准确性是根据留一交叉验证策略公平评估的。然后，我们传播更多的光从拟合的标度关系的残差的分析，以提供更多有用的信息所扮演的角色，由不同的变量在其与黑洞质量的相关性。从六个样本的结果进行了讨论。
英文摘要：
In the context of scaling relations between Supermassive Black Holes and host-galaxy properties, we aim to enhance the comparison between $M_{\bullet} - M_{G}σ^2$ and $M_{\bullet} - σ$ 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.
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