  Given the significant advancement in Bayesian inference of nuclear Equation
of State (EOS) from gravitational wave and X-ray observations of neutron stars
(NSs), especially since GW170817, is there a data-driven and robust empirical
formula for the radius $R_{1.4}$ of canonical NSs in terms of the
characteristic EOS parameters (features)? What is the single most important but
currently poorly known EOS parameter for determining the $R_{1.4}$? We study
these questions by extending the traditional Bayesian analysis which normally
ends at presenting the marginalized posterior probability distribution
functions (PDFs) of individual EOS parameters and their correlations (or
sometimes only the Pearson correlation coefficients which are only reliably
useful when the variables are linearly correlated while they are actually often
not). Using three regression model-building methodologies: bidirectional
step-wise feature selection, Least Absolute Shrinkage Selection Operator
(LASSO) regression, and neural network regression on a large set of posterior
EOSs and the corresponding $R_{1.4}$ values inferred from earlier comprehensive
Bayesian analyses of NS observational data, we systematically and rigorously
develop the most probable $R_{1.4}$ formulas with varying statistical accuracy
and technical complexity. The most important EOS parameters for determining
$R_{1.4}$ are found consistently in each of the feature/model selection
processes to be (in order of decreasing importance): curvature $K_{sym}$, slope
$L$, skewness $J_{sym}$ of nuclear symmetry energy, skewness $J_{0}$,
incompressibility $K_{0}$ of symmetric nuclear matter, and the magnitude
$E_{sym} (\rho_0)$ of symmetry energy at the saturation density $\rho_0$ of
nuclear matter.
