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The $\beta$-decay half-lives of nuclei are sensitive to the values of$Q_{\beta}$. For accurate theoretical predictions, it is essential to developan effective interaction or an energy density functional (EDF) that cansystematically reproduce experimental $Q_{\beta}$ values. The challenge lies inidentifying an appropriate EDF for an accurate $Q_{\beta}$ prediction. Toaddress this, we focus on the bulk properties of nuclei that have correlationswith $Q_{\beta}$. The primary objective of this study is to determine whichnuclear bulk properties are sensitive to $Q_{\beta}$, providing information onthe key nuclear characteristics that influence $\beta$-decay calculations. Weemploy the Skyrme energy-density functionals to find correlations between$Q_{\beta}$ and the nuclear bulk properties, assuming spherical symmetry. Using$42$ different Skyrme EDFs, we analyze these correlations by evaluating Pearsonlinear coefficients, focusing particularly on the relationship between$Q_{\beta}$ and various nuclear properties. We found that the symmetry energyat low densities shows a correlation with the $Q_{\beta}$ value. In particular,this correlation becomes stronger for functionals with an effective mass closeto $1$. However, as the nuclear density increases, the correlation weakens.From our analysis, we found that a symmetry energy of $32.8\pm0.7$~MeV andeffective mass of $m^{*}/m\ge0.75$ at the saturation density is the most likelyto systematically reproduce the experimental data of $Q_{\beta}$systematically.

Correlations of $Q_{\beta}$-values with symmetry energy and effective mass studied within Skyrme energy--density functionals