High-temperature superconductivity occurs in strongly correlated materials
such as copper oxides and iron-based superconductors. Numerous experimental and
theoretical works have been done to identify the key parameters that induce
high-temperature superconductivity. However, the key parameters governing the
high-temperature superconductivity remain still unclear, which hamper the
prediction of superconducting critical temperatures ($T_\text{c}$s) of strongly
correlated materials. Here by using data-science techniques, we clarified how
the microscopic parameters in the $ab$ $initio$ effective Hamiltonians
correlate with the experimental $T_\text{c}$s in iron-based superconductors. We
showed that a combination of microscopic parameters can characterize the
compound-dependence of $T_\text{c}$ using the principal component analysis. We
also constructed a linear regression model that reproduces the experimental
$T_\text{c}$ from the microscopic parameters. Based on the regression model, we
showed a way for increasing $T_\text{c}$ by changing the lattice parameters.
The developed methodology opens a new field of materials informatics for
strongly correlated electron systems.