  The metallicity of exoplanet systems serves as a critical diagnostic of
planet formation mechanisms. Previous studies have demonstrated the
planet-metallicity correlation for large planets ($R_P\ \geq\ 4\ R_E$);
however, a correlation has not been found for smaller planets. With a sample of
406 $Kepler$ Objects of Interest whose stellar properties are determined
spectroscopically, we reveal a universal planet-metallicity correlation: not
only gas-giant planets ($3.9\ R_E\ < R_P\ \leq\ 22.0\ R_E$) but also gas-dwarf
($1.7\ R_E\ < R_P\ \leq\ 3.9\ R_E$) and terrestrial planets ($R_P\ \leq\ 1.7\
R_E$) occur more frequently in metal-rich stars. The planet occurrence rates of
gas-giant planets, gas-dwarf planets, and terrestrial planets are
$9.30^{+5.62}_{-3.04}$, $2.03^{+0.29}_{-0.26}$, and $1.72^{+0.19}_{-0.17}$
times higher for metal-rich stars than for metal-poor stars, respectively.
