  The two prevailing planet formation scenarios, core-accretion and disk
instability, predict distinct planetary mass-metallicity relations. Yet, the
detection of this trend remains challenging due to inadequate data on planet
atmosphere abundance and inhomogeneities in both planet and host stellar
abundance measurements. Here we analyze high-resolution spectra for the host
stars of 19 transiting exoplanets to derive the C, O, Na, S, and K abundances,
including planetary types from cool mini-Neptunes to hot Jupiters ($T_{\rm eq}\
\sim$ 300 - 2700 K; planet radius $\sim$ 0.1 - 2 $R_{\rm J}$). Our Monte Carlo
simulations suggest that the current dataset, updated based on Welbanks et al.
2019, is unable to distinguish between a linear relation and an independent
distribution model for the abundance-mass correlation for water, Na, or K. To
detect a trend with strong evidence (Bayes factor > 10) at the 2$\sigma$
confidence interval, we recommend a minimum sample of 58 planets with HST
measurements of water abundances coupled with [O/H] of the host stars, or 45
planets at the JWST precision. Coupled with future JWST or ground-based high
resolution data, this well-characterized sample of planets with precise host
star abundances constitute an important ensemble of planets to further probe
the abundance-mass correlation.
