The goal of this study is to explore time-resolved spectral-luminosity correlation by doing time-resolved analysis of GRB sample with certain characteristics (pulse-like lightcurve and known redshift), detected by Fermi GBM instrument, via a hierarchical Bayesian model. Correlation study could posibly put some constraints on physics of prompt emission of gamma-ray burst phenomena (GRB), and also show if there is universality in this correlation. Many theoretical models have been presented in the literature in order to explain the wide variety of observations, but each model has some advantages as well as drawbacks, and the use of the phenomenological correlations can boost the understanding of the mechanism responsible for the prompt emission. If the universality of the correlation is shown, it could be used as a redshift estimator for GRBs. Results of hierarchical modeling are parameters and Nrest, which represent slope and intercept of spectral-luminosity correlation, respectively. Results showed clustering of values around 2, which indicates that the underlying emission mechanism could be synchrotron radiation. Results of hierarchical modeling also showed clustering of Nrest values around value of 1051 erg/s, but the scatter in distribution indicates that GRBs do not possess common rest-frame normalization, thus eliminating use of correlation as a cosmological tool.