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We present a multi-variable regression analysis to several observablequantities for a sample of 15 gamma-ray bursts (GRBs). The observables used inthe analysis includes the isotropic gamma-ray energy (E_{gamma,iso}), the peakenergy of the nu F_nu spectrum in the rest frame (E_p'), and the rest framebreak time of the optical afterglow light curves(t_b'). A strong dependence ofE_{gamma, iso on E_p' and t_b' is derived. We also extend the analysis to theisotropic afterglow energies in the X-ray and the optical bands, respectively,and find that they are essentially not correlated with E_p' and t_b'. Regardingthe E_{gamma, iso(E_p', t_b') relationship as a luminosity indicator, weexplore the possible constraints on the cosmological parameters using the GRBsample. Our results indicate 0.13<omega_M<0.49 and 0.50<Omega_Lambda<0.85 for aflat Universe. The decelerating factor and its cosmological evolution, and thetransition redshift are also investigated. Through Monte Carlo simulations, wefind that the GRB sample satisfying our relationship observationally tends tobe a soft and bright one, and that the contraints on the cosmologicalparameters can be much improved either by the enlargement of the sample size orby the increase of the observational precision. Furthermore, the detections ofa few high redshift GRBs satisfying the correlation could greatly tighten theconstraints (abridged).Comment: 10 pages (emulateapj) plus 12 figures, accepted for publication in  Ap

Model‐independent Multivariable Gamma‐Ray Burst Luminosity Indicator and Its Possible Cosmological Implications