A new method for measuring the hardness-intensity correlation (HIC) present in gamma-ray bursts (GRB) is developed. This method is used to measure the HIC for 100 single-peak gamma-ray bursts, 17 with known redshifts. The HIC is thus shown to be a consequence of energy-dependent lag times between hard and soft photons. Parameters derived from time profile fits using a modified double sigmoidal function are used to calculate a new set of lag time parameters for bursts, and these parameters are analyzed statistically to look for correlations with intrinsic GRB properties. This analysis shows that GRB red shift is related to lag times between hard and soft photons and that, to within 65% accuracy, GRB redshift can be predicted by the equation: z = 2.49 - 0.131(dpeak) - 0.473(MADS_dpeak)+ 0.143(decay_lag)