We have numerically investigated the dependence of pedestal properties such as the pedestal height and the pedestal width on the normalized pressure gradient () in the connection region, . We used an ideal MHD stability code, MISHKA, and the pedestal predictive model, EPED1, to analyze the effect of on the edge stability and predict pedestal structure. Edge stability is affected by because the unstable mode extends radially into the core. Improvement of pedestal properties can be achieved by reducing . Effect of on the edge instability is largest for the intermediate mode n. Larger gradient of Shafranov shift, , also improves the pedestal width and height by stabilizing peeling-ballooning mode (PBM). Our result has been applied to JET hybrid discharges to explain the coupling between core and edge pressure profile in H-mode plasma configuration through and . The extended correlation loop between poloidal beta and the pedestal parameters is presented.