In this paper, we perform an econometric analysis on the benefits of introducing flexibility in the Danish/Nordic regulating power market. The paper investigates the relationships between market power prices and regulation volumes, in order to quantify the effects of flexibility on regulating power prices. Further, we analyze the benefit for various types of flexibility and market objectives, to detect the type of energy flexibility that maximizes the benefits. Results show that if 3.87% of total demand is flexible, the market can reduce the regulation cost by 49% and the regulation volume by 29.4%.