It is well known that knowledge is the source of modern economic growth, but the roles of library and information services on sustainable economic growth had not been well established. Thus, a case investigation was designed to identify the roles of library services in public libraries with the population, education, and income as a comparison on sustainable regional economic development. Such an investigation was based on organically combining correlation calculation, principal component calculation, and linear regression calculation. Results prove that some library services in public libraries have the highest contribution to the first principal component. It also demonstrates that the first principal component explains 85.0%, 95.0%, and 64.2% of the variation in the normalized gross regional products of Jiangsu Province, Hunan Province, and Gansu Province in China, respectively. Library services in public libraries, the population, education, and income appear to have a similarly important effect on sustainable regional development. Component score coefficients and linear relationships between the principal components and regional gross regional product can be used together to investigate the relationship between library services and sustainable economic growth. The proposed method provides new ideas for evaluating the roles of library services in sustainable economic growth.