Signed efficiency measures with relevant nonlinear integrals can be used to treat data that have strong interaction among contributions from various attributes towards a certain objective attribute. The Choquet integral is the most common nonlinear integral. The nonlinear multiregression based on the Choquet integral can well describe the nonlinear relation how the objective attribute depends on the predictive attributes. This research is to extend the nonlinear multiregression model from using a linear core to adopting a quadratic core in the Choquet integral. It can describe some more complex interaction among attributes and, therefore, can significantly improve the accuracy of nonlinear multiregression. The unknown parameters of the model involve the coefficients in the quadratic core and the values of the signed efficiency measure. They should be optimally determined via a genetic algorithm based on the given data. The results of the new model are compared with that of the linear core as well as the classic linear multiregression that can be solved by an algebraic method.