On the basis of linear multiple regression methods such as PLSR and ICR, this paper introduces the kernel function to kernelize these linear multiple statistical regression methods, derives the KPLSR and KICR algorithms, and gives the specific implementation process. Then kernel-based multiple regression methods are applied to analyze the English teaching mode using a cognitive coupling network. According to the students’ learning data under the English teaching mode of cognitive coupling network, then the students’ learning situation and other precise calculations and statistics, so as to truly reflect the student’s learning status, presenting the students’ learning process in need of an urgent solution. Finally, the correlation between students’ multi-sensory learning styles and English performance is analyzed, and the results show that visual, auditory, kinesthetic, experiential, and independent styles all show a significant positive correlation to the total English performance, with correlation coefficients of 0.416, 0.158, 0.349, 0.339, and 0.327, respectively, among which the correlation coefficient of the visual type of perception is the largest.