Research on the Optimization of English Teaching Mode and Personalized Learning Path in Colleges and Universities Based on Big Data Regression Analysis

English is a very important basic course in higher education, and how its teaching quality is directly related to the quality of talents in the new century as well as the practical working ability of talents. Taking the English teaching mode in colleges and universities as the research object, the ordered multicategorical logistic regression model is used to analyze the influencing factors of English teaching mode in colleges and universities. Then the English teaching mode in the background of information technology support is proposed to integrate the two English teaching modes, modern and traditional, and a learner state model is constructed based on the online learning behavior of learners, which is mainly used to assess the learning state of learners, and on the basis of which an accurate personalized learning path planning based on the state of learners is designed to ultimately realize the optimization of English teaching mode in colleges and universities. The results show that learner factors, curriculum factors and environmental factors have a significant effect on the college English teaching mode and the test effect of the model is more satisfactory, indicating that the ordered multicategorical logistic regression model can well represent the college English teaching mode. In addition, five complete learning paths were obtained, and the paths ks6→ks11 and ks4→ks11 had the highest selection ratio.