There are a lot of environmental protection musicals and dances in public entertainment life to support the concept of environmental protection and to entice people to support the cause of environmental protection. As we all know, in a musical performance, the distance between the audience and the actors, the design of the stage environment, the training of the actors, the costumes of the actors, the makeup of the actors, and the musical accompaniment will all have more or less influence on the stage performance effects. In order to make environmental protection music and dance dramas profoundly meaningful to social production and human activities, it is especially important to analyze the stage performance of such music and dance dramas. The analysis of stage performance effects is not only beneficial to making the ideas spread by the music and dance drama penetrate into people's hearts but can also provide guiding suggestions for the production of music and dance drama. Therefore, this paper proposes a linear regression algorithm based on artificial intelligence to deeply explore and analyze the influence of the above six factors on the stage performance effects of environmental protection music and dance drama. In our method, first we preprocess the data collected by classification to remove the odd values from the data so that the various types of data conform to a normal distribution. Secondly, we obtained linear fit plots of the six factors with the stage performance effect scores by using a linear regression algorithm to deeply analyze the correlation between various types of data and the stage performance effect scores. Finally, through numerical calculations, we found that the distance between the audience and the actors, the training of the actors, and the musical accompaniment have a greater influence on the performance effect of the musical cabaret in the environmental protection category. Meanwhile, the costumes of the actors, the makeup of the actors, and the design of the stage environment have less influence on the performance effect of the musical cabaret. Therefore, in the production and performance of environmental protection music and dance dramas, producers and performers should pay more attention to the distance between the audience and the actors, the design of musical accompaniment, and the training of actors. To sum up, this paper has made a scientific, detailed, and reasonable analysis of the performance effect of environmental protection music and dance dramas on stage, contributing to the dissemination of environmental protection ideas.