In this article, I propose a constrained optimization method to revise the panel regression model. This method can be implemented under different settings in both the least squares and maximum likelihood paradigms. In section two, I provide a comprehensive discussion of the methodological problems of the panel regression model. Next, I explain how to revise the panel regression given different scenarios: (1) taking least squares or maximum likelihood assumptions (2) whether to adopt the demeaning-bias correction. Then, I carry out a comparative study in the admissibility of parameter estimates for the current panel regression and various revised models, which is followed by the discussion and conclusion sections.