Abstract:On the basis of linear regression model, considering the measurement errors of independent variables and dependent variables at the same time, this paper first unifies many models to be selected into the linear regression model with constraints, adopts the hypothesis testing theory with multiple alternative hypotheses, and then constructs the hypothesis testing statistics with Lagrange multipliers. We propose the optimum selection algorithm of the linear regression model. The experimental results show that the proposed algorithm can obtain the optimum linear regression model, which is in accordance with actual observations and simpler than the improved linear hypothesis method.