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四、各自变量的显著性检验回归方程经显著性检验之后,若线性回归关系显著,只能说明因变量 y 和诸自变量的总体回归效果显著。各自变量对因变量所起的作用通常并不一样,不见得每个自变量对因变量都有显著作用。如果把那些次要的、可有可无的变量剔除掉,而只保留对因变量贡献显著的重要变量,重新建立起较简单的稳定的回归方程,无疑会更有利于对因变量的预测和控制。某个自变量 x_i 的作用不显著,表示回归模型中该变量前的系数β_i 可取值为0,所以检验 x_i 是否显著等价于检验原假设 H_0∶β_i=0。可以证明在这样的原假设下
Significant test of the respective variables After the regression test of the regression equation, if the linear regression is significant, it can only show that the overall regression results of the dependent variable y and the independent variables are significant. The effect of each variable on dependent variables is usually not the same, not every independent variable has a significant effect on dependent variables. If we remove those secondary and optional variables and keep only those important variables that make significant contributions to the dependent variable and rebuild the simpler and stable regression equation, it will undoubtedly be more conducive to the prediction of dependent variables and control. The effect of an independent variable x_i is not significant, indicating that the coefficient β_i in front of the variable in the regression model is 0, so whether x_i is significantly equivalent to test the null hypothesis H_0: β_i = 0. It can be proved under such null hypothesis