一元线性回归最重要的统计前提有以下五个：
The five most important statistical prerequisites for univariate linear regression are as follows：

1、因变量与自变量的关系应该是线性的。如果变量间的关系是非线性，但是有单调性，那么可以通过代数操作达成线性。如果是U型曲线，则需要特殊处理。

• The relationship between the dependent and independent variables should be linear. If the relationship between the variables is nonlinear, but has monotonicity, then linearity can be reached through algebraic manipulation. If it is a U-curve, then special treatment is required.

2、 没有非常值，包括一元和二元非常值。

• There are no outliers, including one- and two-dimensional outliers.

3、 因变量残差正态分布。

• The residuals of the dependent variable conform to a normal distribution.

4、 残差与自变量不相关。

• The residuals are not correlated with the independent variables.

5、 在因变量预测值的所有水平上，残差的方差相等。

• The variance of the residuals is equal at all levels of the predicted value of the dependent variable.