4.3 The Coefficient of Determination
为评估模型,我们可以使用以下方法:
(1) the total variation in the observed values of the response variable(观察值中的y)
(2) the amount of variation in the observed values of the response variable that is explained by the regression.(用回归估计出来的y)
引入以下三个评估参数:
对应图是:
评判标准:
The coeffificient of determination, r 2, always lies between 0 and 1. A value of r 2 near 0 suggests that the regression equation is not very useful for making predictions,whereas a value of r 2 near 1 suggests that the regression equation is quite useful for making predictions
三者关系为:
继而得到coeffificient of determination的另一种表达:
并组合前文所述的Sx x &Sx y & Syy(为了计算方便),可以得到:
推导:
因为
所以:
为了便于计算: