问题如下:
If independent variables are added to the model, what’s the impact on R² and adjusted R² ?
选项:
A. Both of them will increase.
B. R² will increase and adjusted R² may decrease.
C. Both of them will decrease.
解释:
B is correct.
考点: R-squared and adjusted R-squared.
解析: 当自变量的数量增加时,R²都会增加。因为多增加的变量X或多或少都会对因变量Y有一些解释(蝴蝶效应),但是对因变量的解释力度可能不会很大。所以只有当新增加变量对Y的解释力度很强的时候,adjusted R²会增加。但当新增加的自变量对模型的贡献很低时,adjusted R²就会减小。
对答案B无异议,但是其实答案A是否也存在可能性?