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西红柿面 · 2024年05月11日

多重共线性和adjusted R2有关系吗

NO.PZ2023040502000007

问题如下:

Mike is investigating whether any significant relationship exists between a company’s profitability and either of these two characteristics, management turnover and publicly available environmental, social, and governance (ESG) ratings.

He determines that dividend growth is not a linear combination of CEO tenure and ESG rating. He is unclear about how additional independent variables would affect the significance of the regression, so he asks you, “Will both R2 and adjusted R2 automatically increase if I add dividend growth as a third independent variable?”

Your best answer is:

选项:

A.

no for R2 and no for adjusted R2

B.

yes for R2 and no for adjusted R2

C.

yes for R2 and yes for adjusted R2

解释:

When you add an additional independent variable to the regression model, the amount of unexplained variance will decrease, provided the new variable explains any of the previously unexplained variation. This result occurs as long as the new variable is even slightly correlated with the dependent variable.

dividend growth is not a linear combination of CEO tenure and ESG rating,这句话的意思是没有多重共线性,我理解的就是如果没有多重共线性,adjusted R2会上升,但事实上这两者其实并没有关系吗?

1 个答案
已采纳答案

品职助教_七七 · 2024年05月11日

嗨,从没放弃的小努力你好:


1)本题问的是增加一个正常的变量,R方和adjusted R2如何变化。和多重共线性无关;

2)多重共线性的结论是如果有则会导致高的R方。不涉及adjusted R2

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