多重共线性和adjusted R2有关系吗

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.