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What can we expect to happen to R-squared and adjusted R-squared after including an additional explanatory variable to a regression?

What can we expect to happen to R-squared and adjusted R-squared after including an additional explanatory variable to a regression?

O Both R-squared and adjusted R-squared will increase.

O Both R-squared and adjusted R-squared will decrease.

O R-squared will decrease but adjusted R-squared will increase.

O R-squared will increase but adjusted R-squared will decrease.

O More information is needed to answer.

Solutions

Expert Solution

R-squared will increase but adjusted R-squared will decrease

 

Explanation:

Adjusted R2 also indicates how well terms fit a curve or line, but adjusts for the number of terms in a model. If you add more and more useless variables to a model, adjusted r-squared will decrease. If you add more useful variables, adjusted r-squared will increase. Adjusted R2 will always be less than or equal to R2.

R-squared will increase but adjusted R-squared will decrease

Junaid answered 2 years ago
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