How can adjusted r squared be negative?
Elliana Molina
Answered question
2022-11-02
Answer & Explanation
Raven Hawkins
Beginner2022-11-03Added 19 answers
, the coefficient of multiple determination, is defined as or,
equivalently, . measures the proportionate reduction in variation of Y, associated with the set of X predictors. will be inflated as more X variables are added. The adjusted was therefore derived, as
If , and you have . If the ratio is close enough to 1, then you can see how the . Can be negative. [In which case it can be interpreted as zero.]
[If negative] (...); you have too many predictors chasing too little information (a la small n). Just because one can run a model with n=60, and 10 predictors, does not mean that one should.
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