The adjusted R-squared is a modified version of R-squared that has been adjusted for the number of predictors in the model.

The adjusted R-squared increases only if the new term improves the model more than would be expected by chance.

It decreases when a predictor improves the model by less than expected by chance.

The adjusted R-squared can be negative, but it’s usually not.  It is always lower than the R-squared.

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