Adjusted R-Squared

Evaluate model fit while accounting for the number of predictors.

Model Parameters

Raw R-Squared (R²)

Sample Size (n)

Predictors (k)

Fit Analysis

Adjusted R²0.8420Reliability Score

Overfitting Penalty

0.0080

Degrees of Freedom

Stability Note

Model appears stable. The adjustment penalty is minor.

Overview

Adjusted R-squared is a modified version of R-squared that has been adjusted for the number of predictors in the model. While R-squared always increases as you add more variables, Adjusted R-squared only increases if the new term improves the model more than would be expected by chance.

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Pro Tips

Use Adjusted R² when comparing models with a different number of predictors.
If Adjusted R² is much lower than R², consider removing weak or redundant variables.
Always ensure your sample size (n) is significantly larger than your predictor count (k).

Mathematical Formula

The adjustment penalty is applied based on the ratio of sample size to predictors:

R̄² = 1 - [ (1 - R²)(n - 1) / (n - k - 1) ]

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