About the Adjusted R-Squared
This calculator adjusts a regression model's R-squared value for the number of predictors used and the sample size, producing a fit measure that penalizes adding variables that don't meaningfully improve the model. It is meant to be used after a regression has already been run, when you have the R-squared, sample size, and predictor count on hand. It is especially useful for comparing models that don't have the same number of predictors.
How It Works
You enter the model's unadjusted R-squared, the sample size used to fit the model, and the number of predictor variables included. The calculator applies a correction that scales the unexplained variance, 1 minus R-squared, by the ratio of degrees of freedom used for the total variance versus the residual variance, then subtracts that scaled figure from 1. The result is always less than or equal to the original R-squared, with the gap growing as more predictors are added relative to the sample size.
Examples
Moderate model, well-supported by data
With the default inputs, an R-squared of 0.82, 50 observations, and 4 predictors, the adjusted R-squared comes out to about 0.804, a small penalty reflecting a reasonable ratio of predictors to sample size.
Overfit model with too many predictors
For a model with an R-squared of 0.95 but only 20 observations and 15 predictors, the adjusted R-squared drops sharply to about 0.7625, exposing how much of the apparent fit was likely due to having nearly as many predictors as data points.
Advantages
- Lets you compare models with different numbers of predictors on a fairer basis than raw R-squared, which always favors the model with more variables.
- Quantifies the overfitting cost of adding weak predictors as a single, interpretable number rather than a vague warning.
- Requires only three known values from an already-fitted model, so there's no need to rerun the full regression to get the adjusted figure.
Common Mistakes
- Comparing plain R-squared across models with different numbers of predictors, which mechanically favors whichever model has more variables regardless of whether they add real explanatory power.
- Treating adjusted R-squared as a significance test or p-value, when it is a descriptive fit measure, not a formal hypothesis test.
- Ignoring the requirement that sample size must clearly exceed the predictor count; with too few observations relative to predictors, the statistic becomes unstable or undefined.
Edge Cases to Watch For
- The sample size must exceed the number of predictors by more than one, meaning n - k - 1 must be positive; otherwise the denominator is zero or negative and the calculator returns an error instead of a meaningless result.
- When a model has many predictors relative to its sample size, adjusted R-squared can drop sharply below the unadjusted value, and in extreme cases can even go negative, signaling that the model fits worse than a simple average would.
- This calculator takes R-squared as a direct input rather than computing it from raw data, so its output is only as reliable as the R-squared, sample size, and predictor count it's given.
Common Use Cases
- Researchers and analysts comparing regression models that use different sets of predictor variables.
- Students learning why adding more variables to a model doesn't automatically make it better.
- Anyone reporting model fit who wants to account for model complexity rather than citing raw R-squared alone.