Adjusted R-Squared Calculator

R-squared
Adjusted R-squared

What this answers

Adjusted R-squared answers "how well does this model actually fit, once I account for how many predictors it used to get there?" Ordinary R-squared always increases (or stays the same) as you add more predictors, even completely useless ones, purely because more predictors give a model more flexibility to fit noise in your specific sample. Adjusted R-squared corrects for that by penalizing extra predictors, making it a fairer way to compare models with different numbers of predictors.

How it is calculated

R-squared is 1 minus the ratio of the sum of squared errors (SSE) to the total sum of squares (SST). Adjusted R-squared modifies this using the sample size and the number of predictors, shrinking the reported fit downward as more predictors are added relative to the sample size, and shrinking it more sharply for a small sample with many predictors.

Worked example

For a model with SSE of 0 (a perfect fit) and SST of 100: R-squared is exactly 1 regardless of how many predictors were used, and adjusted R-squared stays at 1 as well, since a perfect fit cannot be penalized further. Try a more realistic case, such as SSE=20 and SST=100 with 10 predictors on a sample of 15, to see how sharply adjusted R-squared drops below the raw R-squared of .8 when predictors are numerous relative to sample size.

Assumption audit

Calculated from your data: R-squared and adjusted R-squared directly from the SSE, SST, sample size, and predictor count you supplied.

Evidence to review: a large gap between R-squared and adjusted R-squared signals the model may include predictors that are not earning their keep, worth reviewing individually rather than assuming they all help.

You must verify: that comparing adjusted R-squared across models is appropriate for your situation. It compares in-sample fit, not out-of-sample predictive accuracy, which is a different and often more important question for real forecasting use.

Common mistakes

A common mistake is comparing adjusted R-squared across models fit on different samples or different outcome variables; the comparison is only meaningful when the outcome and the underlying data are the same across the models being compared. Another is treating a small adjusted R-squared as automatically meaning the model is useless; in some fields (a single human behavior measured cross-sectionally, for instance) even a modest adjusted R-squared can reflect a real, useful relationship. A third is entering predictor count incorrectly by forgetting to count the intercept consistently with how SSE and SST were originally computed, which throws off the penalty term.

Limitations

Both R-squared and adjusted R-squared are descriptive, in-sample fit measures. Neither proves the model's predictors are causally related to the outcome, and neither guarantees good performance predicting new, unseen data.