Enter your observed R², sample size, and number of predictors to get the Adjusted R-Squared value — a corrected measure of model fit that penalizes overfitting from too many predictors. Unlike plain R², the adjusted version gives a more honest picture of how well your regression model explains variance in the dependent variable.
Adjusted R²
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Observed R²
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R² Reduction (Penalty)
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Degrees of Freedom (n − k − 1)
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Adjusted R-Squared is a modified version of R² that accounts for the number of predictors in a regression model. While R² always increases (or stays the same) when you add more predictors, Adjusted R² penalizes the addition of predictors that do not meaningfully improve the model. This makes it a more reliable indicator of model fit, especially in multiple regression.
The formula is: Adj. R² = 1 − [(1 − R²)(n − 1) / (n − k − 1)], where R² is the observed (sample) R-squared, n is the sample size, and k is the number of predictors (excluding the intercept). The formula adjusts R² downward based on how many predictors are used relative to the sample size.
R-Squared measures the proportion of variance in the dependent variable explained by the model, but it always increases as you add more predictors — even irrelevant ones. Adjusted R-Squared corrects for this by penalizing unnecessary predictors, making it a better metric for comparing models with different numbers of variables. For simple regression with one predictor, both values are nearly identical.
Yes, Adjusted R-Squared can be negative. This happens when the model fits the data worse than a simple horizontal line (the mean). It typically indicates that the chosen predictors have no real explanatory power, or that the model is severely misspecified with too many predictors relative to sample size.
In Excel, you can use the formula =1-((1-RSQ(known_ys, known_xs))*(n-1)/(n-k-1)), where n is your sample size and k is the number of predictors. Alternatively, if you run a regression using the Data Analysis ToolPak, Excel reports Adjusted R-Square automatically in the regression output summary.
A 'good' Adjusted R² depends on the field and context. In social sciences, values above 0.5 are often considered acceptable. In physical sciences or engineering, values above 0.9 may be expected. The key is to compare models: a higher Adjusted R² indicates a better-fitting model relative to others being compared, as long as added predictors genuinely improve fit.
Use Adjusted R-Squared whenever you are working with multiple regression — that is, any model with more than one predictor. It is especially important when comparing models with different numbers of predictors, as it prevents overfitting from inflating your apparent model performance. For simple linear regression with one predictor, the distinction matters less.
Adjusted R-Squared decreases when a newly added predictor does not improve the model enough to justify the loss of a degree of freedom. The formula penalizes each additional predictor; if the predictor's contribution to R² is smaller than this penalty, the Adjusted R² drops. This serves as a built-in guard against overfitting your model.