# Adjusted R-Squared Calculator Calculate adjusted R squared from R squared, sample size, and predictor count > Canonical page: https://elysiatools.com/en/tools/adjusted-r-squared-calculator - **Category:** Math & Numbers - **Keywords:** adjusted r squared, r squared, regression metrics, predictor count, calculator ## Overview The Adjusted R-Squared Calculator is a statistical tool designed to refine the ordinary R-squared value by accounting for the number of predictors in a regression model. Unlike standard R-squared, which always increases as more variables are added, the adjusted version penalizes the inclusion of non-significant predictors, providing a more accurate measure of a model's explanatory power relative to its complexity. ## Inputs - **R Squared** (number) - **Sample Size** (number) - **Predictor Count** (number) - **Decimal Places** (number) ## When to use - Comparing regression models that have a different number of independent variables. - Evaluating if adding a new predictor significantly improves the model's fit or leads to overfitting. - Reporting model performance for small sample sizes where ordinary R-squared may be overly optimistic. ## How it works - Enter the ordinary R-squared value obtained from your regression analysis (between 0 and 1). - Input the total sample size (number of observations) and the number of independent predictors used in the model. - Specify the desired decimal precision for the final calculation results. - The tool applies the adjusted R-squared formula to calculate the penalized score and the percentage of explained variance. ## Use cases - Academic research for validating the strength of multivariate regression models in social sciences. - Data science workflows to select the most efficient model features and avoid redundant variables. - Financial forecasting to ensure predictive models are not artificially inflated by irrelevant economic indicators. ## Frequently asked questions ### Why is adjusted R-squared usually lower than ordinary R-squared? It includes a mathematical penalty for every predictor added to the model to account for the possibility that variables improve the fit by chance. ### Can adjusted R-squared be negative? Yes, if the model's R-squared is very low and the number of predictors is high relative to the sample size, the result can be negative. ### What is the minimum sample size required for this calculation? The tool requires a minimum sample size of 2, though for valid results, the sample size must exceed the number of predictors plus one. ### Does this tool work for multiple regression models? Yes, it is specifically designed for multiple regression where you need to balance model complexity with predictive power. ### What does the 'penalty' value in the results represent? The penalty represents the difference between the ordinary R-squared and the adjusted R-squared, showing how much the score was reduced due to model complexity. ## Related tools - [Absolute Value Calculator](https://elysiatools.com/en/tools/absolute-value-calculator): Calculate the absolute value of positive, negative, or decimal numbers and explain the sign relationship - [Conditional Probability Calculator](https://elysiatools.com/en/tools/conditional-probability-calculator): Calculate P(A given B) from joint probability P(A and B) and condition probability P(B) - [Correlation Calculator](https://elysiatools.com/en/tools/correlation-calculator): Calculate Pearson and Spearman correlation coefficients from paired numeric data - [Covariance Calculator](https://elysiatools.com/en/tools/covariance-calculator): Calculate sample and population covariance from paired numeric data - [Enzyme Kinetics Calculator (Michaelis-Menten)](https://elysiatools.com/en/tools/enzyme-kinetics-calculator): Calculate reaction velocity with Michaelis-Menten, estimate Km/Vmax via Lineweaver-Burk, and model enzyme inhibition. - [F Distribution Calculator](https://elysiatools.com/en/tools/f-distribution-calculator): Calculate F distribution density, cumulative probability, and right-tail probability from numerator and denominator degrees of freedom - [Flywheel Energy Storage Calculator](https://elysiatools.com/en/tools/flywheel-energy-storage): Calculate the kinetic energy stored in a flywheel. 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