R-Squared vs. Adjusted R-Squared: An Overview

R-squared (R2) and adjusted R-square allow an investor to measure the value of a mutual fund against the value of a benchmark. Investors may also use this calculation to measure their portfolio against a given benchmark.

These values range between 0 and 100. The resulting figure does not indicate how well a particular group of securities is performing, and it only measures how closely the returns from the holdings align to those of the measured benchmark.

R-squared—also known as the coefficient of determination—is a statistical analysis tool used to predict the future outcome of an investment and how closely it aligns to a single measured model.

Adjusted R-squared compares the correlation of the investment to several measured models.

R-Squared

R-squared cannot verify whether the coefficient ballpark figure and its predictions are prejudiced. It also does not show if a regression model is satisfactory; it can show an R-squared figure for a good model or a high R-squared figure for a model that doesn’t fit. The lower the value of the R2 the less the two variables correlate to one another. Results higher than 70% usually indicate that a portfolio closely follows the measured benchmark. Higher R-squared values also indicate the reliability of beta readings. Beta measures the volatility of a security or a portfolio.

One major difference between R-squared and the adjusted R-squared is that R2 assumes every independent variable—benchmark—in the model explains the variation in the dependent variable—mutual fund or portfolio. It gives the percentage of explained variation as if all independent variables in the model affect the dependent variable. In the real world, this one-to-one relationship rarely happens. Adjusted R-squared, on the other hand, gives the percentage of variation explained by only those independent variables that, in reality, affect the dependent variable.

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Adjusted R-Squared

The adjusted R-squared compares the descriptive power of regression models—two or more variables—that include a diverse number of independent variables—known as a predictor. Every predictor or independent variable, added to a model increases the R-squared value and never decreases it. So, a model that includes several predictors will return higher R2 values and may seem to be a better fit. However, this result is due to it including more terms.

The adjusted R-squared compensates for the addition of variables and only increases if the new predictor enhances the model above what would be obtained by probability. Conversely, it will decrease when a predictor improves the model less than what is predicted by chance.

When too few data points are used in a statistical model it is called overfitting. Overfitting can return an unwarranted high R-squared value. This incorrect figure can lead to a decreased ability to predict performance outcomes. The adjusted R-squared is a modified version of R2 for the number of predictors in a model. The adjusted R-squared can be negative but isn't always.

While an R-squared value between 0 and 100 and shows the linear relationship in the sample of data even when there is no basic relationship, the adjusted R-squared gives the best estimate of the degree of relationship in the basic population.

To show the correlation of models with R-squared, pick the model with the highest limit. However, the best, and easiest, way to compare models is to select one with the smaller adjusted R-squared. Adjusted R-squared is not a typical model for comparing nonlinear models but, instead, shows multiple linear regressions.

Key Takeaways

  • One major difference between R-squared and the adjusted R-squared is that R-squared supposes that every independent variable in the model explains the variation in the dependent variable.
  • R-squared cannot verify whether the coefficient ballpark figure and its predictions are prejudiced.
  • The adjusted R-squared is a modified version of R-squared for the number of predictors in a model.