R Squared Calculator

R Squared Formula:

\[ R^2 = 1 - \frac{\sum (y_i - \hat{y}_i)^2}{\sum (y_i - \bar{y})^2} \]

R Squared Value:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is R Squared?

R-squared (R²) is a statistical measure that represents the proportion of the variance for a dependent variable that's explained by an independent variable or variables in a regression model. It indicates how well data points fit a statistical model.

2. How Does the Calculator Work?

The calculator uses the R-squared formula:

\[ R^2 = 1 - \frac{\sum (y_i - \hat{y}_i)^2}{\sum (y_i - \bar{y})^2} \]

Where:

\( y_i \) — Observed values
\( \hat{y}_i \) — Predicted values from the model
\( \bar{y} \) — Mean of the observed values
\( \sum \) — Summation of all values

Explanation: R-squared compares the variance explained by the model to the total variance in the data. A value of 1 indicates perfect prediction, while 0 indicates the model explains none of the variability.

3. Interpretation of R Squared

Details: R-squared values range from 0 to 1. Higher values generally indicate a better fit, but context matters. In some fields, even low R-squared values can be meaningful if they represent real relationships.

4. Using the Calculator

Tips: Enter observed and predicted values as comma-separated lists. Ensure both lists have the same number of values. The calculator will compute R-squared based on these inputs.

5. Frequently Asked Questions (FAQ)

Q1: What is a good R-squared value?
A: This depends on the field of study. In social sciences, 0.2-0.3 might be acceptable, while in physics, values closer to 1 are expected.

Q2: Can R-squared be negative?
A: Yes, but only if the model performs worse than simply using the mean of the dependent variable. This indicates a very poor model fit.

Q3: What are limitations of R-squared?
A: R-squared always increases with more predictors, even if they're irrelevant. It doesn't indicate whether the regression coefficients are statistically significant.

Q4: How is R-squared different from adjusted R-squared?
A: Adjusted R-squared penalizes for adding unnecessary predictors, providing a more accurate measure when comparing models with different numbers of predictors.

Q5: When should I not use R-squared?
A: R-squared is less useful for nonlinear models and can be misleading when comparing models across different datasets or with different transformations.