R-Squared Calculator: Coefficient of Determination
Easily calculate the R-squared value, also known as the coefficient of determination, to evaluate the goodness of fit of your regression model. Input your observed and predicted Y values for instant results.
R-Squared Calculator
Enter your observed and predicted Y values to calculate the R-squared value, a key indicator of regression model fit.
Enter comma-separated values.
Enter comma-separated values.
R-squared Value:
R-squared Visualization
The R-squared value, also known as the coefficient of determination, ranges from 0 to 1. It represents the proportion of the variance in the dependent variable that is predictable from the independent variable(s).
- An R-squared of 1 indicates that the model perfectly explains all the variability in the response data.
- An R-squared of 0 means the model explains none of the variability.
Generally, a higher R-squared indicates a better fit.
R-squared:
Understanding R-Squared
R-squared, or the coefficient of determination, 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. In simpler terms, it shows how well the data fit the regression line.
Formula
The formula for R-squared is given by:
- \( \(R^2\) \) is the R-squared value.
- \( \(RSS\) \) is the Residual Sum of Squares, the sum of the squares of the residuals (the difference between observed and predicted values).
- \( \(TSS\) \) is the Total Sum of Squares, the sum of the squares of the deviations of the observed values from their mean.
- \( \(y_i\) \) are the observed y-values.
- \( \(\hat{y}_i\) \) are the predicted y-values from the regression model.
- \( \(\bar{y}\) \) is the mean of the observed y-values.
How to Use This Calculator
1. **Enter Observed Y Values:** Input the actual or observed values of the dependent variable, separated by commas. 2. **Enter Predicted Y Values:** Input the values predicted by your regression model, corresponding to the observed Y values, also comma-separated. 3. **Click 'Calculate R-Squared':** The calculator will compute the R-squared value and display it along with a visual representation. 4. **Interpret the Result:** Review the R-squared value and the visualization to understand the goodness of fit of your model. A value closer to 1 indicates a better fit.
For more in-depth information about R-squared, you can refer to resources like Wikipedia or statistical textbooks.