Unlock the Power of R-Squared: Understand Your Regression Model

Dive deep into your data and measure the goodness of fit for your regression models with our interactive R-Squared Calculator. Get instant insights and visualize your model's performance.

R-Squared Calculator

Enter your observed and predicted Y values to calculate the R-squared value, a key indicator of regression model fit.

Observed Y Values (comma-separated)

Enter comma-separated values.

Predicted Y Values (comma-separated)

Enter comma-separated values.

R-squared Value:

R² =

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:

$$R^2 = 1 - \frac{RSS}{TSS} = 1 - \frac{\sum_{i=1}^{n}(y_i - \hat{y}_i)^2}{\sum_{i=1}^{n}(y_i - \bar{y})^2}$$

$ \(R^2$ \) 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.