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R-Squared Value Calculator

Formula

The formula to calculate the R-squared value is:

$R^2 = 1 - \left(\frac{SSR}{SST}\right)$

Where:

R² is the R-squared value
SSR is the sum of squares of the residuals
SST is the total sum of squares

What is R-Squared?

R-squared, also known as 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. It provides a measure of how well observed outcomes are replicated by the model, based on the proportion of total variation of outcomes explained by the model. R-squared values range from 0 to 1, where a higher value generally indicates a better fit of the model.

Example Calculation

Example 1:

Sum of Squares of the Residuals (SSR): 50
Total Sum of Squares (SST): 200

Step 1: Calculate the R-squared value:

$R^2 = 1 - \left(\frac{50}{200}\right) = 1 - 0.25 = 0.75$

Example 2:

Sum of Squares of the Residuals (SSR): 30
Total Sum of Squares (SST): 150

Step 1: Calculate the R-squared value:

$R^2 = 1 - \left(\frac{30}{150}\right) = 1 - 0.2 = 0.8$