Enter the sum of squares of the residuals and the total sum of squares into the calculator to determine the R-squared value. This calculator can also evaluate any of the variables given the others are known.

R-Squared Formula

The following formula is used to calculate the R-squared value, also known as the coefficient of determination.

R^2 = 1 - (SSR / SST)

Variables:

  • R^2 is the R-squared value SSR is the sum of squares of the residuals SST is the total sum of squares

To calculate the R-squared value, first calculate the sum of squares of the residuals and the total sum of squares. Then, divide the sum of squares of the residuals by the total sum of squares. Subtract this quotient from 1 to get the R-squared value.

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.

How to Calculate R-Squared?

The following steps outline how to calculate the R-Squared value.


  1. First, determine the sum of squares of the residuals (SSR).
  2. Next, determine the total sum of squares (SST).
  3. Next, use the formula R^2 = 1 – (SSR / SST) to calculate the R-Squared value.
  4. Finally, calculate the R-Squared value.
  5. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

R^2 – R-squared value

SSR – Sum of squares of the residuals

SST – Total sum of squares