Coefficient of Determination Calculator

Formula

To calculate the coefficient of determination (\(R^2\)):

\[ R^2 = 1 - \left( \frac{RSS}{TSS} \right) \]

Where:

\(R^2\) is the coefficient of determination
\(RSS\) is the sum of squares of residuals
\(TSS\) is the total sum of squares

What is the Sum of Squares of Residuals (RSS)?

The sum of squares of residuals (RSS) represents the variation in the dataset that is not explained by the model. It’s a measure of the discrepancy between the data points and the model’s predicted values.

Example Calculation 1

Let's assume the following values:

Sum of Squares of Residuals (\(RSS\)) = 50
Total Sum of Squares (\(TSS\)) = 200

Using the formula:

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

The coefficient of determination is 0.75.

Example Calculation 2

Let's assume the following values:

Sum of Squares of Residuals (\(RSS\)) = 30
Total Sum of Squares (\(TSS\)) = 150

Using the formula:

\[ R^2 = 1 - \left( \frac{30}{150} \right) = 1 - 0.20 = 0.80 \]

The coefficient of determination is 0.80.