# Coefficient of Determination Calculator

## About Coefficient of Determination Calculator (Formula)

A Coefficient of Determination Calculator is a tool used to quantify the proportion of variability in a dependent variable that can be explained by an independent variable in a statistical model. It’s also known as R-squared (R²) and provides insights into how well the independent variable predicts the dependent variable’s variations. The formula to calculate the coefficient of determination is as follows:

Coefficient of Determination (R²) = 1 – (Sum of Squared Residuals / Total Sum of Squares)

Where:

• Sum of Squared Residuals (RSS): The sum of the squared differences between the actual values and the predicted values from the model.
• Total Sum of Squares (TSS): The sum of the squared differences between the actual values and the mean value of the dependent variable.

R² is a value between 0 and 1. A higher R² indicates that a larger proportion of the variability in the dependent variable is explained by the independent variable. Conversely, a lower R² suggests that the independent variable has less explanatory power.

For example, if the sum of squared residuals is 50 and the total sum of squares is 100, the coefficient of determination would be:

Coefficient of Determination (R²) = 1 – (50 / 100) = 0.5

This means that 50% of the variability in the dependent variable is explained by the independent variable in the model.

The Coefficient of Determination Calculator is commonly used in regression analysis to evaluate the goodness of fit of a model. It helps assess the strength of the relationship between variables and whether the model provides meaningful predictions.