Coefficient of Determination Calculator

The Coefficient of Determination (R²) Calculator helps you understand how well a regression model predicts the outcome by comparing observed and expected values.

Input Parameters

Calculation Results

Calculation Formula

R² = 1 - (SS_res / SS_tot)

Where:
SS_res = Sum of Squared Residuals
SS_tot = Total Sum of Squares

Coefficient of Determination Calculator Usage Guide

Learn how to use the Coefficient of Determination Calculator and its working principles

How to Use the Calculator

  1. Enter the observed values (Y) in the first input field, separated by commas (e.g., 2, 4, 6, 8).
  2. Enter the expected values (Ŷ) in the second input field, also separated by commas (e.g., 1, 3, 5, 7).
  3. Click the "Calculate" button to compute the Coefficient of Determination (R²).
  4. The result will be displayed in the third input field.

Understanding the Coefficient of Determination (R²)

The Coefficient of Determination (R²) is a statistical measure that represents the proportion of the variance for the dependent variable that's explained by the independent variable(s) in a regression model.

It ranges from 0 to 1:

  • R² = 1: The regression model perfectly explains the variance in the dependent variable.
  • R² = 0: The regression model does not explain any of the variance in the dependent variable.

For example, an R² of 0.85 means that 85% of the variance in the dependent variable is predictable from the independent variable(s).