Statistics
R-Squared (Coefficient of Determination) - Statistics
Learn the r-squared (coefficient of determination) with examples, step-by-step guide, and calculator tools. Proportion of variance explained
The r-squared (coefficient of determination) is a fundamental concept in statistics. Proportion of variance explained. This page provides a comprehensive guide with worked examples and practical applications.
The Formula
\[R^2 = 1 - \frac{SS_{\text{res}}}{SS_{\text{tot}}}\]
Variables
R²
Coefficient of determination
SSᵣₑₛ
Residual sum of squares
SSₜₒₜ
Total sum of squares
Step-by-Step Guide
- 1
Step 1: Gather your data values
- 2
Step 2: Apply the formula
- 3
Step 3: Perform the calculations
- 4
Step 4: Interpret the result
Examples
Example 1
Example 1: [] → R² = 0.85 means 85% of variance explained
Example 2
Example 2: 0.85
Frequently Asked Questions
What is the r-squared (coefficient of determination)?
Proportion of variance explained
How do I calculate r-squared (coefficient of determination)?
Use the formula: R^2 = 1 - \frac{SS_{\text{res}}}{SS_{\text{tot}}}. Follow the steps provided above.
What tools can help with r-squared (coefficient of determination)?
We provide online calculators: correlation-calculator