How To Calculate R Squared In Regression Analysis

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. In other words, it tells you how well your regression predictions perform.

How to Use This Calculator

1. Enter the slope (b1) and intercept (b0) values from your regression equation.
2. Enter the number of observations (n) used in your regression analysis.
3. Click the “Calculate R-Squared” button.

Formula & Methodology

The formula for calculating R-squared is:

R² = 1 – (∑(yi – ŷi)² / ∑(yi – ȳ)²)

Where:

• yi = actual value
• ŷi = predicted value
• ȳ = mean of actual values

Real-World Examples

Data & Statistics

Expert Tips

• R-squared values range from 0 to 1. A value of 1 means that the regression predictions perfectly fit the data.
• While a high R-squared value indicates a good fit, it’s not the only metric to consider. Always evaluate your model’s assumptions and residuals.

Interactive FAQ

What does R-squared tell me about my model?

R-squared tells you how well your regression model fits your data. A high R-squared value indicates that your model explains a large portion of the variance in your dependent variable.

For more information, see these authoritative sources:

• UCLA Statistical Consulting Group
• Nature – The meaning and misuse of R-squared