R² and Residuals Demonstration
Explore how the coefficient of determination (R²) relates to the spread of residuals around the regression line.
Actual R²
Correlation (r)
Slope (b)
Intercept (a)
Residual SD
Variance Decomposition
Understanding R² and Residuals
R² (coefficient of determination) represents the proportion of variance
in Y that is predictable from X. When R² is high, points cluster tightly around the regression line and
residuals (vertical distances from points to the line) are small.
Residuals are the vertical distances between observed values and
predicted values (the line). As R² decreases, residual variance increases—the points scatter more widely
around the line, making predictions less precise.
Key relationship: Residual Variance = Total Variance × (1 - R²)