In the full lesson
- R² Formula (formula)
- Relationship to r (text)
- Interpretation Example (example)
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Module 6 · Regression & Correlation · Topic 6
R-Squared
Coefficient of Determination (R²). R² is the proportion of the total variation in y that is explained by the linear relationship with x. For the usual in-sample least-squares regression with an intercept and nonconstant y, it ranges from 0 (no explanatory power) to 1 (perfect prediction).
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Key formulas
From the Regression & Correlation formula sheet
- Least-Squares Regression Line:
yhat = a + bx- Line that minimizes the sum of squared residuals. - Pearson Correlation:
r = sum((x_i-xbar)(y_i-ybar)) / sqrt(sum((x_i-xbar)^2)sum((y_i-ybar)^2))- Measures direction and strength of a linear association.
Related glossary terms
- Residual: The observed value minus the predicted value. Example: If y = 12 and yhat = 9, the residual is 3.
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