Coefficient of Determination Calculator Formula
Understand the math behind the coefficient of determination calculator. Each variable explained with a worked example.
Formulas Used
R-squared
r_squared = pow(r, 2)Variance Explained (%)
r_sq_pct = pow(r, 2) * 1001 - R-squared
unexplained = 1 - pow(r, 2)Unexplained Variance (%)
unexplained_pct = (1 - pow(r, 2)) * 100Variables
| Variable | Description | Default |
|---|---|---|
r | Correlation Coefficient (r) | 0.85 |
How It Works
How to Calculate the Coefficient of Determination
Formula
R-squared = r^2
R-squared is the square of the Pearson correlation coefficient. It represents the proportion of variance in the dependent variable that is predictable from the independent variable. The remaining 1 - R^2 is unexplained variance.
Worked Example
If r = 0.85, how much variance does X explain in Y?
- 01R-squared = 0.85^2 = 0.7225
- 02X explains 72.25% of the variance in Y
- 03Unexplained variance = 1 - 0.7225 = 0.2775 or 27.75%
Frequently Asked Questions
What is a good R-squared value?
It depends on the field. In physical sciences, R^2 > 0.9 is typical. In social sciences, R^2 > 0.3 may be noteworthy. In stock prediction, even R^2 = 0.05 can be valuable.
Can R-squared be negative?
In simple linear regression, R^2 = r^2 and is always between 0 and 1. In multiple regression with poor models, adjusted R-squared can be negative, indicating the model is worse than simply predicting the mean.
What is adjusted R-squared?
Adjusted R-squared penalizes for the number of predictors. It can decrease if a predictor does not improve the model enough to justify the lost degree of freedom. It is preferred for comparing models with different numbers of predictors.
Ready to run the numbers?
Open Coefficient of Determination Calculator