1. What is the Coefficient of Determination (R²)?

The Coefficient of Determination (R²) is a statistical measure that represents the proportion of the variance in the dependent variable that is predictable from the independent variable(s) in a regression model. It ranges from 0 to 1, with higher values indicating better model fit.

2. How Does the Calculator Work?

The calculator uses the R² formula:

Where:

• \( SS_{res} \) — Sum of squares of residuals (unexplained variance)
• \( SS_{tot} \) — Total sum of squares (total variance)

Explanation: R² measures how well the regression predictions approximate the real data points. An R² of 1 indicates perfect fit.

3. Importance of R² in Regression

Details: R² is crucial for assessing the goodness-of-fit of a regression model. It helps determine how much of the variability in the outcome can be explained by the predictors.

4. Using the Calculator

Tips: Enter the residual sum of squares (SS_res) and total sum of squares (SS_tot). Both values must be positive numbers, with SS_tot greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a good R² value?
A: This depends on the field. In social sciences, 0.2 might be acceptable, while in physics 0.9+ might be expected. Always compare to similar studies.

Q2: Can R² be negative?
A: Yes, but only when the model fits worse than a horizontal line (typically indicates a serious problem with model specification).

Q3: What's the difference between R² and adjusted R²?
A: Adjusted R² accounts for the number of predictors in the model and prevents overestimation of fit when adding more variables.

Q4: Does high R² mean causation?
A: No! R² only measures correlation. High R² doesn't imply the independent variables cause changes in the dependent variable.

Q5: When shouldn't I use R²?
A: R² can be misleading for nonlinear models, when comparing models with different dependent variables, or when the intercept is suppressed.