Calculate Coefficient of Determination for Regression by Hand
Introduction & Importance
The coefficient of determination, often denoted as R², 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. Calculating it by hand is crucial for understanding and validating your regression models.
How to Use This Calculator
- Enter comma-separated X values in the ‘X values’ field.
- Enter comma-separated Y values in the ‘Y values’ field.
- Click ‘Calculate’.
Formula & Methodology
The formula for calculating R² is:
R² = 1 – (SS_Res / SS_Tot)
Where:
- SS_Res is the sum of squares of residuals (difference between observed and predicted values).
- SS_Tot is the total sum of squares (difference between observed values and mean of observed values).
Real-World Examples
Data & Statistics
| X | Y |
|---|---|
| 1 | 2 |
| 2 | 4 |
| 3 | 6 |
| SS_Res | SS_Tot | R² |
|---|---|---|
| 2 | 6 | 0.6667 |
Expert Tips
- Always check the assumptions of your regression model before calculating R².
- R² can only increase as you add more predictors to your model. Use adjusted R² for models with different numbers of predictors.
Interactive FAQ
What does R² represent?
R² represents the proportion of the variance in the dependent variable that’s explained by the independent variable(s) in the model.