What is Coefficient of Determination (R²) and Why Should You Care?
Ever wondered how well your statistical model is performing? That's where the coefficient of determination, often denoted as R², comes in. This important statistical measure gives you a clear picture of how well your model's predictions match the actual data. Essentially, R² represents the proportion of the variance in the dependent variable that is predictable from the independent variables in your model.
Formula:
[R^2 = 1 - \frac{\text{RSS}}{\text{TSS}}]
Where:
- RSS (sum of squares of residuals) is the variation in the dataset not explained by the model.
- TSS (total sum of squares) represents the total variation in the dataset.
Calculation Example:
- Sum of Squares of Residuals (RSS): 40
- Total Sum of Squares (TSS): 100
[R^2 = 1 - \frac{40}{100} = 1 - 0.4 = 0.6]
So, our coefficient of determination, R², is 0.6. This means 60% of the variation in the dependent variable is explained by the model.