R²: Coefficient of Determination

The value R² expresses the deviations between the calculated model curves and the experimental data compared to the deviations of the experimental data from their average value.

If the experimental data y_j measured at the points x_j for the curve i, and the model function f(x) is calculated at these points, then the regression values are f(x_j).

The residual between the experimental value and model value for i^th curve isy_i,j – f(x_i,j).

1. The Sum of the Residual Squares

If the model curve is drawn exactly through the experimental points, then all Residuals are zero and RSS is zero too.

The closer the calculated model curve is to the experimental data, the closer is RSS to zero.

2. The average of all experimental points

3. The variance of all experimental points

4. The coefficient of determination

The closer the calculated model curve is to the experimental data compared to the average, the closer is RSS to zero and the closer is R² to 1.