Coefficient of Determination

Tags: #machine learning #metric

Equation

$$SS_{res} = \sum_{i} (y_{i} - f_{i})^{2} = \sum_{i} e_{i}^{2}, SS_{total} = \sum_{i} (y_{i} - \bar{y} )^{2}, y=\frac{1}{n} \sum^{n}_{i=1} y_{i}, R^{2} = 1 - \frac{SS_{res}}{SS_{total}}$$

Latex Code

Have Fun

Let's Vote for the Most Difficult Equation!

Introduction

$$f_{i}$$: prediction values of original observed value $$ y_{i} $$.
$$ SS_{res} $$: denotes the residual sum of squares, which is the sum of square of residual value $$e_{i}$$.
$$ SS_{tot} $$: denotes total sum of squares.
$$ R^{2} $$: Coefficient of Determination or R-squared, which measures how good the modeled values $$f_{i}$$ exactly match the observed values $$y_{i} $$ .

References

Wikipedia: Coefficient of determination