## 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

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}}

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### 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## Discussion

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