# RSM Error Metrics¶

There are five error metrics available to assess the quality of a surrogate model in the Model tab of the Response Surface node. The commonly used metrics are defined below where $$r_i$$ is taken to be the response of the actual (full) model and $$f_i$$ is the response surface model evaluated at the $$i^\textrm{th}$$ (input) sample index ranging. In the following definitions, $$i$$ is simply taken to range from 1 to $$n$$, however it should be noted that this range may be applied to either the complete dataset or the holdout data if cross-validation is being considered, see Model for more details.

## Mean Squared Error¶

$\textrm{MSE} = \frac{{1}}{{n}} {\sum_{i=1}^n \left(r_i - f_i \right)^2 }$

## Sum of Squared Error¶

$\textrm{SSE} = {\sum_{i=1}^n \left(r_i - f_i \right)^2 }$

## R squared¶

$\textrm{R}^2 = 1 - \frac{{\sum_{i=1}^n \left( r_i - f_i \right)^2}} {{\sum_{i=1}^n \left( r_i - \bar{r} \right)^2}}$

where

$\bar{r} = \frac{{1}}{{n}} {\sum_{i=1}^n r_i }$

is the mean response.

## L_infinity norm¶

$\textrm{L}_\infty = \frac{{ \max \left| r_i - f_i \right| }}{{ \max \left| r_i \right| }}$

## L_1 norm¶

$\textrm{L}_1 = \frac{{ \sum_{i=1}^n \left| r_i - f_i \right| }} {{ \sum_{i=1}^n \left| r_i \right| }}$

## L_2 norm¶

$\textrm{L}_2 = \frac{{ \sum_{i=1}^n \left( r_i - f_i \right)^2 }} {{ \sum_{i=1}^n r_i^2 }}$