Regression measure defined as $$ 1 - \frac{\sum_{i=1}^n \left( t_i - r_i \right)^2}{\sum_{i=1}^n \left( t_i - \bar{t} \right)^2}. $$ Also known as coefficient of determination or explained variation. Substracts the rse() from 1, hence it compares the squared error of the predictions relative to a naive model predicting the mean.

rsq(truth, response, na_value = NaN, ...)

Arguments

truth

:: numeric()
True (observed) values. Must have the same length as response.

response

:: numeric()
Predicted response values. Must have the same length as truth.

na_value

:: numeric(1)
Value that should be returned if the measure is not defined for the input (as described in the note). Default is NaN.

...

:: any
Additional arguments. Currently ignored.

Value

Performance value as numeric(1).

Note

This measure is undefined for constant \(t\).

Meta Information

  • Type: "regr"

  • Range: \((-\infty, 1]\)

  • Minimize: FALSE

  • Required prediction: response

See also

Other Regression Measures: bias(), ktau(), mae(), mape(), maxae(), maxse(), medae(), medse(), mse(), msle(), pbias(), rae(), rmse(), rmsle(), rrse(), rse(), sae(), smape(), srho(), sse()

Examples

set.seed(1) truth = 1:10 response = truth + rnorm(10) rsq(truth, response)
#> [1] 0.9314108