R Squared

Measure to compare true observed response with predicted response in regression tasks.

Usage

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).

Details

R Squared is defined as $1 - \frac{\sum_{i = 1}^{n} {(t_{i} - r_{i})}^{2}}{\sum_{i = 1}^{n} {(t_{i} - \bar{t})}^{2}},$ where $\bar{t} = \sum_{i = 1}^{n} t_{i}$ .

Also known as coefficient of determination or explained variation. Subtracts the rse() from 1, hence it compares the squared error of the predictions relative to a naive model predicting the mean.

This measure is undefined for constant $t$ .

Meta Information

Type: "regr"
Range: $(- \infty, 1]$
Minimize: FALSE
Required prediction: response

Examples

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