mlr_measures_regr.rsq: R-Squared

In mlr-org/mlr3: Machine Learning in R - Next Generation

R-Squared

Description

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

Details

R Squared is defined as

1 - \frac{\sum_{i=1}^n w_i \left( t_i - r_i \right)^2}{\sum_{i=1}^n w_i \left( t_i - \bar{t} \right)^2},

where \bar{t} = \frac{1}{n} \sum_{i=1}^n t_i and w_i are weights.

Also known as coefficient of determination or explained variation. It compares the squared error of the predictions relative to a naive model predicting the mean.

Note that weights are used to scale the squared error of individual predictions (both in the numerator and in the denominator), but the "plug in" value \bar{t} is computed without weights.

This measure is undefined for constant t.

Dictionary

This Measure can be instantiated via the dictionary mlr_measures or with the associated sugar function msr():

mlr_measures$get("regr.rsq")
msr("regr.rsq")

Meta Information

• Task type: “regr”

• Range: (-\infty, 1]

• Minimize: FALSE

• Average: macro

• Required Prediction: “response”

• Required Packages: mlr3

Parameters

Empty ParamSet

Super classes

mlr3::Measure -> mlr3::MeasureRegr -> MeasureRSQ

Methods

Public methods

• MeasureRegrRSQ$new()

• MeasureRegrRSQ$clone()

Inherited methods

• mlr3::Measure$aggregate()
• mlr3::Measure$format()
• mlr3::Measure$help()
• mlr3::Measure$print()
• mlr3::Measure$score()

---

Method new()

Creates a new instance of this R6 class.

Usage

MeasureRegrRSQ$new(pred_set_mean = TRUE)

Arguments

pred_set_mean

logical(1)
If TRUE, the mean of the true values is calculated on the prediction set. If FALSE, the mean of the true values is calculated on the training set.

---

Method clone()

The objects of this class are cloneable with this method.

Usage

MeasureRegrRSQ$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

See Also

• Chapter in the mlr3book: https://mlr3book.mlr-org.com/chapters/chapter2/data_and_basic_modeling.html#sec-eval

• Package mlr3measures for the scoring functions. Dictionary of Measures: mlr_measures as.data.table(mlr_measures) for a table of available Measures in the running session (depending on the loaded packages).

• Extension packages for additional task types:

  • mlr3proba for probabilistic supervised regression and survival analysis.

  • mlr3cluster for unsupervised clustering.

Other Measure: Measure, MeasureClassif, MeasureRegr, MeasureSimilarity, mlr_measures, mlr_measures_aic, mlr_measures_bic, mlr_measures_classif.costs, mlr_measures_debug_classif, mlr_measures_elapsed_time, mlr_measures_internal_valid_score, mlr_measures_oob_error, mlr_measures_regr.pinball, mlr_measures_selected_features

mlr-org/mlr3 documentation built on July 4, 2025, 3:40 a.m.