# Regression Metrics

    library(SLmetrics)

In this vignette, a brief overview of the regression metrics in {SLmetrics} is provided. The regression interface is based on [numeric] vectors and uses `foo.numeric()` and `weighted.foo.numeric()` methods for unweighted and weighted regression metrics, respectively.

Throughout this vignette, the following data will be used:

    # 1) seed
    set.seed(1903)

    # 2) actual values
    actual <- rnorm(
        n = 100
    )

    # 3) predicted values
    predicted <- actual + rnorm(n = 100)

    # 4) sample weights
    weights <- runif(
        n = length(actual)
    )

Assume that the `predicted` values come from a trained machine learning model. This vignette introduces a subset of the metrics available in {SLmetrics}; see the online documentation for more details and other metrics.

## Computing regression metrics

One of the most common metrics for regression tasks is the root mean squared error (RMSE) which can be computed with or without sample weights:

    # 1) calculate unweighted RMSE
    rmse(
        actual    = actual,
        predicted = predicted
    )
    #> [1] 0.9085512

    # 2) calculate weighted RMSE
    weighted.rmse(
        actual    = actual,
        predicted = predicted,
        w         = weights
    )
    #> [1] 0.9368692

Another metric is the relative root mean squared error (RRMSE). It applies a normalization factor to the RMSE, which can help compare errors across datasets with different scales. The RRMSE can be computed with three possible normalization methods:

    # 1) calculate RRMSE
    # with mean normalization
    rrmse(
        actual = actual,
        predicted = predicted,
        normalization = 0
    )
    #> [1] 6.935011

    # 2) calculate RRSME
    # with range normalization
    rrmse(
        actual = actual,
        predicted = predicted,
        normalization = 1
    )
    #> [1] 0.1711166

    # 3) calculate RRSME
    # with IQR normalization
    rrmse(
        actual = actual,
        predicted = predicted,
        normalization = 2
    )
    #> [1] 0.6977752

The parameter `normalization` determines the normalization factor of the RMSE;

- 0: Mean normalization
- 1: Range normalization (`max` - `min`)
- 2: Interquartile normalization (\(q_{75}\) - \(q_{25}\))

The interface for all regression metrics in {SLmetrics} follows the same basic signature: two numeric vectors (actual and predicted) and, optionally, sample weights (w) or other metric-specific parameters.