root relative squared error

rrse.numeric

R Documentation

Description

The rrse()-function calculates the root relative squared error between the predicted and observed <numeric> vectors. The weighted.rrse() function computes the weighed root relative squared errorr.

Usage

## S3 method for class 'numeric'
rrse(actual, predicted, ...)

## S3 method for class 'numeric'
weighted.rrse(actual, predicted, w, ...)

rrse(...)

weighted.rrse(...)

Arguments

actual	A <numeric>-vector of length \(n\). The observed (continuous) response variable.
predicted	A <numeric>-vector of length \(n\). The estimated (continuous) response variable.
…	Arguments passed into other methods.
w	A <numeric>-vector of length \(n\). The weight assigned to each observation in the data.

Value

A <numeric> vector of length 1.

Calculation

The metric is calculated as,

\[ \text{RRSE} = \sqrt{\frac{\sum_{i=1}^n (y_i - \upsilon_i)^2}{\sum_{i=1}^n (y_i - \bar{y})^2}} \]

Where \(y_i\) are the actual values, \(\upsilon_i\) are the predicted values, and \(\bar{y}\) is the mean of the actual values.

Examples

# 1) fit a linear
# regression
model <- lm(
  mpg ~ .,
  data = mtcars
)

# 1.1) define actual
# and predicted values
# to measure performance
actual    <- mtcars$mpg
predicted <- fitted(model)

# 2) evaluate in-sample model
# performance using Relative Root Squared Errror (RRSE)
cat(
  "Relative Root Squared Errror", rrse(
    actual    = actual,
    predicted = predicted,
  ),
  "Relative Root Squared Errror (weighted)", weighted.rrse(
    actual    = actual,
    predicted = predicted,
    w         = mtcars$mpg/mean(mtcars$mpg)
  ),
  sep = "\n"
)