root mean squared error

rmse.numeric

R Documentation

Description

The rmse()-function computes the root mean squared error between the observed and predicted <numeric> vectors. The weighted.rmse() function computes the weighted root mean squared error.

Usage

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

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

rmse(...)

weighted.rmse(...)

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,

\[ \sqrt{\frac{1}{n} \sum_i^n (y_i - \upsilon_i)^2} \]

Where \(y_i\) and \(\upsilon_i\) are the actual and predicted values respectively.

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 Root Mean Squared Error (RMSE)
cat(
  "Root Mean Squared Error", rmse(
    actual    = actual,
    predicted = predicted,
  ),
  "Root Mean Squared Error (weighted)", weighted.rmse(
    actual    = actual,
    predicted = predicted,
    w         = mtcars$mpg/mean(mtcars$mpg)
  ),
  sep = "\n"
)