Coefficient of Determination

rsq.numeric

R Documentation

Description

A generic function for the \(R^2\). The unadjusted \(R^2\) is returned by default. Use weighted.rsq() for the weighted \(R^2\).

Usage

## S3 method for class 'numeric'
rsq(actual, predicted, k = 0, ...)

## S3 method for class 'numeric'
weighted.rsq(actual, predicted, w, k = 0, ...)

## Generic S3 method
rsq(
 ...,
 k = 0
)

## Generic S3 method
weighted.rsq(
 ...,
 w,
 k = 0
)

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.
`k`	A `<numeric>`-vector of length 1 (default: 0). For adjusted \(R^2\) set \(k = \kappa - 1\), where \(\kappa\) is the number of parameters.
`…`	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.

Definition

Let \(R^2 \in [-\infty, 1]\) be the explained variation. The \(R^2\) is calculated as,

\[ R^2 = 1 - \frac{\sum{(y_i - \hat{y}_i)^2}}{\sum{(y_i-\bar{y})^2}} \frac{n-1}{n - (k + 1)} \]

Where:

\(n\) is the number of observations
\(k\) is the number of features
\(y\) is the actual values
\(\hat{y}_i\) is the predicted values
\(\sum{(y_i - \hat{y}_i)^2}\) is the sum of squared errors and,
\(\sum{(y_i-\bar{y})^2}\) is total sum of squared errors

Examples

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

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

# 2) calculate performance
# using R squared adjusted and
# unadjused for features
cat(
  "Rsq", rsq(
    actual    = actual,
    predicted = fitted(model)
  ),
  "Rsq (Adjusted)", rsq(
    actual    = actual,
    predicted = fitted(model),
    k = ncol(model.matrix(model)) - 1
  ),
  sep = "\n"
)