compositions (version 2.0-8)

R2: R square

Description

The R2 measure of determination for linear models

Usage

R2(object,...)
# S3 method for lm
R2(object,...,adjust=TRUE,ref=0)
# S3 method for default
R2(object,...,ref=0)

Value

The R2 measure of determination.

Arguments

object

a statistical model

...

further not yet used parameters

adjust

Logical, whether the estimate of R2 should be adjusted for the degrees of freedom of the model.

ref

A reference model for computation of a relative \(R^2\).

Author

K.Gerald v.d. Boogaart http://www.stat.boogaart.de

Details

The \(R^2\) measure of determination is defined as: $$R^2=1-\frac{var(residuals)}{var(data)}$$

and provides the portion of variance explained by the model. It is a number between 0 and 1, where 1 means the model perfectly explains the data and 0 means that the model has no better explanation of the data than a constant mean. In case of multivariate models metric variances are used.

If a reference model is given by ref, the variance of the residuals of that models rather than the variance of the data is used. The value of such a relative \(R^2\) estimates how much of the residual variance is explained.

If adjust=TRUE the unbiased estiamators for the variances are used, to avoid the automatisme that a more parameters automatically lead to a higher \(R^2\).

See Also

lm, mvar, AIC

Examples

data(Orange)
R2(lm(circumference~age,data=Orange))
R2(lm(log(circumference)~log(age),data=Orange))