R2: R square

In compositions: Compositional Data Analysis

R square

Description

The R2 measure of determination for linear models

Usage

R2(object,...)
## S3 method for class 'lm'
R2(object,...,adjust=TRUE,ref=0)
## Default S3 method:
R2(object,...,ref=0)
          

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.

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.

Value

The R2 measure of determination.

Author(s)

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

See Also

lm, mvar, AIC

Examples

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

compositions documentation built on June 22, 2024, 12:15 p.m.