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: $R^{2} = 1 - \frac{v a r (r e s i d u a l s)}{v a r (d a t a)}$

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 $R^{2}$ .

Examples

Run this code

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

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