Calculate the adjusted determination coefficient

Calculate the adjusted coefficient of determination by entering the regression model and coefficient of determination. See details.

Usage

r2_adjusted(model, r2)

Arguments

model: A linear model or power regression model of the lm.
r2: A numeric. Coefficient of determination.

Value

A numeric vector or a list of class r2_kvr2 containing the adjusted $R^2$ values. Each element represents the adjusted version of the corresponding $R^2$ definition, accounting for the degrees of freedom.

Details

The adjustment factor $a$ is calculated using the following formula. $$a = (n - 1) / (n - k - 1)$$ $n$ is the sample size, and $k$ is the number of parameters in the regression model.

$R^2_a$ ($R^2 adjusted$) is calculated using the following formula. $$R^2_a = 1 - a (1 - R^2)$$

This function performs freedom-of-degrees adjustment for all coefficients based on the above formula. However, Kvalseth (1985) recommends applying freedom-of-degrees adjustment only to $R^2_1$ and $R^2_9$, based on the principle of consistency in coefficients. Furthermore, there is no basis for applying the same type of adjustment to $R^2_6$ (the square of the correlation coefficient) or to $R^2_7$ and $R^2_8$, which depend on specific model forms.

For details on each coefficient of determination, refer to r2().

References