Radj2: Adjusted R2

R2 always increases when explanatory variables are added to a model. As such it can create the illusion of a better fit as more terms are added.

Radj2 adjusts for number of explanatory terms in a model relative to the number of data points. Unlike R2, the Radj2 increases only when the increase in R2 (due to inclusion of variable) is more than one would expect to see by chance.

$$ R_{adj}^2 = 1 – \frac{(1 – R^2)× (n – 1)}{n – k – 1}$$

Where k is the number of explanatory variables, and n is sample size.

In the development of the regression model, as explanatory variables are added to a regression in order of importance, the point before Radj2 starts to decrease, is where the stepwise selection of variables should conclude.

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