[Ganchrow]

Originally Posted by BuddyBear

Sorry, but it ALWAYS increases it.

The R² is only weakly increasing in the number of model regressors. There do exist pathological cases where the addition of a variable to a regression will have no effect on the coefficient of determination (R²). To wit:

What if the variable being introduced were collinear with an existing variable?

And as corollaries to the above:

What if every observation of the introduced variable were identical and there already existed a constant term?

With or without a constant term, what if the introduced variable were merely a column of 0s?

What if the R² of the regression were already 1?