Adjusted determination coefficient (R2adj) is the determination coefficient adjusted for the number of factors and not sensitive to the number of regressors. R2adj is calculated by the formula:
Where:
R2. Determination coefficient.
For R2adj calculated by this formula, the relation 0 ≤ R2adj ≤ 1 is satisfied only for the model with an estimated constant.
Uncentered adjusted determination coefficient (
) takes this condition into account and is calculated depending on the constant:
| The constant value is estimated | The constant is not used | The constant value is defined manually |
 |
 |
 |
Where:
. Determination coefficient (uncentered).
k. The number of factors included into the model.
N. Number of observations.
When k>1 R2adj ≤ R2.
The preferred model is a model with the largest criterion value. Therefore, when comparing multiple regression models, it is advisable to take into account R2adj value.
See also:
Library of Methods and Models | Determination Coefficient | ISummaryStatistics.AdjR2 | ISummaryStatistics.AdjR2_2