Question

The adjusted R2 accounts for the number of independent variables by _______.

(A) adding one to the R2
(B) using the degrees of freedom
(C) multiplying by the multiple standard error of the estimate
(D) using a subscript for R2

Answer 1

Option (B) using the degrees of freedom

Explanation:

The adjusted R squared value is given by:

`\text{Adjusted }R^2 = 1 - \displaystyle((1-R^2)(n-1))/(n-k-1)`

where is the number of data points and k is the number of independent regressors, that is the number of variables in the model.

• The adjusted R squared is explained by dependent variable with the R square value and the number of total variables.
• So the independent variables are accounted by using the degrees of freedom as it includes the number of variables and deduct it from R square.

The adjusted R square accounts for the number of independent variables by

Option (B) using the degrees of freedom