关于VIF

问题如下：

Question In the process of quantifying multicollinearity issues in a multiple regression, the coefficient of determination obtained from regressing X_j on the remaining independent variables is R_j² = 0.7. The variance inflation factor for X_j is closest to:

选项：

A.A.0.67. B.B.1.96. C.C.3.33.

解释：

• A is Incorrect because the plus sign is used instead of the minus sign in the correct formula, i.e., 1/(1 + R_j²) = 1/(1 + 0.7²) = 0.6711 ≈ 0.67.

• B is Correct because, by regressing one independent variable (X_j) on the remaining k – 1 independent variables, we obtain R_j² for the regression—the variation in X_j explained by the other k – 1 independent variables—from which the VIF for X_j is VIF_j = 1/(1 – R_j²) = 1/(1 – 0.7²) = 1.9608 ≈ 1.96.

  The variance inflation factor (VIF) is used to quantify multicollinearity issues.

• C is Incorrect because R_j in the correct formula is not squared, i.e., 1/(1 – R_j) = 1/(1 – 0.7) = 3.3333 ≈ 3.33.