To begin – I am extremely bad at stats.
I am running a multiple regression analysis on a dataset to predict one variable from two others. There were three independent variables(IV) before, although I chose to remove one as it was shown to be a non-sig predictor by SPSS. Once removed my VIF scores became identical at 4.538 and my tolerance scores .220 for both predictor variables. There is also very high correlation between the two IV's (r = 0.883). I cant even imagine two VIF scores being identical by chance, there must be a reason for it. Any help would be appreciated.
Solved – Identical VIF/Tolerance scores – Multiple regression
multiple regressionregressionspssvariance-inflation-factor
Best Answer
This will always be the case.
The VIF (variance inflation factor) of any regressor depends only on the coefficient of determination ($R^2$) of its regression against all the other regressors. When there are just two regressors, those $R^2$ will be identical, because each one of them is the square of the correlation between the regressors.
In your example, this correlation is $r = 0.883$. The VIF of either variable therefore is
$$\text{VIF} = \frac{1}{1-R^2} = \frac{1}{1-0.883^2} \approx 4.54.$$
That is consistent with what SPSS reports.