I have a linear regression problem with about 120 predictors and I tried to remove a number of predictors from it. First I tried to remove multi-collinearities by calculating the variance inflation factor. This left me with about 20 different (hopefully not collinear anymore) predictors. Then I used a PCA to reduce dimensionality even further. Because the predictors' variances are very different to one another I used the correlation matrix for this.
I can get the 'final' data when I multiply the eigenvectors with the largest eigenvalues with my original data, right?
In the end I want to find out which original predictors are left and how I can recover the 'new' original data. But for some reason I am not able to recover correct numbers.