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I performed a PCA on some data related to habitat (different types of vegetation cover, soil water etc.), but there were some variables that I did not include in the PCA because they were not strongly correlated with any of the other variables. I selected the first three principal components from the PCA whose eigenvalues were above 1.
Now I want to run a multiple regression to analyse what variables will predict bird density. Is it valid to include my three principal components as well as the variables that I did not include in the PCA into this regression?