One of the data sets I am working upon had 3 variables which were having almost 100% correlation among themselves. Since I am learning regression modelling I thought I'll do principal component regression. However there is another variable in my data set whose partial residual plot suggested that I use a cubic term for it in my model. The t-test p-value is significant for it at 95% level.
So now I am wondering if it makes sense for me to include polynomial terms of predictors while doing PCA? because I want to assign meaning to principal components, I am not sure how will I assign meaning to a principal component which is made of polynomial terms of original variables. Or should I first calculate Principal Components and then if needed include polynomial terms of principal components in regression?
Apologies if this isn't the right kind of post for this forum.