Thanks to @amoeba, I learned that standardized eigenvectors are sometimes calculated, i.e., eigenvectors are divided by the square root of their eigenvalues.
Now, when I want to do principal component regression (PCR), I first calculate the components that I subsequently use in regression. There are two procedures that can be used:
I calculate my components once as raw components, that is I do not standardize the eigenvectors.
I calculate my components as components based on standardized eigenvectors.
Now, I do PCR once with the components in situation 1, and once with the components in situation 2.
- What are the implications (a) for the coefficients, (b) for the interpretation in the two cases?
- What are the main differences?
- I know that the variance of the components will differ, but how does that change the behaviour in regression, or does it at all?
- Is there any recommendation to whether I should use the one but not the other?