Let's say I have X variables that I want to use to predict Y (Response). Should I provide all X variables to perform Principal components regression (PCR) or should I provide only the significantly correlated variables (obtained from finding partial correlation for controlling confounding factors using Spearman correlation) for predicting the response using PCR? Would the results change? I'm a biologist and a novice in this field. Please help.
First, it's not clear that you should use principal components regression; partial least squares is often a better method when you have a lot of independent variables that you want to combine into a few in order to use them in regression.
Second, no, you shouldn't filter out the variables based on correlation with the DV, you should use any IVs that you are interested in. For one thing, it could be that some combination of variables is a good predictor.