Let's say I have a response variable (let's say brain pathology of Parkinson's disease patients) and
p input variables (let's say expression of
p genes). I want to find a subset of genes which might be driving the pathology of the patients.
One way is to simply check the Pearson's correlation of each gene with the pathology and choose the genes with the highest absolute correlation, or apply a linear regression and select the genes with highest absolute regression coefficients.
A more sophisticated way could be to do regularized regression (let's say Elastic Net or LASSO) to assign nonzero coefficients to only a subset of genes.
I am wondering whether those genes that are assigned nonzero coefficients by Elastic Net or Lasso will be the same as the genes that have the highest Pearson's correlation, or the genes that have the highest coefficients assigned by a simple linear regression? I can code and see whether they are the same or not, but I am also wondering the intuition behind they being the same or different; that's why I am asking here. Thanks!