I have a very basic question. When we are regressing Y on X1, X2, X3, I understand we need to perform some kind of normalization for X1, X2, X3 columns but what about Y. Do we need to normalize that as well while running regression?
You can do normalization to what ever you choose. I'd say most likely you'd want to normalize both x and y but you have to be doing it to make sense. For instance I probably wouldn't standardize dollars because this unit of measurement is already pretty interpretable. But scores on a test (lets say you could get a 0-60) well this doesn't really register in my known measurement units. What's a good score? What's an ok score? It is hard to interpret, so a standardizing of the variable in this case makes sense. Just keep in mind any transformation to data that you do may hinder your explanation of the results.