I develop price prediction data model using multiple linear regression, ridge, lasso and elastic net regression, initially I had 215 variables. after creating models I ran a python code to check how many variables have used in final models, this is python code which i use for the detect number of variables in ridge regression,
print("Ridge Regression Selected " + str(sum(coef_ridge != 0)) + " Variables and Neglected " + str(sum(coef_ridge == 0)) + " Variables")
This is a out put which I got
Ridge Regression Selected 209 Variables and Neglected 6 Variables
above code ran for all other modeling methods separably. then Multiple regression 212 variables selected, Ridge 209 variables selected, Lasso 68 variables selected and Elastic net regression 77 variables selected.
my question is according to my knowledge lasso and elastic net regression already use variables selection method because of that, number of selected variables reduced up to 68 and 77 but how multiple linear regression neglect 3 variables and ridge regression reduce 6 variables? that mean multiple and ridge regression also use variable selection method in their code? please someone explain these scenario