# Selection of regressors

I have a question about the package leaps which I am using for model selection.

I would like to compare 4 different selection methods: forward, backward, stepwise and best subset. I used the code below:

library(leaps)
forward <- regsubsets(Response ~.,data = mydata, method = "forward", nbest=1)
backward <- regsubsets(Response ~.,data = mydata, method = "backward", nbest=1)
stepwise <- regsubsets(Response ~., data = mydata, method = "seqrep", nbest=1)
best subset <- regsubsets(Response ~.,data = mydata, method = "exhaustive", nbest=1)
opt = par (mfrow =c(2,2))
plot(forward, scale = "adjr2", main = "Forward Selection")
plot(backward, scale = "adjr2", main = "Backward Selection")
plot(stepwise, scale = "adjr2", main = "Stepwise selection")
plot(best subset, scale = "adjr2", main = "Best subset selection")


Using these commands I obtained figures below:

I am wondering why figure A and D are similar to each other (and also figure B and C). I would expect different algorithms to select models in a different way. For instance models selected with forward selection method should be chosen based on the significance level/ AIC value. On the other hand models selected with best subset selection method should be chosen based on the sample statistics.

I am also wondering why forward selection does not choose one variable at the time adding it to the existing model?

Also Fig B shows that backward selection starts with eight variables in the model. Why it does not start with all the variables and excludes one at the time?