Estimating linear regression with Gradient Descent (Steepest Descent)

Question

Example data

X<-matrix(c(rep(1,97),runif(97)) , nrow=97, ncol=2)
y<-matrix(runif(97), nrow= 97 , ncol =1)

I have succeed in creating

Answer 1

The crossprod makes it surprisingly slower then the previous methods :

Previous method (14 secs mean on 50 iterations):

Crossprod method (16 secs mean on 50 iterations):