sg <- function(b, m, data, LR){
  b_grad <- 0
  m_grad <- 0
  n <- nrow(data)
  result <- data.frame('b' = rep(NA, times = n),
                       'm' = rep(NA, times = n),
                       'i' = rep(NA, times = n))

  for(i in 1:n){
    b_grad <- b_grad + -(2/n) * (data$y[i] - ((m * data$x[i]) + b))
    m_grad <- m_grad + -(2/n) * data$x[i] * (data$y[i] - ((m * data$x[i]) + b))
    new_b <- b - (LR * b_grad)
    new_m <- m - (LR * m_grad)

    result[i,] <- cbind(new_b, new_m, i)
  }
  return(result)
}

(p <- data.frame('x' = rnorm(10, 5, 1.5), 'y' = rpois(10, 2)))
sg(0, 0, p, .001)
sg(0, 0, p, .01)
sg(0, 0, p, .02)

# enhance
sg.iterate <- function(b, m, data, LR, n.iter){
  i.res <- data.frame('b' = b,
                      'm' = m,
                      'i' = 0)
  for(i in 1:n.iter){
    i.res <- rbind(i.res, sg(b, m, data, LR))
    b <- i.res$b[nrow(i.res)]
    m <- i.res$m[nrow(i.res)]
  }
  return(i.res)
}

sg.iterate(0, 0, p, .001, 100)