validationCurve <- function(X, y, Xval, yval) {
  
  #   Generate the train and validation errors needed to
  #   plot a validation curve that we can use to select lambda
  #   
  #   lambda_vec, error_train, error_val <- ...
  #       validationCurve(X, y, Xval, yval) returns the train
  #       and validation errors (in error_train, error_val)
  #       for different values of lambda. You are given the training set (X,
  #       y) and validation set (Xval, yval).
  #
  
  # Selected values of lambda 
  lambda_vec <- seq(0, 10, 0.01)
  
  # You need to return these variables correctly.
  error_train <- rep(0, length(lambda_vec))
  error_val <- rep(0,length(lambda_vec))
  
  # ======================= YOUR CODE HERE ========================
  # Instructions: Fill in this function to return training errors in
  #               error_train and the validation errors in error_val. The
  #               vector lambda_vec contains the different lambda parameters
  #               to use for each calculation of the errors, i.e,
  #               error_train[i], and error_val[i] should give
  #               you the errors obtained after training with
  #               lambda <- lambda_vec[i]
  #
  # Note: You can loop over lambda_vec with the following:
  #
  #       for (i in 1:length(lambda_vec)) {
  #           lambda <- lambda_vec[i]
  #           # Compute train / val errors when training linear
  #           # regression with regularization parameter lambda
  #           # You should store the result in error_train[i]
  #           # and error_val[i]
  #           ....
  #
  #       }
  #
  #
  
  
 
  # ===============================================================
  
  return(list(lambda_vec = lambda_vec, error_train = error_train, error_val = error_val))
}