validationCurve.m

function [lambda_vec, error_train, error_val] = ...
    validationCurve(X, y, Xval, yval)
  %VALIDATIONCURVE 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 (you should not change this)
  lambda_vec = [0 0.001 0.003 0.01 0.03 0.1 0.3 1 3 10]';

  % You need to return these variables correctly.
  error_train = zeros(length(lambda_vec), 1);
  error_val = zeros(length(lambda_vec), 1);

  for i = 1:length(lambda_vec)
    lambda = lambda_vec(i);
    theta = trainLinearReg(X, y, lambda);
    error_train(i) = linearRegCostFunction(X, y, theta, 0);
    error_val(i) = linearRegCostFunction(Xval, yval, theta, 0);
  endfor
end