How to Submit Form on Select Change

Your form is missing an action value, which prevents submitting the form at the end. But in the mid-time you should correct this code:

$(document).ready(function() {
  $('#cars').on('change', function() {
     document.forms[myFormName].submit();
  });
});

You can also submit a form by triggering submit button click event:

$(document).ready(function() {
  $('#cars').on('change', function() {
    var $form = $(this).closest('form');
    $form.find('input[type=submit]').click();
  });
});

In my case, this works perfectly well, and it works with or without the submit button.

<form action="" method="post">
    <select name="id" id="cars">
        <option value="">Choose</option>
        <option value="1">Toyota</option>
        <option value="2">Nissan</option>
        <option value="3">Dodge</option>
    </select> 
</form>

 <script type="text/javascript">

  jQuery(function() {
    jQuery('#car').change(function() {
        this.form.submit();
    });
});
</script>