How to target a select option based on data attribute?

How to select option matching data-id value depends on another select option data-id value. #jQuery

$(function() {
    $('#first_select').change(function() {
        var typeId = $(this).find('option:selected').data('id');
        $('#second_select').attr('id', typeId).trigger('change');
     });
});

#HTML

<select id="first_select">
        <option value="" >Select</option>
        <option data-id="11">111</option>
        <option data-id="22">222</option>
        <option data-id="33">333</option>
    </select>

    <select id="second_select">
        <option value="">Select</option>
        <option data-id="11">111</option>
        <option data-id="22">222</option>
        <option data-id="33">333</option>
    </select>