I will start by making a few clarifications to the user, you should study how to work with javascript and jQuery, you cannot try to build up something and, if it's not working, ask here. This is a little help that could address you in a quite-right way.
Substitute your submit input with this:
<input type="submit" id="sendform" value="Send">
Then, PLEASE, add jQuery from CDN in the section of your page, then try this code (add what is missing, like code for name and sex...):
<script type="text/javascript">
$(document).ready(function() {
$("#sendform").click(function() {
var year = $("select[name=select_year]:selected").val();
var month = $("select[name=select_month]:selected").val();
var day = $("select[name=select_day]:selected").val();
$.get("page.php",{'year': year, 'month': month... })
.done(function(msg) {
alert("do whatever you want with the php response in "+msg);
});
});
});
</script>