Generating routes in javascript with Twig and Symfony2
You can use the FOSJsRoutingBundle.
I know it's an old question, but just in case you don't want to install a bundle like FOSJsRoutingBundle, here's a little hack:
var url = '{{ path("yourroute", {'region_id': 'region_id'}) }}';
url = url.replace("region_id", this.value);
'region_id' is just used as a placeholder, then you replace it in JS with your actual variable this.value