How to fix google page speed insights issue?
With AdvAgg enabled go to the status report page admin/reports/status. It should offer advice on how to fix gzip and browser caching for css/js aggregates. Also see the readme, under troubleshooting there are some tips for getting apache to do what you need it to.

If advagg doesn't report any issues then check and see what kinds of resources google is complaining about in terms of browser caching (.jpg) and compression (fonts). Also remember that if these are coming from an external domain (google analytics) there isn't a lot you can do as you don't control that server.

Edit: Guide here - https://groups.drupal.org/node/517292. It's the AdvAgg Readme file as well.